method of analysis in research paper

• Skip to main content
• Skip to primary sidebar
• Skip to footer
• QuestionPro

• Solutions Industries Gaming Automotive Sports and events Education Government Travel & Hospitality Financial Services Healthcare Cannabis Technology Use Case NPS+ Communities Audience Contactless surveys Mobile LivePolls Member Experience GDPR Positive People Science 360 Feedback Surveys
• Resources Blog eBooks Survey Templates Case Studies Training Help center

Home Market Research

Data Analysis in Research: Types & Methods

Content Index

Why analyze data in research?

Types of data in research, finding patterns in the qualitative data, methods used for data analysis in qualitative research, preparing data for analysis, methods used for data analysis in quantitative research, considerations in research data analysis, what is data analysis in research.

Definition of research in data analysis: According to LeCompte and Schensul, research data analysis is a process used by researchers to reduce data to a story and interpret it to derive insights. The data analysis process helps reduce a large chunk of data into smaller fragments, which makes sense. 

Three essential things occur during the data analysis process — the first is data organization . Summarization and categorization together contribute to becoming the second known method used for data reduction. It helps find patterns and themes in the data for easy identification and linking. The third and last way is data analysis – researchers do it in both top-down and bottom-up fashion.

LEARN ABOUT: Research Process Steps

On the other hand, Marshall and Rossman describe data analysis as a messy, ambiguous, and time-consuming but creative and fascinating process through which a mass of collected data is brought to order, structure and meaning.

We can say that “the data analysis and data interpretation is a process representing the application of deductive and inductive logic to the research and data analysis.”

Researchers rely heavily on data as they have a story to tell or research problems to solve. It starts with a question, and data is nothing but an answer to that question. But, what if there is no question to ask? Well! It is possible to explore data even without a problem – we call it ‘Data Mining’, which often reveals some interesting patterns within the data that are worth exploring.

Irrelevant to the type of data researchers explore, their mission and audiences’ vision guide them to find the patterns to shape the story they want to tell. One of the essential things expected from researchers while analyzing data is to stay open and remain unbiased toward unexpected patterns, expressions, and results. Remember, sometimes, data analysis tells the most unforeseen yet exciting stories that were not expected when initiating data analysis. Therefore, rely on the data you have at hand and enjoy the journey of exploratory research. 

Create a Free Account

Every kind of data has a rare quality of describing things after assigning a specific value to it. For analysis, you need to organize these values, processed and presented in a given context, to make it useful. Data can be in different forms; here are the primary data types.

• Qualitative data: When the data presented has words and descriptions, then we call it qualitative data . Although you can observe this data, it is subjective and harder to analyze data in research, especially for comparison. Example: Quality data represents everything describing taste, experience, texture, or an opinion that is considered quality data. This type of data is usually collected through focus groups, personal qualitative interviews , qualitative observation or using open-ended questions in surveys.
• Quantitative data: Any data expressed in numbers of numerical figures are called quantitative data . This type of data can be distinguished into categories, grouped, measured, calculated, or ranked. Example: questions such as age, rank, cost, length, weight, scores, etc. everything comes under this type of data. You can present such data in graphical format, charts, or apply statistical analysis methods to this data. The (Outcomes Measurement Systems) OMS questionnaires in surveys are a significant source of collecting numeric data.
• Categorical data: It is data presented in groups. However, an item included in the categorical data cannot belong to more than one group. Example: A person responding to a survey by telling his living style, marital status, smoking habit, or drinking habit comes under the categorical data. A chi-square test is a standard method used to analyze this data.

Learn More : Examples of Qualitative Data in Education

Data analysis in qualitative research

Data analysis and qualitative data research work a little differently from the numerical data as the quality data is made up of words, descriptions, images, objects, and sometimes symbols. Getting insight from such complicated information is a complicated process. Hence it is typically used for exploratory research and data analysis .

Although there are several ways to find patterns in the textual information, a word-based method is the most relied and widely used global technique for research and data analysis. Notably, the data analysis process in qualitative research is manual. Here the researchers usually read the available data and find repetitive or commonly used words. 

For example, while studying data collected from African countries to understand the most pressing issues people face, researchers might find  “food”  and  “hunger” are the most commonly used words and will highlight them for further analysis.

LEARN ABOUT: Level of Analysis

The keyword context is another widely used word-based technique. In this method, the researcher tries to understand the concept by analyzing the context in which the participants use a particular keyword.  

For example , researchers conducting research and data analysis for studying the concept of ‘diabetes’ amongst respondents might analyze the context of when and how the respondent has used or referred to the word ‘diabetes.’

The scrutiny-based technique is also one of the highly recommended  text analysis  methods used to identify a quality data pattern. Compare and contrast is the widely used method under this technique to differentiate how a specific text is similar or different from each other. 

For example: To find out the “importance of resident doctor in a company,” the collected data is divided into people who think it is necessary to hire a resident doctor and those who think it is unnecessary. Compare and contrast is the best method that can be used to analyze the polls having single-answer questions types .

Metaphors can be used to reduce the data pile and find patterns in it so that it becomes easier to connect data with theory.

Variable Partitioning is another technique used to split variables so that researchers can find more coherent descriptions and explanations from the enormous data.

LEARN ABOUT: Qualitative Research Questions and Questionnaires

There are several techniques to analyze the data in qualitative research, but here are some commonly used methods,

• Content Analysis:  It is widely accepted and the most frequently employed technique for data analysis in research methodology. It can be used to analyze the documented information from text, images, and sometimes from the physical items. It depends on the research questions to predict when and where to use this method.
• Narrative Analysis: This method is used to analyze content gathered from various sources such as personal interviews, field observation, and  surveys . The majority of times, stories, or opinions shared by people are focused on finding answers to the research questions.
• Discourse Analysis:  Similar to narrative analysis, discourse analysis is used to analyze the interactions with people. Nevertheless, this particular method considers the social context under which or within which the communication between the researcher and respondent takes place. In addition to that, discourse analysis also focuses on the lifestyle and day-to-day environment while deriving any conclusion.
• Grounded Theory:  When you want to explain why a particular phenomenon happened, then using grounded theory for analyzing quality data is the best resort. Grounded theory is applied to study data about the host of similar cases occurring in different settings. When researchers are using this method, they might alter explanations or produce new ones until they arrive at some conclusion.

LEARN ABOUT: 12 Best Tools for Researchers

Data analysis in quantitative research

The first stage in research and data analysis is to make it for the analysis so that the nominal data can be converted into something meaningful. Data preparation consists of the below phases.

Phase I: Data Validation

Data validation is done to understand if the collected data sample is per the pre-set standards, or it is a biased data sample again divided into four different stages

• Fraud: To ensure an actual human being records each response to the survey or the questionnaire
• Screening: To make sure each participant or respondent is selected or chosen in compliance with the research criteria
• Procedure: To ensure ethical standards were maintained while collecting the data sample
• Completeness: To ensure that the respondent has answered all the questions in an online survey. Else, the interviewer had asked all the questions devised in the questionnaire.

Phase II: Data Editing

More often, an extensive research data sample comes loaded with errors. Respondents sometimes fill in some fields incorrectly or sometimes skip them accidentally. Data editing is a process wherein the researchers have to confirm that the provided data is free of such errors. They need to conduct necessary checks and outlier checks to edit the raw edit and make it ready for analysis.

Phase III: Data Coding

Out of all three, this is the most critical phase of data preparation associated with grouping and assigning values to the survey responses . If a survey is completed with a 1000 sample size, the researcher will create an age bracket to distinguish the respondents based on their age. Thus, it becomes easier to analyze small data buckets rather than deal with the massive data pile.

LEARN ABOUT: Steps in Qualitative Research

After the data is prepared for analysis, researchers are open to using different research and data analysis methods to derive meaningful insights. For sure, statistical analysis plans are the most favored to analyze numerical data. In statistical analysis, distinguishing between categorical data and numerical data is essential, as categorical data involves distinct categories or labels, while numerical data consists of measurable quantities. The method is again classified into two groups. First, ‘Descriptive Statistics’ used to describe data. Second, ‘Inferential statistics’ that helps in comparing the data .

Descriptive statistics

This method is used to describe the basic features of versatile types of data in research. It presents the data in such a meaningful way that pattern in the data starts making sense. Nevertheless, the descriptive analysis does not go beyond making conclusions. The conclusions are again based on the hypothesis researchers have formulated so far. Here are a few major types of descriptive analysis methods.

Measures of Frequency

• Count, Percent, Frequency
• It is used to denote home often a particular event occurs.
• Researchers use it when they want to showcase how often a response is given.

Measures of Central Tendency

• Mean, Median, Mode
• The method is widely used to demonstrate distribution by various points.
• Researchers use this method when they want to showcase the most commonly or averagely indicated response.

Measures of Dispersion or Variation

• Range, Variance, Standard deviation
• Here the field equals high/low points.
• Variance standard deviation = difference between the observed score and mean
• It is used to identify the spread of scores by stating intervals.
• Researchers use this method to showcase data spread out. It helps them identify the depth until which the data is spread out that it directly affects the mean.

Measures of Position

• Percentile ranks, Quartile ranks
• It relies on standardized scores helping researchers to identify the relationship between different scores.
• It is often used when researchers want to compare scores with the average count.

For quantitative research use of descriptive analysis often give absolute numbers, but the in-depth analysis is never sufficient to demonstrate the rationale behind those numbers. Nevertheless, it is necessary to think of the best method for research and data analysis suiting your survey questionnaire and what story researchers want to tell. For example, the mean is the best way to demonstrate the students’ average scores in schools. It is better to rely on the descriptive statistics when the researchers intend to keep the research or outcome limited to the provided  sample  without generalizing it. For example, when you want to compare average voting done in two different cities, differential statistics are enough.

Descriptive analysis is also called a ‘univariate analysis’ since it is commonly used to analyze a single variable.

Inferential statistics

Inferential statistics are used to make predictions about a larger population after research and data analysis of the representing population’s collected sample. For example, you can ask some odd 100 audiences at a movie theater if they like the movie they are watching. Researchers then use inferential statistics on the collected  sample  to reason that about 80-90% of people like the movie. 

Here are two significant areas of inferential statistics.

• Estimating parameters: It takes statistics from the sample research data and demonstrates something about the population parameter.
• Hypothesis test: I t’s about sampling research data to answer the survey research questions. For example, researchers might be interested to understand if the new shade of lipstick recently launched is good or not, or if the multivitamin capsules help children to perform better at games.

These are sophisticated analysis methods used to showcase the relationship between different variables instead of describing a single variable. It is often used when researchers want something beyond absolute numbers to understand the relationship between variables.

Here are some of the commonly used methods for data analysis in research.

• Correlation: When researchers are not conducting experimental research or quasi-experimental research wherein the researchers are interested to understand the relationship between two or more variables, they opt for correlational research methods.
• Cross-tabulation: Also called contingency tables,  cross-tabulation  is used to analyze the relationship between multiple variables.  Suppose provided data has age and gender categories presented in rows and columns. A two-dimensional cross-tabulation helps for seamless data analysis and research by showing the number of males and females in each age category.
• Regression analysis: For understanding the strong relationship between two variables, researchers do not look beyond the primary and commonly used regression analysis method, which is also a type of predictive analysis used. In this method, you have an essential factor called the dependent variable. You also have multiple independent variables in regression analysis. You undertake efforts to find out the impact of independent variables on the dependent variable. The values of both independent and dependent variables are assumed as being ascertained in an error-free random manner.
• Frequency tables: The statistical procedure is used for testing the degree to which two or more vary or differ in an experiment. A considerable degree of variation means research findings were significant. In many contexts, ANOVA testing and variance analysis are similar.
• Analysis of variance: The statistical procedure is used for testing the degree to which two or more vary or differ in an experiment. A considerable degree of variation means research findings were significant. In many contexts, ANOVA testing and variance analysis are similar.
• Researchers must have the necessary research skills to analyze and manipulation the data , Getting trained to demonstrate a high standard of research practice. Ideally, researchers must possess more than a basic understanding of the rationale of selecting one statistical method over the other to obtain better data insights.
• Usually, research and data analytics projects differ by scientific discipline; therefore, getting statistical advice at the beginning of analysis helps design a survey questionnaire, select data collection methods , and choose samples.

LEARN ABOUT: Best Data Collection Tools

• The primary aim of data research and analysis is to derive ultimate insights that are unbiased. Any mistake in or keeping a biased mind to collect data, selecting an analysis method, or choosing  audience  sample il to draw a biased inference.
• Irrelevant to the sophistication used in research data and analysis is enough to rectify the poorly defined objective outcome measurements. It does not matter if the design is at fault or intentions are not clear, but lack of clarity might mislead readers, so avoid the practice.
• The motive behind data analysis in research is to present accurate and reliable data. As far as possible, avoid statistical errors, and find a way to deal with everyday challenges like outliers, missing data, data altering, data mining , or developing graphical representation.

LEARN MORE: Descriptive Research vs Correlational Research The sheer amount of data generated daily is frightening. Especially when data analysis has taken center stage. in 2018. In last year, the total data supply amounted to 2.8 trillion gigabytes. Hence, it is clear that the enterprises willing to survive in the hypercompetitive world must possess an excellent capability to analyze complex research data, derive actionable insights, and adapt to the new market needs.

LEARN ABOUT: Average Order Value

QuestionPro is an online survey platform that empowers organizations in data analysis and research and provides them a medium to collect data by creating appealing surveys.

MORE LIKE THIS

21 Best Customer Advocacy Software for Customers in 2024

Apr 19, 2024

10 Quantitative Data Analysis Software for Every Data Scientist

Apr 18, 2024

11 Best Enterprise Feedback Management Software in 2024

17 Best Online Reputation Management Software in 2024

Apr 17, 2024

Other categories

• Academic Research
• Artificial Intelligence
• Assessments
• Brand Awareness
• Case Studies
• Communities
• Consumer Insights
• Customer effort score
• Customer Engagement
• Customer Experience
• Customer Loyalty
• Customer Research
• Customer Satisfaction
• Employee Benefits
• Employee Engagement
• Employee Retention
• Friday Five
• General Data Protection Regulation
• Insights Hub
• Life@QuestionPro
• Market Research
• Mobile diaries
• Mobile Surveys
• New Features
• Online Communities
• Question Types
• Questionnaire
• QuestionPro Products
• Release Notes
• Research Tools and Apps
• Revenue at Risk
• Survey Templates
• Training Tips
• Uncategorized
• Video Learning Series
• What’s Coming Up
• Workforce Intelligence

When you choose to publish with PLOS, your research makes an impact. Make your work accessible to all, without restrictions, and accelerate scientific discovery with options like preprints and published peer review that make your work more Open.

• PLOS Biology
• PLOS Climate
• PLOS Complex Systems
• PLOS Computational Biology
• PLOS Digital Health
• PLOS Genetics
• PLOS Global Public Health
• PLOS Medicine
• PLOS Mental Health
• PLOS Neglected Tropical Diseases
• PLOS Pathogens
• PLOS Sustainability and Transformation
• PLOS Collections
• How to Write Your Methods

Ensure understanding, reproducibility and replicability

What should you include in your methods section, and how much detail is appropriate?

Why Methods Matter

The methods section was once the most likely part of a paper to be unfairly abbreviated, overly summarized, or even relegated to hard-to-find sections of a publisher’s website. While some journals may responsibly include more detailed elements of methods in supplementary sections, the movement for increased reproducibility and rigor in science has reinstated the importance of the methods section. Methods are now viewed as a key element in establishing the credibility of the research being reported, alongside the open availability of data and results.

A clear methods section impacts editorial evaluation and readers’ understanding, and is also the backbone of transparency and replicability.

For example, the Reproducibility Project: Cancer Biology project set out in 2013 to replicate experiments from 50 high profile cancer papers, but revised their target to 18 papers once they understood how much methodological detail was not contained in the original papers.

What to include in your methods section

What you include in your methods sections depends on what field you are in and what experiments you are performing. However, the general principle in place at the majority of journals is summarized well by the guidelines at PLOS ONE : “The Materials and Methods section should provide enough detail to allow suitably skilled investigators to fully replicate your study. ” The emphases here are deliberate: the methods should enable readers to understand your paper, and replicate your study. However, there is no need to go into the level of detail that a lay-person would require—the focus is on the reader who is also trained in your field, with the suitable skills and knowledge to attempt a replication.

A constant principle of rigorous science

A methods section that enables other researchers to understand and replicate your results is a constant principle of rigorous, transparent, and Open Science. Aim to be thorough, even if a particular journal doesn’t require the same level of detail . Reproducibility is all of our responsibility. You cannot create any problems by exceeding a minimum standard of information. If a journal still has word-limits—either for the overall article or specific sections—and requires some methodological details to be in a supplemental section, that is OK as long as the extra details are searchable and findable .

Imagine replicating your own work, years in the future

As part of PLOS’ presentation on Reproducibility and Open Publishing (part of UCSF’s Reproducibility Series ) we recommend planning the level of detail in your methods section by imagining you are writing for your future self, replicating your own work. When you consider that you might be at a different institution, with different account logins, applications, resources, and access levels—you can help yourself imagine the level of specificity that you yourself would require to redo the exact experiment. Consider:

• Which details would you need to be reminded of? 
• Which cell line, or antibody, or software, or reagent did you use, and does it have a Research Resource ID (RRID) that you can cite?
• Which version of a questionnaire did you use in your survey? 
• Exactly which visual stimulus did you show participants, and is it publicly available? 
• What participants did you decide to exclude? 
• What process did you adjust, during your work? 

Tip: Be sure to capture any changes to your protocols

You yourself would want to know about any adjustments, if you ever replicate the work, so you can surmise that anyone else would want to as well. Even if a necessary adjustment you made was not ideal, transparency is the key to ensuring this is not regarded as an issue in the future. It is far better to transparently convey any non-optimal methods, or methodological constraints, than to conceal them, which could result in reproducibility or ethical issues downstream.

Visual aids for methods help when reading the whole paper

Consider whether a visual representation of your methods could be appropriate or aid understanding your process. A visual reference readers can easily return to, like a flow-diagram, decision-tree, or checklist, can help readers to better understand the complete article, not just the methods section.

Ethical Considerations

In addition to describing what you did, it is just as important to assure readers that you also followed all relevant ethical guidelines when conducting your research. While ethical standards and reporting guidelines are often presented in a separate section of a paper, ensure that your methods and protocols actually follow these guidelines. Read more about ethics .

Existing standards, checklists, guidelines, partners

While the level of detail contained in a methods section should be guided by the universal principles of rigorous science outlined above, various disciplines, fields, and projects have worked hard to design and develop consistent standards, guidelines, and tools to help with reporting all types of experiment. Below, you’ll find some of the key initiatives. Ensure you read the submission guidelines for the specific journal you are submitting to, in order to discover any further journal- or field-specific policies to follow, or initiatives/tools to utilize.

Tip: Keep your paper moving forward by providing the proper paperwork up front

Be sure to check the journal guidelines and provide the necessary documents with your manuscript submission. Collecting the necessary documentation can greatly slow the first round of peer review, or cause delays when you submit your revision.

Randomized Controlled Trials – CONSORT The Consolidated Standards of Reporting Trials (CONSORT) project covers various initiatives intended to prevent the problems of  inadequate reporting of randomized controlled trials. The primary initiative is an evidence-based minimum set of recommendations for reporting randomized trials known as the CONSORT Statement . 

Systematic Reviews and Meta-Analyses – PRISMA The Preferred Reporting Items for Systematic Reviews and Meta-Analyses ( PRISMA ) is an evidence-based minimum set of items focusing  on the reporting of  reviews evaluating randomized trials and other types of research.

Research using Animals – ARRIVE The Animal Research: Reporting of In Vivo Experiments ( ARRIVE ) guidelines encourage maximizing the information reported in research using animals thereby minimizing unnecessary studies. (Original study and proposal , and updated guidelines , in PLOS Biology .) 

Laboratory Protocols Protocols.io has developed a platform specifically for the sharing and updating of laboratory protocols , which are assigned their own DOI and can be linked from methods sections of papers to enhance reproducibility. Contextualize your protocol and improve discovery with an accompanying Lab Protocol article in PLOS ONE .

Consistent reporting of Materials, Design, and Analysis – the MDAR checklist A cross-publisher group of editors and experts have developed, tested, and rolled out a checklist to help establish and harmonize reporting standards in the Life Sciences . The checklist , which is available for use by authors to compile their methods, and editors/reviewers to check methods, establishes a minimum set of requirements in transparent reporting and is adaptable to any discipline within the Life Sciences, by covering a breadth of potentially relevant methodological items and considerations. If you are in the Life Sciences and writing up your methods section, try working through the MDAR checklist and see whether it helps you include all relevant details into your methods, and whether it reminded you of anything you might have missed otherwise.

Summary Writing tips

The main challenge you may find when writing your methods is keeping it readable AND covering all the details needed for reproducibility and replicability. While this is difficult, do not compromise on rigorous standards for credibility!

• Keep in mind future replicability, alongside understanding and readability.
• Follow checklists, and field- and journal-specific guidelines.
• Consider a commitment to rigorous and transparent science a personal responsibility, and not just adhering to journal guidelines.
• Establish whether there are persistent identifiers for any research resources you use that can be specifically cited in your methods section.
• Deposit your laboratory protocols in Protocols.io, establishing a permanent link to them. You can update your protocols later if you improve on them, as can future scientists who follow your protocols.
• Consider visual aids like flow-diagrams, lists, to help with reading other sections of the paper.
• Be specific about all decisions made during the experiments that someone reproducing your work would need to know.

Don’t

• Summarize or abbreviate methods without giving full details in a discoverable supplemental section.
• Presume you will always be able to remember how you performed the experiments, or have access to private or institutional notebooks and resources.
• Attempt to hide constraints or non-optimal decisions you had to make–transparency is the key to ensuring the credibility of your research.
• How to Write a Great Title
• How to Write an Abstract
• How to Report Statistics
• How to Write Discussions and Conclusions
• How to Edit Your Work

The contents of the Peer Review Center are also available as a live, interactive training session, complete with slides, talking points, and activities. …

The contents of the Writing Center are also available as a live, interactive training session, complete with slides, talking points, and activities. …

There’s a lot to consider when deciding where to submit your work. Learn how to choose a journal that will help your study reach its audience, while reflecting your values as a researcher…

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Dissertation
• What Is a Research Methodology? | Steps & Tips

What Is a Research Methodology? | Steps & Tips

Published on 25 February 2019 by Shona McCombes . Revised on 10 October 2022.

Your research methodology discusses and explains the data collection and analysis methods you used in your research. A key part of your thesis, dissertation, or research paper, the methodology chapter explains what you did and how you did it, allowing readers to evaluate the reliability and validity of your research.

It should include:

• The type of research you conducted
• How you collected and analysed your data
• Any tools or materials you used in the research
• Why you chose these methods
• Your methodology section should generally be written in the past tense .
• Academic style guides in your field may provide detailed guidelines on what to include for different types of studies.
• Your citation style might provide guidelines for your methodology section (e.g., an APA Style methods section ).

Instantly correct all language mistakes in your text

Be assured that you'll submit flawless writing. Upload your document to correct all your mistakes.

Table of contents

How to write a research methodology, why is a methods section important, step 1: explain your methodological approach, step 2: describe your data collection methods, step 3: describe your analysis method, step 4: evaluate and justify the methodological choices you made, tips for writing a strong methodology chapter, frequently asked questions about methodology.

Prevent plagiarism, run a free check.

Your methods section is your opportunity to share how you conducted your research and why you chose the methods you chose. It’s also the place to show that your research was rigorously conducted and can be replicated .

It gives your research legitimacy and situates it within your field, and also gives your readers a place to refer to if they have any questions or critiques in other sections.

You can start by introducing your overall approach to your research. You have two options here.

Option 1: Start with your “what”

What research problem or question did you investigate?

• Aim to describe the characteristics of something?
• Explore an under-researched topic?
• Establish a causal relationship?

And what type of data did you need to achieve this aim?

• Quantitative data , qualitative data , or a mix of both?
• Primary data collected yourself, or secondary data collected by someone else?
• Experimental data gathered by controlling and manipulating variables, or descriptive data gathered via observations?

Option 2: Start with your “why”

Depending on your discipline, you can also start with a discussion of the rationale and assumptions underpinning your methodology. In other words, why did you choose these methods for your study?

• Why is this the best way to answer your research question?
• Is this a standard methodology in your field, or does it require justification?
• Were there any ethical considerations involved in your choices?
• What are the criteria for validity and reliability in this type of research ?

Once you have introduced your reader to your methodological approach, you should share full details about your data collection methods .

Quantitative methods

In order to be considered generalisable, you should describe quantitative research methods in enough detail for another researcher to replicate your study.

Here, explain how you operationalised your concepts and measured your variables. Discuss your sampling method or inclusion/exclusion criteria, as well as any tools, procedures, and materials you used to gather your data.

Surveys Describe where, when, and how the survey was conducted.

• How did you design the questionnaire?
• What form did your questions take (e.g., multiple choice, Likert scale )?
• Were your surveys conducted in-person or virtually?
• What sampling method did you use to select participants?
• What was your sample size and response rate?

Experiments Share full details of the tools, techniques, and procedures you used to conduct your experiment.

• How did you design the experiment ?
• How did you recruit participants?
• How did you manipulate and measure the variables ?
• What tools did you use?

Existing data Explain how you gathered and selected the material (such as datasets or archival data) that you used in your analysis.

• Where did you source the material?
• How was the data originally produced?
• What criteria did you use to select material (e.g., date range)?

The survey consisted of 5 multiple-choice questions and 10 questions measured on a 7-point Likert scale.

The goal was to collect survey responses from 350 customers visiting the fitness apparel company’s brick-and-mortar location in Boston on 4–8 July 2022, between 11:00 and 15:00.

Here, a customer was defined as a person who had purchased a product from the company on the day they took the survey. Participants were given 5 minutes to fill in the survey anonymously. In total, 408 customers responded, but not all surveys were fully completed. Due to this, 371 survey results were included in the analysis.

Qualitative methods

In qualitative research , methods are often more flexible and subjective. For this reason, it’s crucial to robustly explain the methodology choices you made.

Be sure to discuss the criteria you used to select your data, the context in which your research was conducted, and the role you played in collecting your data (e.g., were you an active participant, or a passive observer?)

Interviews or focus groups Describe where, when, and how the interviews were conducted.

• How did you find and select participants?
• How many participants took part?
• What form did the interviews take ( structured , semi-structured , or unstructured )?
• How long were the interviews?
• How were they recorded?

Participant observation Describe where, when, and how you conducted the observation or ethnography .

• What group or community did you observe? How long did you spend there?
• How did you gain access to this group? What role did you play in the community?
• How long did you spend conducting the research? Where was it located?
• How did you record your data (e.g., audiovisual recordings, note-taking)?

Existing data Explain how you selected case study materials for your analysis.

• What type of materials did you analyse?
• How did you select them?

In order to gain better insight into possibilities for future improvement of the fitness shop’s product range, semi-structured interviews were conducted with 8 returning customers.

Here, a returning customer was defined as someone who usually bought products at least twice a week from the store.

Surveys were used to select participants. Interviews were conducted in a small office next to the cash register and lasted approximately 20 minutes each. Answers were recorded by note-taking, and seven interviews were also filmed with consent. One interviewee preferred not to be filmed.

Mixed methods

Mixed methods research combines quantitative and qualitative approaches. If a standalone quantitative or qualitative study is insufficient to answer your research question, mixed methods may be a good fit for you.

Mixed methods are less common than standalone analyses, largely because they require a great deal of effort to pull off successfully. If you choose to pursue mixed methods, it’s especially important to robustly justify your methods here.

The only proofreading tool specialized in correcting academic writing

The academic proofreading tool has been trained on 1000s of academic texts and by native English editors. Making it the most accurate and reliable proofreading tool for students.

Correct my document today

Next, you should indicate how you processed and analysed your data. Avoid going into too much detail: you should not start introducing or discussing any of your results at this stage.

In quantitative research , your analysis will be based on numbers. In your methods section, you can include:

• How you prepared the data before analysing it (e.g., checking for missing data , removing outliers , transforming variables)
• Which software you used (e.g., SPSS, Stata or R)
• Which statistical tests you used (e.g., two-tailed t test , simple linear regression )

In qualitative research, your analysis will be based on language, images, and observations (often involving some form of textual analysis ).

Specific methods might include:

• Content analysis : Categorising and discussing the meaning of words, phrases and sentences
• Thematic analysis : Coding and closely examining the data to identify broad themes and patterns
• Discourse analysis : Studying communication and meaning in relation to their social context

Mixed methods combine the above two research methods, integrating both qualitative and quantitative approaches into one coherent analytical process.

Above all, your methodology section should clearly make the case for why you chose the methods you did. This is especially true if you did not take the most standard approach to your topic. In this case, discuss why other methods were not suitable for your objectives, and show how this approach contributes new knowledge or understanding.

In any case, it should be overwhelmingly clear to your reader that you set yourself up for success in terms of your methodology’s design. Show how your methods should lead to results that are valid and reliable, while leaving the analysis of the meaning, importance, and relevance of your results for your discussion section .

• Quantitative: Lab-based experiments cannot always accurately simulate real-life situations and behaviours, but they are effective for testing causal relationships between variables .
• Qualitative: Unstructured interviews usually produce results that cannot be generalised beyond the sample group , but they provide a more in-depth understanding of participants’ perceptions, motivations, and emotions.
• Mixed methods: Despite issues systematically comparing differing types of data, a solely quantitative study would not sufficiently incorporate the lived experience of each participant, while a solely qualitative study would be insufficiently generalisable.

Remember that your aim is not just to describe your methods, but to show how and why you applied them. Again, it’s critical to demonstrate that your research was rigorously conducted and can be replicated.

1. Focus on your objectives and research questions

The methodology section should clearly show why your methods suit your objectives  and convince the reader that you chose the best possible approach to answering your problem statement and research questions .

2. Cite relevant sources

Your methodology can be strengthened by referencing existing research in your field. This can help you to:

• Show that you followed established practice for your type of research
• Discuss how you decided on your approach by evaluating existing research
• Present a novel methodological approach to address a gap in the literature

3. Write for your audience

Consider how much information you need to give, and avoid getting too lengthy. If you are using methods that are standard for your discipline, you probably don’t need to give a lot of background or justification.

Regardless, your methodology should be a clear, well-structured text that makes an argument for your approach, not just a list of technical details and procedures.

Methodology refers to the overarching strategy and rationale of your research. Developing your methodology involves studying the research methods used in your field and the theories or principles that underpin them, in order to choose the approach that best matches your objectives.

Methods are the specific tools and procedures you use to collect and analyse data (e.g. interviews, experiments , surveys , statistical tests ).

In a dissertation or scientific paper, the methodology chapter or methods section comes after the introduction and before the results , discussion and conclusion .

Depending on the length and type of document, you might also include a literature review or theoretical framework before the methodology.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to test a hypothesis by systematically collecting and analysing data, while qualitative methods allow you to explore ideas and experiences in depth.

A sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect data from in your research.

For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

Statistical sampling allows you to test a hypothesis about the characteristics of a population. There are various sampling methods you can use to ensure that your sample is representative of the population as a whole.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2022, October 10). What Is a Research Methodology? | Steps & Tips. Scribbr. Retrieved 22 April 2024, from https://www.scribbr.co.uk/thesis-dissertation/methodology/

Is this article helpful?

Shona McCombes

Other students also liked, how to write a dissertation proposal | a step-by-step guide, what is a literature review | guide, template, & examples, what is a theoretical framework | a step-by-step guide.

Qualitative Data Analysis Methods 101:

The “big 6” methods + examples.

By: Kerryn Warren (PhD) | Reviewed By: Eunice Rautenbach (D.Tech) | May 2020 (Updated April 2023)

Qualitative data analysis methods. Wow, that’s a mouthful. 

If you’re new to the world of research, qualitative data analysis can look rather intimidating. So much bulky terminology and so many abstract, fluffy concepts. It certainly can be a minefield!

Don’t worry – in this post, we’ll unpack the most popular analysis methods , one at a time, so that you can approach your analysis with confidence and competence – whether that’s for a dissertation, thesis or really any kind of research project.

What (exactly) is qualitative data analysis?

To understand qualitative data analysis, we need to first understand qualitative data – so let’s step back and ask the question, “what exactly is qualitative data?”.

Qualitative data refers to pretty much any data that’s “not numbers” . In other words, it’s not the stuff you measure using a fixed scale or complex equipment, nor do you analyse it using complex statistics or mathematics.

So, if it’s not numbers, what is it?

Words, you guessed? Well… sometimes , yes. Qualitative data can, and often does, take the form of interview transcripts, documents and open-ended survey responses – but it can also involve the interpretation of images and videos. In other words, qualitative isn’t just limited to text-based data.

So, how’s that different from quantitative data, you ask?

Simply put, qualitative research focuses on words, descriptions, concepts or ideas – while quantitative research focuses on numbers and statistics . Qualitative research investigates the “softer side” of things to explore and describe , while quantitative research focuses on the “hard numbers”, to measure differences between variables and the relationships between them. If you’re keen to learn more about the differences between qual and quant, we’ve got a detailed post over here .

So, qualitative analysis is easier than quantitative, right?

Not quite. In many ways, qualitative data can be challenging and time-consuming to analyse and interpret. At the end of your data collection phase (which itself takes a lot of time), you’ll likely have many pages of text-based data or hours upon hours of audio to work through. You might also have subtle nuances of interactions or discussions that have danced around in your mind, or that you scribbled down in messy field notes. All of this needs to work its way into your analysis.

Making sense of all of this is no small task and you shouldn’t underestimate it. Long story short – qualitative analysis can be a lot of work! Of course, quantitative analysis is no piece of cake either, but it’s important to recognise that qualitative analysis still requires a significant investment in terms of time and effort.

Need a helping hand?

In this post, we’ll explore qualitative data analysis by looking at some of the most common analysis methods we encounter. We’re not going to cover every possible qualitative method and we’re not going to go into heavy detail – we’re just going to give you the big picture. That said, we will of course includes links to loads of extra resources so that you can learn more about whichever analysis method interests you.

Without further delay, let’s get into it.

The “Big 6” Qualitative Analysis Methods 

There are many different types of qualitative data analysis, all of which serve different purposes and have unique strengths and weaknesses . We’ll start by outlining the analysis methods and then we’ll dive into the details for each.

The 6 most popular methods (or at least the ones we see at Grad Coach) are:

• Content analysis
• Narrative analysis
• Discourse analysis
• Thematic analysis
• Grounded theory (GT)
• Interpretive phenomenological analysis (IPA)

Let’s take a look at each of them…

QDA Method #1: Qualitative Content Analysis

Content analysis is possibly the most common and straightforward QDA method. At the simplest level, content analysis is used to evaluate patterns within a piece of content (for example, words, phrases or images) or across multiple pieces of content or sources of communication. For example, a collection of newspaper articles or political speeches.

With content analysis, you could, for instance, identify the frequency with which an idea is shared or spoken about – like the number of times a Kardashian is mentioned on Twitter. Or you could identify patterns of deeper underlying interpretations – for instance, by identifying phrases or words in tourist pamphlets that highlight India as an ancient country.

Because content analysis can be used in such a wide variety of ways, it’s important to go into your analysis with a very specific question and goal, or you’ll get lost in the fog. With content analysis, you’ll group large amounts of text into codes , summarise these into categories, and possibly even tabulate the data to calculate the frequency of certain concepts or variables. Because of this, content analysis provides a small splash of quantitative thinking within a qualitative method.

Naturally, while content analysis is widely useful, it’s not without its drawbacks . One of the main issues with content analysis is that it can be very time-consuming , as it requires lots of reading and re-reading of the texts. Also, because of its multidimensional focus on both qualitative and quantitative aspects, it is sometimes accused of losing important nuances in communication.

Content analysis also tends to concentrate on a very specific timeline and doesn’t take into account what happened before or after that timeline. This isn’t necessarily a bad thing though – just something to be aware of. So, keep these factors in mind if you’re considering content analysis. Every analysis method has its limitations , so don’t be put off by these – just be aware of them ! If you’re interested in learning more about content analysis, the video below provides a good starting point.

QDA Method #2: Narrative Analysis 

As the name suggests, narrative analysis is all about listening to people telling stories and analysing what that means . Since stories serve a functional purpose of helping us make sense of the world, we can gain insights into the ways that people deal with and make sense of reality by analysing their stories and the ways they’re told.

You could, for example, use narrative analysis to explore whether how something is being said is important. For instance, the narrative of a prisoner trying to justify their crime could provide insight into their view of the world and the justice system. Similarly, analysing the ways entrepreneurs talk about the struggles in their careers or cancer patients telling stories of hope could provide powerful insights into their mindsets and perspectives . Simply put, narrative analysis is about paying attention to the stories that people tell – and more importantly, the way they tell them.

Of course, the narrative approach has its weaknesses , too. Sample sizes are generally quite small due to the time-consuming process of capturing narratives. Because of this, along with the multitude of social and lifestyle factors which can influence a subject, narrative analysis can be quite difficult to reproduce in subsequent research. This means that it’s difficult to test the findings of some of this research.

Similarly, researcher bias can have a strong influence on the results here, so you need to be particularly careful about the potential biases you can bring into your analysis when using this method. Nevertheless, narrative analysis is still a very useful qualitative analysis method – just keep these limitations in mind and be careful not to draw broad conclusions . If you’re keen to learn more about narrative analysis, the video below provides a great introduction to this qualitative analysis method.

QDA Method #3: Discourse Analysis 

Discourse is simply a fancy word for written or spoken language or debate . So, discourse analysis is all about analysing language within its social context. In other words, analysing language – such as a conversation, a speech, etc – within the culture and society it takes place. For example, you could analyse how a janitor speaks to a CEO, or how politicians speak about terrorism.

To truly understand these conversations or speeches, the culture and history of those involved in the communication are important factors to consider. For example, a janitor might speak more casually with a CEO in a company that emphasises equality among workers. Similarly, a politician might speak more about terrorism if there was a recent terrorist incident in the country.

So, as you can see, by using discourse analysis, you can identify how culture , history or power dynamics (to name a few) have an effect on the way concepts are spoken about. So, if your research aims and objectives involve understanding culture or power dynamics, discourse analysis can be a powerful method.

Because there are many social influences in terms of how we speak to each other, the potential use of discourse analysis is vast . Of course, this also means it’s important to have a very specific research question (or questions) in mind when analysing your data and looking for patterns and themes, or you might land up going down a winding rabbit hole.

Discourse analysis can also be very time-consuming  as you need to sample the data to the point of saturation – in other words, until no new information and insights emerge. But this is, of course, part of what makes discourse analysis such a powerful technique. So, keep these factors in mind when considering this QDA method. Again, if you’re keen to learn more, the video below presents a good starting point.

QDA Method #4: Thematic Analysis

Thematic analysis looks at patterns of meaning in a data set – for example, a set of interviews or focus group transcripts. But what exactly does that… mean? Well, a thematic analysis takes bodies of data (which are often quite large) and groups them according to similarities – in other words, themes . These themes help us make sense of the content and derive meaning from it.

Let’s take a look at an example.

With thematic analysis, you could analyse 100 online reviews of a popular sushi restaurant to find out what patrons think about the place. By reviewing the data, you would then identify the themes that crop up repeatedly within the data – for example, “fresh ingredients” or “friendly wait staff”.

So, as you can see, thematic analysis can be pretty useful for finding out about people’s experiences , views, and opinions . Therefore, if your research aims and objectives involve understanding people’s experience or view of something, thematic analysis can be a great choice.

Since thematic analysis is a bit of an exploratory process, it’s not unusual for your research questions to develop , or even change as you progress through the analysis. While this is somewhat natural in exploratory research, it can also be seen as a disadvantage as it means that data needs to be re-reviewed each time a research question is adjusted. In other words, thematic analysis can be quite time-consuming – but for a good reason. So, keep this in mind if you choose to use thematic analysis for your project and budget extra time for unexpected adjustments.

QDA Method #5: Grounded theory (GT) 

Grounded theory is a powerful qualitative analysis method where the intention is to create a new theory (or theories) using the data at hand, through a series of “ tests ” and “ revisions ”. Strictly speaking, GT is more a research design type than an analysis method, but we’ve included it here as it’s often referred to as a method.

What’s most important with grounded theory is that you go into the analysis with an open mind and let the data speak for itself – rather than dragging existing hypotheses or theories into your analysis. In other words, your analysis must develop from the ground up (hence the name). 

Let’s look at an example of GT in action.

Assume you’re interested in developing a theory about what factors influence students to watch a YouTube video about qualitative analysis. Using Grounded theory , you’d start with this general overarching question about the given population (i.e., graduate students). First, you’d approach a small sample – for example, five graduate students in a department at a university. Ideally, this sample would be reasonably representative of the broader population. You’d interview these students to identify what factors lead them to watch the video.

After analysing the interview data, a general pattern could emerge. For example, you might notice that graduate students are more likely to read a post about qualitative methods if they are just starting on their dissertation journey, or if they have an upcoming test about research methods.

From here, you’ll look for another small sample – for example, five more graduate students in a different department – and see whether this pattern holds true for them. If not, you’ll look for commonalities and adapt your theory accordingly. As this process continues, the theory would develop . As we mentioned earlier, what’s important with grounded theory is that the theory develops from the data – not from some preconceived idea.

So, what are the drawbacks of grounded theory? Well, some argue that there’s a tricky circularity to grounded theory. For it to work, in principle, you should know as little as possible regarding the research question and population, so that you reduce the bias in your interpretation. However, in many circumstances, it’s also thought to be unwise to approach a research question without knowledge of the current literature . In other words, it’s a bit of a “chicken or the egg” situation.

Regardless, grounded theory remains a popular (and powerful) option. Naturally, it’s a very useful method when you’re researching a topic that is completely new or has very little existing research about it, as it allows you to start from scratch and work your way from the ground up .

QDA Method #6:   Interpretive Phenomenological Analysis (IPA)

Interpretive. Phenomenological. Analysis. IPA . Try saying that three times fast…

Let’s just stick with IPA, okay?

IPA is designed to help you understand the personal experiences of a subject (for example, a person or group of people) concerning a major life event, an experience or a situation . This event or experience is the “phenomenon” that makes up the “P” in IPA. Such phenomena may range from relatively common events – such as motherhood, or being involved in a car accident – to those which are extremely rare – for example, someone’s personal experience in a refugee camp. So, IPA is a great choice if your research involves analysing people’s personal experiences of something that happened to them.

It’s important to remember that IPA is subject – centred . In other words, it’s focused on the experiencer . This means that, while you’ll likely use a coding system to identify commonalities, it’s important not to lose the depth of experience or meaning by trying to reduce everything to codes. Also, keep in mind that since your sample size will generally be very small with IPA, you often won’t be able to draw broad conclusions about the generalisability of your findings. But that’s okay as long as it aligns with your research aims and objectives.

Another thing to be aware of with IPA is personal bias . While researcher bias can creep into all forms of research, self-awareness is critically important with IPA, as it can have a major impact on the results. For example, a researcher who was a victim of a crime himself could insert his own feelings of frustration and anger into the way he interprets the experience of someone who was kidnapped. So, if you’re going to undertake IPA, you need to be very self-aware or you could muddy the analysis.

How to choose the right analysis method

In light of all of the qualitative analysis methods we’ve covered so far, you’re probably asking yourself the question, “ How do I choose the right one? ”

Much like all the other methodological decisions you’ll need to make, selecting the right qualitative analysis method largely depends on your research aims, objectives and questions . In other words, the best tool for the job depends on what you’re trying to build. For example:

• Perhaps your research aims to analyse the use of words and what they reveal about the intention of the storyteller and the cultural context of the time.
• Perhaps your research aims to develop an understanding of the unique personal experiences of people that have experienced a certain event, or
• Perhaps your research aims to develop insight regarding the influence of a certain culture on its members.

As you can probably see, each of these research aims are distinctly different , and therefore different analysis methods would be suitable for each one. For example, narrative analysis would likely be a good option for the first aim, while grounded theory wouldn’t be as relevant. 

It’s also important to remember that each method has its own set of strengths, weaknesses and general limitations. No single analysis method is perfect . So, depending on the nature of your research, it may make sense to adopt more than one method (this is called triangulation ). Keep in mind though that this will of course be quite time-consuming.

As we’ve seen, all of the qualitative analysis methods we’ve discussed make use of coding and theme-generating techniques, but the intent and approach of each analysis method differ quite substantially. So, it’s very important to come into your research with a clear intention before you decide which analysis method (or methods) to use.

Start by reviewing your research aims , objectives and research questions to assess what exactly you’re trying to find out – then select a qualitative analysis method that fits. Never pick a method just because you like it or have experience using it – your analysis method (or methods) must align with your broader research aims and objectives.

Let’s recap on QDA methods…

In this post, we looked at six popular qualitative data analysis methods:

• First, we looked at content analysis , a straightforward method that blends a little bit of quant into a primarily qualitative analysis.
• Then we looked at narrative analysis , which is about analysing how stories are told.
• Next up was discourse analysis – which is about analysing conversations and interactions.
• Then we moved on to thematic analysis – which is about identifying themes and patterns.
• From there, we went south with grounded theory – which is about starting from scratch with a specific question and using the data alone to build a theory in response to that question.
• And finally, we looked at IPA – which is about understanding people’s unique experiences of a phenomenon.

Of course, these aren’t the only options when it comes to qualitative data analysis, but they’re a great starting point if you’re dipping your toes into qualitative research for the first time.

If you’re still feeling a bit confused, consider our private coaching service , where we hold your hand through the research process to help you develop your best work.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

You Might Also Like:

84 Comments

This has been very helpful. Thank you.

Thank you madam,

Thank you so much for this information

I wonder it so clear for understand and good for me. can I ask additional query?

Very insightful and useful

Good work done with clear explanations. Thank you.

Thanks so much for the write-up, it’s really good.

Thanks madam . It is very important .

thank you very good

This has been very well explained in simple language . It is useful even for a new researcher.

Great to hear that. Good luck with your qualitative data analysis, Pramod!

This is very useful information. And it was very a clear language structured presentation. Thanks a lot.

Thank you so much.

very informative sequential presentation

Precise explanation of method.

Hi, may we use 2 data analysis methods in our qualitative research?

Thanks for your comment. Most commonly, one would use one type of analysis method, but it depends on your research aims and objectives.

You explained it in very simple language, everyone can understand it. Thanks so much.

Thank you very much, this is very helpful. It has been explained in a very simple manner that even a layman understands

Thank nicely explained can I ask is Qualitative content analysis the same as thematic analysis?

Thanks for your comment. No, QCA and thematic are two different types of analysis. This article might help clarify – https://onlinelibrary.wiley.com/doi/10.1111/nhs.12048

This is my first time to come across a well explained data analysis. so helpful.

I have thoroughly enjoyed your explanation of the six qualitative analysis methods. This is very helpful. Thank you!

Thank you very much, this is well explained and useful

i need a citation of your book.

Thanks a lot , remarkable indeed, enlighting to the best

Hi Derek, What other theories/methods would you recommend when the data is a whole speech?

Keep writing useful artikel.

It is important concept about QDA and also the way to express is easily understandable, so thanks for all.

Thank you, this is well explained and very useful.

Very helpful .Thanks.

Hi there! Very well explained. Simple but very useful style of writing. Please provide the citation of the text. warm regards

The session was very helpful and insightful. Thank you

This was very helpful and insightful. Easy to read and understand

As a professional academic writer, this has been so informative and educative. Keep up the good work Grad Coach you are unmatched with quality content for sure.

Keep up the good work Grad Coach you are unmatched with quality content for sure.

Its Great and help me the most. A Million Thanks you Dr.

It is a very nice work

Very insightful. Please, which of this approach could be used for a research that one is trying to elicit students’ misconceptions in a particular concept ?

This is Amazing and well explained, thanks

great overview

What do we call a research data analysis method that one use to advise or determining the best accounting tool or techniques that should be adopted in a company.

Informative video, explained in a clear and simple way. Kudos

Waoo! I have chosen method wrong for my data analysis. But I can revise my work according to this guide. Thank you so much for this helpful lecture.

This has been very helpful. It gave me a good view of my research objectives and how to choose the best method. Thematic analysis it is.

Very helpful indeed. Thanku so much for the insight.

This was incredibly helpful.

Very helpful.

very educative

Nicely written especially for novice academic researchers like me! Thank you.

choosing a right method for a paper is always a hard job for a student, this is a useful information, but it would be more useful personally for me, if the author provide me with a little bit more information about the data analysis techniques in type of explanatory research. Can we use qualitative content analysis technique for explanatory research ? or what is the suitable data analysis method for explanatory research in social studies?

that was very helpful for me. because these details are so important to my research. thank you very much

I learnt a lot. Thank you

Relevant and Informative, thanks !

Well-planned and organized, thanks much! 🙂

I have reviewed qualitative data analysis in a simplest way possible. The content will highly be useful for developing my book on qualitative data analysis methods. Cheers!

Clear explanation on qualitative and how about Case study

This was helpful. Thank you

This was really of great assistance, it was just the right information needed. Explanation very clear and follow.

Wow, Thanks for making my life easy

This was helpful thanks .

Very helpful…. clear and written in an easily understandable manner. Thank you.

This was so helpful as it was easy to understand. I’m a new to research thank you so much.

so educative…. but Ijust want to know which method is coding of the qualitative or tallying done?

Thank you for the great content, I have learnt a lot. So helpful

precise and clear presentation with simple language and thank you for that.

very informative content, thank you.

You guys are amazing on YouTube on this platform. Your teachings are great, educative, and informative. kudos!

Brilliant Delivery. You made a complex subject seem so easy. Well done.

Beautifully explained.

Thanks a lot

Is there a video the captures the practical process of coding using automated applications?

Thanks for the comment. We don’t recommend using automated applications for coding, as they are not sufficiently accurate in our experience.

content analysis can be qualitative research?

THANK YOU VERY MUCH.

Thank you very much for such a wonderful content

do you have any material on Data collection

What a powerful explanation of the QDA methods. Thank you.

Great explanation both written and Video. i have been using of it on a day to day working of my thesis project in accounting and finance. Thank you very much for your support.

very helpful, thank you so much

Submit a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Print Friendly

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Korean J Anesthesiol
• v.71(2); 2018 Apr

Introduction to systematic review and meta-analysis

1 Department of Anesthesiology and Pain Medicine, Inje University Seoul Paik Hospital, Seoul, Korea

2 Department of Anesthesiology and Pain Medicine, Chung-Ang University College of Medicine, Seoul, Korea

Systematic reviews and meta-analyses present results by combining and analyzing data from different studies conducted on similar research topics. In recent years, systematic reviews and meta-analyses have been actively performed in various fields including anesthesiology. These research methods are powerful tools that can overcome the difficulties in performing large-scale randomized controlled trials. However, the inclusion of studies with any biases or improperly assessed quality of evidence in systematic reviews and meta-analyses could yield misleading results. Therefore, various guidelines have been suggested for conducting systematic reviews and meta-analyses to help standardize them and improve their quality. Nonetheless, accepting the conclusions of many studies without understanding the meta-analysis can be dangerous. Therefore, this article provides an easy introduction to clinicians on performing and understanding meta-analyses.

Introduction

A systematic review collects all possible studies related to a given topic and design, and reviews and analyzes their results [ 1 ]. During the systematic review process, the quality of studies is evaluated, and a statistical meta-analysis of the study results is conducted on the basis of their quality. A meta-analysis is a valid, objective, and scientific method of analyzing and combining different results. Usually, in order to obtain more reliable results, a meta-analysis is mainly conducted on randomized controlled trials (RCTs), which have a high level of evidence [ 2 ] ( Fig. 1 ). Since 1999, various papers have presented guidelines for reporting meta-analyses of RCTs. Following the Quality of Reporting of Meta-analyses (QUORUM) statement [ 3 ], and the appearance of registers such as Cochrane Library’s Methodology Register, a large number of systematic literature reviews have been registered. In 2009, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement [ 4 ] was published, and it greatly helped standardize and improve the quality of systematic reviews and meta-analyses [ 5 ].

Levels of evidence.

In anesthesiology, the importance of systematic reviews and meta-analyses has been highlighted, and they provide diagnostic and therapeutic value to various areas, including not only perioperative management but also intensive care and outpatient anesthesia [6–13]. Systematic reviews and meta-analyses include various topics, such as comparing various treatments of postoperative nausea and vomiting [ 14 , 15 ], comparing general anesthesia and regional anesthesia [ 16 – 18 ], comparing airway maintenance devices [ 8 , 19 ], comparing various methods of postoperative pain control (e.g., patient-controlled analgesia pumps, nerve block, or analgesics) [ 20 – 23 ], comparing the precision of various monitoring instruments [ 7 ], and meta-analysis of dose-response in various drugs [ 12 ].

Thus, literature reviews and meta-analyses are being conducted in diverse medical fields, and the aim of highlighting their importance is to help better extract accurate, good quality data from the flood of data being produced. However, a lack of understanding about systematic reviews and meta-analyses can lead to incorrect outcomes being derived from the review and analysis processes. If readers indiscriminately accept the results of the many meta-analyses that are published, incorrect data may be obtained. Therefore, in this review, we aim to describe the contents and methods used in systematic reviews and meta-analyses in a way that is easy to understand for future authors and readers of systematic review and meta-analysis.

Study Planning

It is easy to confuse systematic reviews and meta-analyses. A systematic review is an objective, reproducible method to find answers to a certain research question, by collecting all available studies related to that question and reviewing and analyzing their results. A meta-analysis differs from a systematic review in that it uses statistical methods on estimates from two or more different studies to form a pooled estimate [ 1 ]. Following a systematic review, if it is not possible to form a pooled estimate, it can be published as is without progressing to a meta-analysis; however, if it is possible to form a pooled estimate from the extracted data, a meta-analysis can be attempted. Systematic reviews and meta-analyses usually proceed according to the flowchart presented in Fig. 2 . We explain each of the stages below.

Flowchart illustrating a systematic review.

Formulating research questions

A systematic review attempts to gather all available empirical research by using clearly defined, systematic methods to obtain answers to a specific question. A meta-analysis is the statistical process of analyzing and combining results from several similar studies. Here, the definition of the word “similar” is not made clear, but when selecting a topic for the meta-analysis, it is essential to ensure that the different studies present data that can be combined. If the studies contain data on the same topic that can be combined, a meta-analysis can even be performed using data from only two studies. However, study selection via a systematic review is a precondition for performing a meta-analysis, and it is important to clearly define the Population, Intervention, Comparison, Outcomes (PICO) parameters that are central to evidence-based research. In addition, selection of the research topic is based on logical evidence, and it is important to select a topic that is familiar to readers without clearly confirmed the evidence [ 24 ].

Protocols and registration

In systematic reviews, prior registration of a detailed research plan is very important. In order to make the research process transparent, primary/secondary outcomes and methods are set in advance, and in the event of changes to the method, other researchers and readers are informed when, how, and why. Many studies are registered with an organization like PROSPERO ( http://www.crd.york.ac.uk/PROSPERO/ ), and the registration number is recorded when reporting the study, in order to share the protocol at the time of planning.

Defining inclusion and exclusion criteria

Information is included on the study design, patient characteristics, publication status (published or unpublished), language used, and research period. If there is a discrepancy between the number of patients included in the study and the number of patients included in the analysis, this needs to be clearly explained while describing the patient characteristics, to avoid confusing the reader.

Literature search and study selection

In order to secure proper basis for evidence-based research, it is essential to perform a broad search that includes as many studies as possible that meet the inclusion and exclusion criteria. Typically, the three bibliographic databases Medline, Embase, and Cochrane Central Register of Controlled Trials (CENTRAL) are used. In domestic studies, the Korean databases KoreaMed, KMBASE, and RISS4U may be included. Effort is required to identify not only published studies but also abstracts, ongoing studies, and studies awaiting publication. Among the studies retrieved in the search, the researchers remove duplicate studies, select studies that meet the inclusion/exclusion criteria based on the abstracts, and then make the final selection of studies based on their full text. In order to maintain transparency and objectivity throughout this process, study selection is conducted independently by at least two investigators. When there is a inconsistency in opinions, intervention is required via debate or by a third reviewer. The methods for this process also need to be planned in advance. It is essential to ensure the reproducibility of the literature selection process [ 25 ].

Quality of evidence

However, well planned the systematic review or meta-analysis is, if the quality of evidence in the studies is low, the quality of the meta-analysis decreases and incorrect results can be obtained [ 26 ]. Even when using randomized studies with a high quality of evidence, evaluating the quality of evidence precisely helps determine the strength of recommendations in the meta-analysis. One method of evaluating the quality of evidence in non-randomized studies is the Newcastle-Ottawa Scale, provided by the Ottawa Hospital Research Institute 1) . However, we are mostly focusing on meta-analyses that use randomized studies.

If the Grading of Recommendations, Assessment, Development and Evaluations (GRADE) system ( http://www.gradeworkinggroup.org/ ) is used, the quality of evidence is evaluated on the basis of the study limitations, inaccuracies, incompleteness of outcome data, indirectness of evidence, and risk of publication bias, and this is used to determine the strength of recommendations [ 27 ]. As shown in Table 1 , the study limitations are evaluated using the “risk of bias” method proposed by Cochrane 2) . This method classifies bias in randomized studies as “low,” “high,” or “unclear” on the basis of the presence or absence of six processes (random sequence generation, allocation concealment, blinding participants or investigators, incomplete outcome data, selective reporting, and other biases) [ 28 ].

The Cochrane Collaboration’s Tool for Assessing the Risk of Bias [ 28 ]

Data extraction

Two different investigators extract data based on the objectives and form of the study; thereafter, the extracted data are reviewed. Since the size and format of each variable are different, the size and format of the outcomes are also different, and slight changes may be required when combining the data [ 29 ]. If there are differences in the size and format of the outcome variables that cause difficulties combining the data, such as the use of different evaluation instruments or different evaluation timepoints, the analysis may be limited to a systematic review. The investigators resolve differences of opinion by debate, and if they fail to reach a consensus, a third-reviewer is consulted.

Data Analysis

The aim of a meta-analysis is to derive a conclusion with increased power and accuracy than what could not be able to achieve in individual studies. Therefore, before analysis, it is crucial to evaluate the direction of effect, size of effect, homogeneity of effects among studies, and strength of evidence [ 30 ]. Thereafter, the data are reviewed qualitatively and quantitatively. If it is determined that the different research outcomes cannot be combined, all the results and characteristics of the individual studies are displayed in a table or in a descriptive form; this is referred to as a qualitative review. A meta-analysis is a quantitative review, in which the clinical effectiveness is evaluated by calculating the weighted pooled estimate for the interventions in at least two separate studies.

The pooled estimate is the outcome of the meta-analysis, and is typically explained using a forest plot ( Figs. 3 and ​ and4). 4 ). The black squares in the forest plot are the odds ratios (ORs) and 95% confidence intervals in each study. The area of the squares represents the weight reflected in the meta-analysis. The black diamond represents the OR and 95% confidence interval calculated across all the included studies. The bold vertical line represents a lack of therapeutic effect (OR = 1); if the confidence interval includes OR = 1, it means no significant difference was found between the treatment and control groups.

Forest plot analyzed by two different models using the same data. (A) Fixed-effect model. (B) Random-effect model. The figure depicts individual trials as filled squares with the relative sample size and the solid line as the 95% confidence interval of the difference. The diamond shape indicates the pooled estimate and uncertainty for the combined effect. The vertical line indicates the treatment group shows no effect (OR = 1). Moreover, if the confidence interval includes 1, then the result shows no evidence of difference between the treatment and control groups.

Forest plot representing homogeneous data.

Dichotomous variables and continuous variables

In data analysis, outcome variables can be considered broadly in terms of dichotomous variables and continuous variables. When combining data from continuous variables, the mean difference (MD) and standardized mean difference (SMD) are used ( Table 2 ).

Summary of Meta-analysis Methods Available in RevMan [ 28 ]

The MD is the absolute difference in mean values between the groups, and the SMD is the mean difference between groups divided by the standard deviation. When results are presented in the same units, the MD can be used, but when results are presented in different units, the SMD should be used. When the MD is used, the combined units must be shown. A value of “0” for the MD or SMD indicates that the effects of the new treatment method and the existing treatment method are the same. A value lower than “0” means the new treatment method is less effective than the existing method, and a value greater than “0” means the new treatment is more effective than the existing method.

When combining data for dichotomous variables, the OR, risk ratio (RR), or risk difference (RD) can be used. The RR and RD can be used for RCTs, quasi-experimental studies, or cohort studies, and the OR can be used for other case-control studies or cross-sectional studies. However, because the OR is difficult to interpret, using the RR and RD, if possible, is recommended. If the outcome variable is a dichotomous variable, it can be presented as the number needed to treat (NNT), which is the minimum number of patients who need to be treated in the intervention group, compared to the control group, for a given event to occur in at least one patient. Based on Table 3 , in an RCT, if x is the probability of the event occurring in the control group and y is the probability of the event occurring in the intervention group, then x = c/(c + d), y = a/(a + b), and the absolute risk reduction (ARR) = x − y. NNT can be obtained as the reciprocal, 1/ARR.

Calculation of the Number Needed to Treat in the Dichotomous table

Fixed-effect models and random-effect models

In order to analyze effect size, two types of models can be used: a fixed-effect model or a random-effect model. A fixed-effect model assumes that the effect of treatment is the same, and that variation between results in different studies is due to random error. Thus, a fixed-effect model can be used when the studies are considered to have the same design and methodology, or when the variability in results within a study is small, and the variance is thought to be due to random error. Three common methods are used for weighted estimation in a fixed-effect model: 1) inverse variance-weighted estimation 3) , 2) Mantel-Haenszel estimation 4) , and 3) Peto estimation 5) .

A random-effect model assumes heterogeneity between the studies being combined, and these models are used when the studies are assumed different, even if a heterogeneity test does not show a significant result. Unlike a fixed-effect model, a random-effect model assumes that the size of the effect of treatment differs among studies. Thus, differences in variation among studies are thought to be due to not only random error but also between-study variability in results. Therefore, weight does not decrease greatly for studies with a small number of patients. Among methods for weighted estimation in a random-effect model, the DerSimonian and Laird method 6) is mostly used for dichotomous variables, as the simplest method, while inverse variance-weighted estimation is used for continuous variables, as with fixed-effect models. These four methods are all used in Review Manager software (The Cochrane Collaboration, UK), and are described in a study by Deeks et al. [ 31 ] ( Table 2 ). However, when the number of studies included in the analysis is less than 10, the Hartung-Knapp-Sidik-Jonkman method 7) can better reduce the risk of type 1 error than does the DerSimonian and Laird method [ 32 ].

Fig. 3 shows the results of analyzing outcome data using a fixed-effect model (A) and a random-effect model (B). As shown in Fig. 3 , while the results from large studies are weighted more heavily in the fixed-effect model, studies are given relatively similar weights irrespective of study size in the random-effect model. Although identical data were being analyzed, as shown in Fig. 3 , the significant result in the fixed-effect model was no longer significant in the random-effect model. One representative example of the small study effect in a random-effect model is the meta-analysis by Li et al. [ 33 ]. In a large-scale study, intravenous injection of magnesium was unrelated to acute myocardial infarction, but in the random-effect model, which included numerous small studies, the small study effect resulted in an association being found between intravenous injection of magnesium and myocardial infarction. This small study effect can be controlled for by using a sensitivity analysis, which is performed to examine the contribution of each of the included studies to the final meta-analysis result. In particular, when heterogeneity is suspected in the study methods or results, by changing certain data or analytical methods, this method makes it possible to verify whether the changes affect the robustness of the results, and to examine the causes of such effects [ 34 ].

Heterogeneity

Homogeneity test is a method whether the degree of heterogeneity is greater than would be expected to occur naturally when the effect size calculated from several studies is higher than the sampling error. This makes it possible to test whether the effect size calculated from several studies is the same. Three types of homogeneity tests can be used: 1) forest plot, 2) Cochrane’s Q test (chi-squared), and 3) Higgins I 2 statistics. In the forest plot, as shown in Fig. 4 , greater overlap between the confidence intervals indicates greater homogeneity. For the Q statistic, when the P value of the chi-squared test, calculated from the forest plot in Fig. 4 , is less than 0.1, it is considered to show statistical heterogeneity and a random-effect can be used. Finally, I 2 can be used [ 35 ].

I 2 , calculated as shown above, returns a value between 0 and 100%. A value less than 25% is considered to show strong homogeneity, a value of 50% is average, and a value greater than 75% indicates strong heterogeneity.

Even when the data cannot be shown to be homogeneous, a fixed-effect model can be used, ignoring the heterogeneity, and all the study results can be presented individually, without combining them. However, in many cases, a random-effect model is applied, as described above, and a subgroup analysis or meta-regression analysis is performed to explain the heterogeneity. In a subgroup analysis, the data are divided into subgroups that are expected to be homogeneous, and these subgroups are analyzed. This needs to be planned in the predetermined protocol before starting the meta-analysis. A meta-regression analysis is similar to a normal regression analysis, except that the heterogeneity between studies is modeled. This process involves performing a regression analysis of the pooled estimate for covariance at the study level, and so it is usually not considered when the number of studies is less than 10. Here, univariate and multivariate regression analyses can both be considered.

Publication bias

Publication bias is the most common type of reporting bias in meta-analyses. This refers to the distortion of meta-analysis outcomes due to the higher likelihood of publication of statistically significant studies rather than non-significant studies. In order to test the presence or absence of publication bias, first, a funnel plot can be used ( Fig. 5 ). Studies are plotted on a scatter plot with effect size on the x-axis and precision or total sample size on the y-axis. If the points form an upside-down funnel shape, with a broad base that narrows towards the top of the plot, this indicates the absence of a publication bias ( Fig. 5A ) [ 29 , 36 ]. On the other hand, if the plot shows an asymmetric shape, with no points on one side of the graph, then publication bias can be suspected ( Fig. 5B ). Second, to test publication bias statistically, Begg and Mazumdar’s rank correlation test 8) [ 37 ] or Egger’s test 9) [ 29 ] can be used. If publication bias is detected, the trim-and-fill method 10) can be used to correct the bias [ 38 ]. Fig. 6 displays results that show publication bias in Egger’s test, which has then been corrected using the trim-and-fill method using Comprehensive Meta-Analysis software (Biostat, USA).

Funnel plot showing the effect size on the x-axis and sample size on the y-axis as a scatter plot. (A) Funnel plot without publication bias. The individual plots are broader at the bottom and narrower at the top. (B) Funnel plot with publication bias. The individual plots are located asymmetrically.

Funnel plot adjusted using the trim-and-fill method. White circles: comparisons included. Black circles: inputted comparisons using the trim-and-fill method. White diamond: pooled observed log risk ratio. Black diamond: pooled inputted log risk ratio.

Result Presentation

When reporting the results of a systematic review or meta-analysis, the analytical content and methods should be described in detail. First, a flowchart is displayed with the literature search and selection process according to the inclusion/exclusion criteria. Second, a table is shown with the characteristics of the included studies. A table should also be included with information related to the quality of evidence, such as GRADE ( Table 4 ). Third, the results of data analysis are shown in a forest plot and funnel plot. Fourth, if the results use dichotomous data, the NNT values can be reported, as described above.

The GRADE Evidence Quality for Each Outcome

N: number of studies, ROB: risk of bias, PON: postoperative nausea, POV: postoperative vomiting, PONV: postoperative nausea and vomiting, CI: confidence interval, RR: risk ratio, AR: absolute risk.

When Review Manager software (The Cochrane Collaboration, UK) is used for the analysis, two types of P values are given. The first is the P value from the z-test, which tests the null hypothesis that the intervention has no effect. The second P value is from the chi-squared test, which tests the null hypothesis for a lack of heterogeneity. The statistical result for the intervention effect, which is generally considered the most important result in meta-analyses, is the z-test P value.

A common mistake when reporting results is, given a z-test P value greater than 0.05, to say there was “no statistical significance” or “no difference.” When evaluating statistical significance in a meta-analysis, a P value lower than 0.05 can be explained as “a significant difference in the effects of the two treatment methods.” However, the P value may appear non-significant whether or not there is a difference between the two treatment methods. In such a situation, it is better to announce “there was no strong evidence for an effect,” and to present the P value and confidence intervals. Another common mistake is to think that a smaller P value is indicative of a more significant effect. In meta-analyses of large-scale studies, the P value is more greatly affected by the number of studies and patients included, rather than by the significance of the results; therefore, care should be taken when interpreting the results of a meta-analysis.

When performing a systematic literature review or meta-analysis, if the quality of studies is not properly evaluated or if proper methodology is not strictly applied, the results can be biased and the outcomes can be incorrect. However, when systematic reviews and meta-analyses are properly implemented, they can yield powerful results that could usually only be achieved using large-scale RCTs, which are difficult to perform in individual studies. As our understanding of evidence-based medicine increases and its importance is better appreciated, the number of systematic reviews and meta-analyses will keep increasing. However, indiscriminate acceptance of the results of all these meta-analyses can be dangerous, and hence, we recommend that their results be received critically on the basis of a more accurate understanding.

1) http://www.ohri.ca .

2) http://methods.cochrane.org/bias/assessing-risk-bias-included-studies .

3) The inverse variance-weighted estimation method is useful if the number of studies is small with large sample sizes.

4) The Mantel-Haenszel estimation method is useful if the number of studies is large with small sample sizes.

5) The Peto estimation method is useful if the event rate is low or one of the two groups shows zero incidence.

6) The most popular and simplest statistical method used in Review Manager and Comprehensive Meta-analysis software.

7) Alternative random-effect model meta-analysis that has more adequate error rates than does the common DerSimonian and Laird method, especially when the number of studies is small. However, even with the Hartung-Knapp-Sidik-Jonkman method, when there are less than five studies with very unequal sizes, extra caution is needed.

8) The Begg and Mazumdar rank correlation test uses the correlation between the ranks of effect sizes and the ranks of their variances [ 37 ].

9) The degree of funnel plot asymmetry as measured by the intercept from the regression of standard normal deviates against precision [ 29 ].

10) If there are more small studies on one side, we expect the suppression of studies on the other side. Trimming yields the adjusted effect size and reduces the variance of the effects by adding the original studies back into the analysis as a mirror image of each study.

• Privacy Policy

Buy Me a Coffee

Home » Research Methodology – Types, Examples and writing Guide

Research Methodology – Types, Examples and writing Guide

Table of Contents

Research Methodology

Definition:

Research Methodology refers to the systematic and scientific approach used to conduct research, investigate problems, and gather data and information for a specific purpose. It involves the techniques and procedures used to identify, collect , analyze , and interpret data to answer research questions or solve research problems . Moreover, They are philosophical and theoretical frameworks that guide the research process.

Structure of Research Methodology

Research methodology formats can vary depending on the specific requirements of the research project, but the following is a basic example of a structure for a research methodology section:

I. Introduction

• Provide an overview of the research problem and the need for a research methodology section
• Outline the main research questions and objectives

II. Research Design

• Explain the research design chosen and why it is appropriate for the research question(s) and objectives
• Discuss any alternative research designs considered and why they were not chosen
• Describe the research setting and participants (if applicable)

III. Data Collection Methods

• Describe the methods used to collect data (e.g., surveys, interviews, observations)
• Explain how the data collection methods were chosen and why they are appropriate for the research question(s) and objectives
• Detail any procedures or instruments used for data collection

IV. Data Analysis Methods

• Describe the methods used to analyze the data (e.g., statistical analysis, content analysis )
• Explain how the data analysis methods were chosen and why they are appropriate for the research question(s) and objectives
• Detail any procedures or software used for data analysis

V. Ethical Considerations

• Discuss any ethical issues that may arise from the research and how they were addressed
• Explain how informed consent was obtained (if applicable)
• Detail any measures taken to ensure confidentiality and anonymity

VI. Limitations

• Identify any potential limitations of the research methodology and how they may impact the results and conclusions

VII. Conclusion

• Summarize the key aspects of the research methodology section
• Explain how the research methodology addresses the research question(s) and objectives

Research Methodology Types

Types of Research Methodology are as follows:

Quantitative Research Methodology

This is a research methodology that involves the collection and analysis of numerical data using statistical methods. This type of research is often used to study cause-and-effect relationships and to make predictions.

Qualitative Research Methodology

This is a research methodology that involves the collection and analysis of non-numerical data such as words, images, and observations. This type of research is often used to explore complex phenomena, to gain an in-depth understanding of a particular topic, and to generate hypotheses.

Mixed-Methods Research Methodology

This is a research methodology that combines elements of both quantitative and qualitative research. This approach can be particularly useful for studies that aim to explore complex phenomena and to provide a more comprehensive understanding of a particular topic.

Case Study Research Methodology

This is a research methodology that involves in-depth examination of a single case or a small number of cases. Case studies are often used in psychology, sociology, and anthropology to gain a detailed understanding of a particular individual or group.

Action Research Methodology

This is a research methodology that involves a collaborative process between researchers and practitioners to identify and solve real-world problems. Action research is often used in education, healthcare, and social work.

Experimental Research Methodology

This is a research methodology that involves the manipulation of one or more independent variables to observe their effects on a dependent variable. Experimental research is often used to study cause-and-effect relationships and to make predictions.

Survey Research Methodology

This is a research methodology that involves the collection of data from a sample of individuals using questionnaires or interviews. Survey research is often used to study attitudes, opinions, and behaviors.

Grounded Theory Research Methodology

This is a research methodology that involves the development of theories based on the data collected during the research process. Grounded theory is often used in sociology and anthropology to generate theories about social phenomena.

Research Methodology Example

An Example of Research Methodology could be the following:

Research Methodology for Investigating the Effectiveness of Cognitive Behavioral Therapy in Reducing Symptoms of Depression in Adults

Introduction:

The aim of this research is to investigate the effectiveness of cognitive-behavioral therapy (CBT) in reducing symptoms of depression in adults. To achieve this objective, a randomized controlled trial (RCT) will be conducted using a mixed-methods approach.

Research Design:

The study will follow a pre-test and post-test design with two groups: an experimental group receiving CBT and a control group receiving no intervention. The study will also include a qualitative component, in which semi-structured interviews will be conducted with a subset of participants to explore their experiences of receiving CBT.

Participants:

Participants will be recruited from community mental health clinics in the local area. The sample will consist of 100 adults aged 18-65 years old who meet the diagnostic criteria for major depressive disorder. Participants will be randomly assigned to either the experimental group or the control group.

Intervention :

The experimental group will receive 12 weekly sessions of CBT, each lasting 60 minutes. The intervention will be delivered by licensed mental health professionals who have been trained in CBT. The control group will receive no intervention during the study period.

Data Collection:

Quantitative data will be collected through the use of standardized measures such as the Beck Depression Inventory-II (BDI-II) and the Generalized Anxiety Disorder-7 (GAD-7). Data will be collected at baseline, immediately after the intervention, and at a 3-month follow-up. Qualitative data will be collected through semi-structured interviews with a subset of participants from the experimental group. The interviews will be conducted at the end of the intervention period, and will explore participants’ experiences of receiving CBT.

Data Analysis:

Quantitative data will be analyzed using descriptive statistics, t-tests, and mixed-model analyses of variance (ANOVA) to assess the effectiveness of the intervention. Qualitative data will be analyzed using thematic analysis to identify common themes and patterns in participants’ experiences of receiving CBT.

Ethical Considerations:

This study will comply with ethical guidelines for research involving human subjects. Participants will provide informed consent before participating in the study, and their privacy and confidentiality will be protected throughout the study. Any adverse events or reactions will be reported and managed appropriately.

Data Management:

All data collected will be kept confidential and stored securely using password-protected databases. Identifying information will be removed from qualitative data transcripts to ensure participants’ anonymity.

Limitations:

One potential limitation of this study is that it only focuses on one type of psychotherapy, CBT, and may not generalize to other types of therapy or interventions. Another limitation is that the study will only include participants from community mental health clinics, which may not be representative of the general population.

Conclusion:

This research aims to investigate the effectiveness of CBT in reducing symptoms of depression in adults. By using a randomized controlled trial and a mixed-methods approach, the study will provide valuable insights into the mechanisms underlying the relationship between CBT and depression. The results of this study will have important implications for the development of effective treatments for depression in clinical settings.

How to Write Research Methodology

Writing a research methodology involves explaining the methods and techniques you used to conduct research, collect data, and analyze results. It’s an essential section of any research paper or thesis, as it helps readers understand the validity and reliability of your findings. Here are the steps to write a research methodology:

• Start by explaining your research question: Begin the methodology section by restating your research question and explaining why it’s important. This helps readers understand the purpose of your research and the rationale behind your methods.
• Describe your research design: Explain the overall approach you used to conduct research. This could be a qualitative or quantitative research design, experimental or non-experimental, case study or survey, etc. Discuss the advantages and limitations of the chosen design.
• Discuss your sample: Describe the participants or subjects you included in your study. Include details such as their demographics, sampling method, sample size, and any exclusion criteria used.
• Describe your data collection methods : Explain how you collected data from your participants. This could include surveys, interviews, observations, questionnaires, or experiments. Include details on how you obtained informed consent, how you administered the tools, and how you minimized the risk of bias.
• Explain your data analysis techniques: Describe the methods you used to analyze the data you collected. This could include statistical analysis, content analysis, thematic analysis, or discourse analysis. Explain how you dealt with missing data, outliers, and any other issues that arose during the analysis.
• Discuss the validity and reliability of your research : Explain how you ensured the validity and reliability of your study. This could include measures such as triangulation, member checking, peer review, or inter-coder reliability.
• Acknowledge any limitations of your research: Discuss any limitations of your study, including any potential threats to validity or generalizability. This helps readers understand the scope of your findings and how they might apply to other contexts.
• Provide a summary: End the methodology section by summarizing the methods and techniques you used to conduct your research. This provides a clear overview of your research methodology and helps readers understand the process you followed to arrive at your findings.

When to Write Research Methodology

Research methodology is typically written after the research proposal has been approved and before the actual research is conducted. It should be written prior to data collection and analysis, as it provides a clear roadmap for the research project.

The research methodology is an important section of any research paper or thesis, as it describes the methods and procedures that will be used to conduct the research. It should include details about the research design, data collection methods, data analysis techniques, and any ethical considerations.

The methodology should be written in a clear and concise manner, and it should be based on established research practices and standards. It is important to provide enough detail so that the reader can understand how the research was conducted and evaluate the validity of the results.

Applications of Research Methodology

Here are some of the applications of research methodology:

• To identify the research problem: Research methodology is used to identify the research problem, which is the first step in conducting any research.
• To design the research: Research methodology helps in designing the research by selecting the appropriate research method, research design, and sampling technique.
• To collect data: Research methodology provides a systematic approach to collect data from primary and secondary sources.
• To analyze data: Research methodology helps in analyzing the collected data using various statistical and non-statistical techniques.
• To test hypotheses: Research methodology provides a framework for testing hypotheses and drawing conclusions based on the analysis of data.
• To generalize findings: Research methodology helps in generalizing the findings of the research to the target population.
• To develop theories : Research methodology is used to develop new theories and modify existing theories based on the findings of the research.
• To evaluate programs and policies : Research methodology is used to evaluate the effectiveness of programs and policies by collecting data and analyzing it.
• To improve decision-making: Research methodology helps in making informed decisions by providing reliable and valid data.

Purpose of Research Methodology

Research methodology serves several important purposes, including:

• To guide the research process: Research methodology provides a systematic framework for conducting research. It helps researchers to plan their research, define their research questions, and select appropriate methods and techniques for collecting and analyzing data.
• To ensure research quality: Research methodology helps researchers to ensure that their research is rigorous, reliable, and valid. It provides guidelines for minimizing bias and error in data collection and analysis, and for ensuring that research findings are accurate and trustworthy.
• To replicate research: Research methodology provides a clear and detailed account of the research process, making it possible for other researchers to replicate the study and verify its findings.
• To advance knowledge: Research methodology enables researchers to generate new knowledge and to contribute to the body of knowledge in their field. It provides a means for testing hypotheses, exploring new ideas, and discovering new insights.
• To inform decision-making: Research methodology provides evidence-based information that can inform policy and decision-making in a variety of fields, including medicine, public health, education, and business.

Advantages of Research Methodology

Research methodology has several advantages that make it a valuable tool for conducting research in various fields. Here are some of the key advantages of research methodology:

• Systematic and structured approach : Research methodology provides a systematic and structured approach to conducting research, which ensures that the research is conducted in a rigorous and comprehensive manner.
• Objectivity : Research methodology aims to ensure objectivity in the research process, which means that the research findings are based on evidence and not influenced by personal bias or subjective opinions.
• Replicability : Research methodology ensures that research can be replicated by other researchers, which is essential for validating research findings and ensuring their accuracy.
• Reliability : Research methodology aims to ensure that the research findings are reliable, which means that they are consistent and can be depended upon.
• Validity : Research methodology ensures that the research findings are valid, which means that they accurately reflect the research question or hypothesis being tested.
• Efficiency : Research methodology provides a structured and efficient way of conducting research, which helps to save time and resources.
• Flexibility : Research methodology allows researchers to choose the most appropriate research methods and techniques based on the research question, data availability, and other relevant factors.
• Scope for innovation: Research methodology provides scope for innovation and creativity in designing research studies and developing new research techniques.

Research Methodology Vs Research Methods

About the author.

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

How to Cite Research Paper – All Formats and...

Data Collection – Methods Types and Examples

Delimitations in Research – Types, Examples and...

Research Paper Format – Types, Examples and...

Research Process – Steps, Examples and Tips

Research Design – Types, Methods and Examples

• How it works

Meta-Analysis – Guide with Definition, Steps & Examples

Published by Owen Ingram at April 26th, 2023 , Revised On April 26, 2023

“A meta-analysis is a formal, epidemiological, quantitative study design that uses statistical methods to generalise the findings of the selected independent studies. “

Meta-analysis and systematic review are the two most authentic strategies in research. When researchers start looking for the best available evidence concerning their research work, they are advised to begin from the top of the evidence pyramid. The evidence available in the form of meta-analysis or systematic reviews addressing important questions is significant in academics because it informs decision-making.

What is Meta-Analysis  

Meta-analysis estimates the absolute effect of individual independent research studies by systematically synthesising or merging the results. Meta-analysis isn’t only about achieving a wider population by combining several smaller studies. It involves systematic methods to evaluate the inconsistencies in participants, variability (also known as heterogeneity), and findings to check how sensitive their findings are to the selected systematic review protocol.   

When Should you Conduct a Meta-Analysis?

Meta-analysis has become a widely-used research method in medical sciences and other fields of work for several reasons. The technique involves summarising the results of independent systematic review studies. 

The Cochrane Handbook explains that “an important step in a systematic review is the thoughtful consideration of whether it is appropriate to combine the numerical results of all, or perhaps some, of the studies. Such a meta-analysis yields an overall statistic (together with its confidence interval) that summarizes the effectiveness of an experimental intervention compared with a comparator intervention” (section 10.2).

A researcher or a practitioner should choose meta-analysis when the following outcomes are desirable. 

For generating new hypotheses or ending controversies resulting from different research studies. Quantifying and evaluating the variable results and identifying the extent of conflict in literature through meta-analysis is possible. 

To find research gaps left unfilled and address questions not posed by individual studies. Primary research studies involve specific types of participants and interventions. A review of these studies with variable characteristics and methodologies can allow the researcher to gauge the consistency of findings across a wider range of participants and interventions. With the help of meta-analysis, the reasons for differences in the effect can also be explored. 

To provide convincing evidence. Estimating the effects with a larger sample size and interventions can provide convincing evidence. Many academic studies are based on a very small dataset, so the estimated intervention effects in isolation are not fully reliable.

Elements of a Meta-Analysis

Deeks et al. (2019), Haidilch (2010), and Grant & Booth (2009) explored the characteristics, strengths, and weaknesses of conducting the meta-analysis. They are briefly explained below. 

Characteristics: 

• A systematic review must be completed before conducting the meta-analysis because it provides a summary of the findings of the individual studies synthesised. 
• You can only conduct a meta-analysis by synthesising studies in a systematic review. 
• The studies selected for statistical analysis for the purpose of meta-analysis should be similar in terms of comparison, intervention, and population. 

Strengths: 

• A meta-analysis takes place after the systematic review. The end product is a comprehensive quantitative analysis that is complicated but reliable. 
• It gives more value and weightage to existing studies that do not hold practical value on their own. 
• Policy-makers and academicians cannot base their decisions on individual research studies. Meta-analysis provides them with a complex and solid analysis of evidence to make informed decisions. 

Criticisms: 

• The meta-analysis uses studies exploring similar topics. Finding similar studies for the meta-analysis can be challenging.
• When and if biases in the individual studies or those related to reporting and specific research methodologies are involved, the meta-analysis results could be misleading.

Steps of Conducting the Meta-Analysis 

The process of conducting the meta-analysis has remained a topic of debate among researchers and scientists. However, the following 5-step process is widely accepted. 

Step 1: Research Question

The first step in conducting clinical research involves identifying a research question and proposing a hypothesis . The potential clinical significance of the research question is then explained, and the study design and analytical plan are justified.

Step 2: Systematic Review 

The purpose of a systematic review (SR) is to address a research question by identifying all relevant studies that meet the required quality standards for inclusion. While established journals typically serve as the primary source for identified studies, it is important to also consider unpublished data to avoid publication bias or the exclusion of studies with negative results.

While some meta-analyses may limit their focus to randomized controlled trials (RCTs) for the sake of obtaining the highest quality evidence, other experimental and quasi-experimental studies may be included if they meet the specific inclusion/exclusion criteria established for the review.

Step 3: Data Extraction

After selecting studies for the meta-analysis, researchers extract summary data or outcomes, as well as sample sizes and measures of data variability for both intervention and control groups. The choice of outcome measures depends on the research question and the type of study, and may include numerical or categorical measures.

For instance, numerical means may be used to report differences in scores on a questionnaire or changes in a measurement, such as blood pressure. In contrast, risk measures like odds ratios (OR) or relative risks (RR) are typically used to report differences in the probability of belonging to one category or another, such as vaginal birth versus cesarean birth.

Step 4: Standardisation and Weighting Studies

After gathering all the required data, the fourth step involves computing suitable summary measures from each study for further examination. These measures are typically referred to as Effect Sizes and indicate the difference in average scores between the control and intervention groups. For instance, it could be the variation in blood pressure changes between study participants who used drug X and those who used a placebo.

Since the units of measurement often differ across the included studies, standardization is necessary to create comparable effect size estimates. Standardization is accomplished by determining, for each study, the average score for the intervention group, subtracting the average score for the control group, and dividing the result by the relevant measure of variability in that dataset.

In some cases, the results of certain studies must carry more significance than others. Larger studies, as measured by their sample sizes, are deemed to produce more precise estimates of effect size than smaller studies. Additionally, studies with less variability in data, such as smaller standard deviation or narrower confidence intervals, are typically regarded as higher quality in study design. A weighting statistic that aims to incorporate both of these factors, known as inverse variance, is commonly employed.

Step 5: Absolute Effect Estimation

The ultimate step in conducting a meta-analysis is to choose and utilize an appropriate model for comparing Effect Sizes among diverse studies. Two popular models for this purpose are the Fixed Effects and Random Effects models. The Fixed Effects model relies on the premise that each study is evaluating a common treatment effect, implying that all studies would have estimated the same Effect Size if sample variability were equal across all studies.

Conversely, the Random Effects model posits that the true treatment effects in individual studies may vary from each other, and endeavors to consider this additional source of interstudy variation in Effect Sizes. The existence and magnitude of this latter variability is usually evaluated within the meta-analysis through a test for ‘heterogeneity.’

Forest Plot

The results of a meta-analysis are often visually presented using a “Forest Plot”. This type of plot displays, for each study, included in the analysis, a horizontal line that indicates the standardized Effect Size estimate and 95% confidence interval for the risk ratio used. Figure A provides an example of a hypothetical Forest Plot in which drug X reduces the risk of death in all three studies.

However, the first study was larger than the other two, and as a result, the estimates for the smaller studies were not statistically significant. This is indicated by the lines emanating from their boxes, including the value of 1. The size of the boxes represents the relative weights assigned to each study by the meta-analysis. The combined estimate of the drug’s effect, represented by the diamond, provides a more precise estimate of the drug’s effect, with the diamond indicating both the combined risk ratio estimate and the 95% confidence interval limits.

Figure-A: Hypothetical Forest Plot

Relevance to Practice and Research 

  Evidence Based Nursing commentaries often include recently published systematic reviews and meta-analyses, as they can provide new insights and strengthen recommendations for effective healthcare practices. Additionally, they can identify gaps or limitations in current evidence and guide future research directions.

The quality of the data available for synthesis is a critical factor in the strength of conclusions drawn from meta-analyses, and this is influenced by the quality of individual studies and the systematic review itself. However, meta-analysis cannot overcome issues related to underpowered or poorly designed studies.

Therefore, clinicians may still encounter situations where the evidence is weak or uncertain, and where higher-quality research is required to improve clinical decision-making. While such findings can be frustrating, they remain important for informing practice and highlighting the need for further research to fill gaps in the evidence base.

Methods and Assumptions in Meta-Analysis 

Ensuring the credibility of findings is imperative in all types of research, including meta-analyses. To validate the outcomes of a meta-analysis, the researcher must confirm that the research techniques used were accurate in measuring the intended variables. Typically, researchers establish the validity of a meta-analysis by testing the outcomes for homogeneity or the degree of similarity between the results of the combined studies.

Homogeneity is preferred in meta-analyses as it allows the data to be combined without needing adjustments to suit the study’s requirements. To determine homogeneity, researchers assess heterogeneity, the opposite of homogeneity. Two widely used statistical methods for evaluating heterogeneity in research results are Cochran’s-Q and I-Square, also known as I-2 Index.

Difference Between Meta-Analysis and Systematic Reviews

Meta-analysis and systematic reviews are both research methods used to synthesise evidence from multiple studies on a particular topic. However, there are some key differences between the two.

Systematic reviews involve a comprehensive and structured approach to identifying, selecting, and critically appraising all available evidence relevant to a specific research question. This process involves searching multiple databases, screening the identified studies for relevance and quality, and summarizing the findings in a narrative report.

Meta-analysis, on the other hand, involves using statistical methods to combine and analyze the data from multiple studies, with the aim of producing a quantitative summary of the overall effect size. Meta-analysis requires the studies to be similar enough in terms of their design, methodology, and outcome measures to allow for meaningful comparison and analysis.

Therefore, systematic reviews are broader in scope and summarize the findings of all studies on a topic, while meta-analyses are more focused on producing a quantitative estimate of the effect size of an intervention across multiple studies that meet certain criteria. In some cases, a systematic review may be conducted without a meta-analysis if the studies are too diverse or the quality of the data is not sufficient to allow for statistical pooling.

Software Packages For Meta-Analysis

Meta-analysis can be done through software packages, including free and paid options. One of the most commonly used software packages for meta-analysis is RevMan by the Cochrane Collaboration.

Assessing the Quality of Meta-Analysis 

Assessing the quality of a meta-analysis involves evaluating the methods used to conduct the analysis and the quality of the studies included. Here are some key factors to consider:

• Study selection: The studies included in the meta-analysis should be relevant to the research question and meet predetermined criteria for quality.
• Search strategy: The search strategy should be comprehensive and transparent, including databases and search terms used to identify relevant studies.
• Study quality assessment: The quality of included studies should be assessed using appropriate tools, and this assessment should be reported in the meta-analysis.
• Data extraction: The data extraction process should be systematic and clearly reported, including any discrepancies that arose.
• Analysis methods: The meta-analysis should use appropriate statistical methods to combine the results of the included studies, and these methods should be transparently reported.
• Publication bias: The potential for publication bias should be assessed and reported in the meta-analysis, including any efforts to identify and include unpublished studies.
• Interpretation of results: The results should be interpreted in the context of the study limitations and the overall quality of the evidence.
• Sensitivity analysis: Sensitivity analysis should be conducted to evaluate the impact of study quality, inclusion criteria, and other factors on the overall results.

Overall, a high-quality meta-analysis should be transparent in its methods and clearly report the included studies’ limitations and the evidence’s overall quality.

Hire an Expert Writer

Orders completed by our expert writers are

• Formally drafted in an academic style
• Free Amendments and 100% Plagiarism Free – or your money back!
• 100% Confidential and Timely Delivery!
• Free anti-plagiarism report
• Appreciated by thousands of clients. Check client reviews

Examples of Meta-Analysis

• STANLEY T.D. et JARRELL S.B. (1989), « Meta-regression analysis : a quantitative method of literature surveys », Journal of Economics Surveys, vol. 3, n°2, pp. 161-170.
• DATTA D.K., PINCHES G.E. et NARAYANAN V.K. (1992), « Factors influencing wealth creation from mergers and acquisitions : a meta-analysis », Strategic Management Journal, Vol. 13, pp. 67-84.
• GLASS G. (1983), « Synthesising empirical research : Meta-analysis » in S.A. Ward and L.J. Reed (Eds), Knowledge structure and use : Implications for synthesis and interpretation, Philadelphia : Temple University Press.
• WOLF F.M. (1986), Meta-analysis : Quantitative methods for research synthesis, Sage University Paper n°59.
• HUNTER J.E., SCHMIDT F.L. et JACKSON G.B. (1982), « Meta-analysis : cumulating research findings across studies », Beverly Hills, CA : Sage.

Frequently Asked Questions

What is a meta-analysis in research.

Meta-analysis is a statistical method used to combine results from multiple studies on a specific topic. By pooling data from various sources, meta-analysis can provide a more precise estimate of the effect size of a treatment or intervention and identify areas for future research.

Why is meta-analysis important?

Meta-analysis is important because it combines and summarizes results from multiple studies to provide a more precise and reliable estimate of the effect of a treatment or intervention. This helps clinicians and policymakers make evidence-based decisions and identify areas for further research.

What is an example of a meta-analysis?

A meta-analysis of studies evaluating physical exercise’s effect on depression in adults is an example. Researchers gathered data from 49 studies involving a total of 2669 participants. The studies used different types of exercise and measures of depression, which made it difficult to compare the results.

Through meta-analysis, the researchers calculated an overall effect size and determined that exercise was associated with a statistically significant reduction in depression symptoms. The study also identified that moderate-intensity aerobic exercise, performed three to five times per week, was the most effective. The meta-analysis provided a more comprehensive understanding of the impact of exercise on depression than any single study could provide.

What is the definition of meta-analysis in clinical research?

Meta-analysis in clinical research is a statistical technique that combines data from multiple independent studies on a particular topic to generate a summary or “meta” estimate of the effect of a particular intervention or exposure.

This type of analysis allows researchers to synthesise the results of multiple studies, potentially increasing the statistical power and providing more precise estimates of treatment effects. Meta-analyses are commonly used in clinical research to evaluate the effectiveness and safety of medical interventions and to inform clinical practice guidelines.

Is meta-analysis qualitative or quantitative?

Meta-analysis is a quantitative method used to combine and analyze data from multiple studies. It involves the statistical synthesis of results from individual studies to obtain a pooled estimate of the effect size of a particular intervention or treatment. Therefore, meta-analysis is considered a quantitative approach to research synthesis.

You May Also Like

Descriptive research is carried out to describe current issues, programs, and provides information about the issue through surveys and various fact-finding methods.

Struggling to figure out “whether I should choose primary research or secondary research in my dissertation?” Here are some tips to help you decide.

Discourse analysis is an essential aspect of studying a language. It is used in various disciplines of social science and humanities such as linguistic, sociolinguistics, and psycholinguistic.

USEFUL LINKS

LEARNING RESOURCES

COMPANY DETAILS

• How It Works

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• My Account Login
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 17 April 2024

The economic commitment of climate change

• Maximilian Kotz   ORCID: orcid.org/0000-0003-2564-5043 1 , 2 ,
• Anders Levermann   ORCID: orcid.org/0000-0003-4432-4704 1 , 2 &
• Leonie Wenz   ORCID: orcid.org/0000-0002-8500-1568 1 , 3  

Nature volume  628 ,  pages 551–557 ( 2024 ) Cite this article

57k Accesses

3393 Altmetric

Metrics details

• Environmental economics
• Environmental health
• Interdisciplinary studies
• Projection and prediction

Global projections of macroeconomic climate-change damages typically consider impacts from average annual and national temperatures over long time horizons 1 , 2 , 3 , 4 , 5 , 6 . Here we use recent empirical findings from more than 1,600 regions worldwide over the past 40 years to project sub-national damages from temperature and precipitation, including daily variability and extremes 7 , 8 . Using an empirical approach that provides a robust lower bound on the persistence of impacts on economic growth, we find that the world economy is committed to an income reduction of 19% within the next 26 years independent of future emission choices (relative to a baseline without climate impacts, likely range of 11–29% accounting for physical climate and empirical uncertainty). These damages already outweigh the mitigation costs required to limit global warming to 2 °C by sixfold over this near-term time frame and thereafter diverge strongly dependent on emission choices. Committed damages arise predominantly through changes in average temperature, but accounting for further climatic components raises estimates by approximately 50% and leads to stronger regional heterogeneity. Committed losses are projected for all regions except those at very high latitudes, at which reductions in temperature variability bring benefits. The largest losses are committed at lower latitudes in regions with lower cumulative historical emissions and lower present-day income.

Similar content being viewed by others

Climate damage projections beyond annual temperature

Paul Waidelich, Fulden Batibeniz, … Sonia I. Seneviratne

Investment incentive reduced by climate damages can be restored by optimal policy

Sven N. Willner, Nicole Glanemann & Anders Levermann

Climate economics support for the UN climate targets

Martin C. Hänsel, Moritz A. Drupp, … Thomas Sterner

Projections of the macroeconomic damage caused by future climate change are crucial to informing public and policy debates about adaptation, mitigation and climate justice. On the one hand, adaptation against climate impacts must be justified and planned on the basis of an understanding of their future magnitude and spatial distribution 9 . This is also of importance in the context of climate justice 10 , as well as to key societal actors, including governments, central banks and private businesses, which increasingly require the inclusion of climate risks in their macroeconomic forecasts to aid adaptive decision-making 11 , 12 . On the other hand, climate mitigation policy such as the Paris Climate Agreement is often evaluated by balancing the costs of its implementation against the benefits of avoiding projected physical damages. This evaluation occurs both formally through cost–benefit analyses 1 , 4 , 5 , 6 , as well as informally through public perception of mitigation and damage costs 13 .

Projections of future damages meet challenges when informing these debates, in particular the human biases relating to uncertainty and remoteness that are raised by long-term perspectives 14 . Here we aim to overcome such challenges by assessing the extent of economic damages from climate change to which the world is already committed by historical emissions and socio-economic inertia (the range of future emission scenarios that are considered socio-economically plausible 15 ). Such a focus on the near term limits the large uncertainties about diverging future emission trajectories, the resulting long-term climate response and the validity of applying historically observed climate–economic relations over long timescales during which socio-technical conditions may change considerably. As such, this focus aims to simplify the communication and maximize the credibility of projected economic damages from future climate change.

In projecting the future economic damages from climate change, we make use of recent advances in climate econometrics that provide evidence for impacts on sub-national economic growth from numerous components of the distribution of daily temperature and precipitation 3 , 7 , 8 . Using fixed-effects panel regression models to control for potential confounders, these studies exploit within-region variation in local temperature and precipitation in a panel of more than 1,600 regions worldwide, comprising climate and income data over the past 40 years, to identify the plausibly causal effects of changes in several climate variables on economic productivity 16 , 17 . Specifically, macroeconomic impacts have been identified from changing daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall that occur in addition to those already identified from changing average temperature 2 , 3 , 18 . Moreover, regional heterogeneity in these effects based on the prevailing local climatic conditions has been found using interactions terms. The selection of these climate variables follows micro-level evidence for mechanisms related to the impacts of average temperatures on labour and agricultural productivity 2 , of temperature variability on agricultural productivity and health 7 , as well as of precipitation on agricultural productivity, labour outcomes and flood damages 8 (see Extended Data Table 1 for an overview, including more detailed references). References  7 , 8 contain a more detailed motivation for the use of these particular climate variables and provide extensive empirical tests about the robustness and nature of their effects on economic output, which are summarized in Methods . By accounting for these extra climatic variables at the sub-national level, we aim for a more comprehensive description of climate impacts with greater detail across both time and space.

Constraining the persistence of impacts

A key determinant and source of discrepancy in estimates of the magnitude of future climate damages is the extent to which the impact of a climate variable on economic growth rates persists. The two extreme cases in which these impacts persist indefinitely or only instantaneously are commonly referred to as growth or level effects 19 , 20 (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for mathematical definitions). Recent work shows that future damages from climate change depend strongly on whether growth or level effects are assumed 20 . Following refs.  2 , 18 , we provide constraints on this persistence by using distributed lag models to test the significance of delayed effects separately for each climate variable. Notably, and in contrast to refs.  2 , 18 , we use climate variables in their first-differenced form following ref.  3 , implying a dependence of the growth rate on a change in climate variables. This choice means that a baseline specification without any lags constitutes a model prior of purely level effects, in which a permanent change in the climate has only an instantaneous effect on the growth rate 3 , 19 , 21 . By including lags, one can then test whether any effects may persist further. This is in contrast to the specification used by refs.  2 , 18 , in which climate variables are used without taking the first difference, implying a dependence of the growth rate on the level of climate variables. In this alternative case, the baseline specification without any lags constitutes a model prior of pure growth effects, in which a change in climate has an infinitely persistent effect on the growth rate. Consequently, including further lags in this alternative case tests whether the initial growth impact is recovered 18 , 19 , 21 . Both of these specifications suffer from the limiting possibility that, if too few lags are included, one might falsely accept the model prior. The limitations of including a very large number of lags, including loss of data and increasing statistical uncertainty with an increasing number of parameters, mean that such a possibility is likely. By choosing a specification in which the model prior is one of level effects, our approach is therefore conservative by design, avoiding assumptions of infinite persistence of climate impacts on growth and instead providing a lower bound on this persistence based on what is observable empirically (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for further exposition of this framework). The conservative nature of such a choice is probably the reason that ref.  19 finds much greater consistency between the impacts projected by models that use the first difference of climate variables, as opposed to their levels.

We begin our empirical analysis of the persistence of climate impacts on growth using ten lags of the first-differenced climate variables in fixed-effects distributed lag models. We detect substantial effects on economic growth at time lags of up to approximately 8–10 years for the temperature terms and up to approximately 4 years for the precipitation terms (Extended Data Fig. 1 and Extended Data Table 2 ). Furthermore, evaluation by means of information criteria indicates that the inclusion of all five climate variables and the use of these numbers of lags provide a preferable trade-off between best-fitting the data and including further terms that could cause overfitting, in comparison with model specifications excluding climate variables or including more or fewer lags (Extended Data Fig. 3 , Supplementary Methods Section  1 and Supplementary Table 1 ). We therefore remove statistically insignificant terms at later lags (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). Further tests using Monte Carlo simulations demonstrate that the empirical models are robust to autocorrelation in the lagged climate variables (Supplementary Methods Section  2 and Supplementary Figs. 4 and 5 ), that information criteria provide an effective indicator for lag selection (Supplementary Methods Section  2 and Supplementary Fig. 6 ), that the results are robust to concerns of imperfect multicollinearity between climate variables and that including several climate variables is actually necessary to isolate their separate effects (Supplementary Methods Section  3 and Supplementary Fig. 7 ). We provide a further robustness check using a restricted distributed lag model to limit oscillations in the lagged parameter estimates that may result from autocorrelation, finding that it provides similar estimates of cumulative marginal effects to the unrestricted model (Supplementary Methods Section 4 and Supplementary Figs. 8 and 9 ). Finally, to explicitly account for any outstanding uncertainty arising from the precise choice of the number of lags, we include empirical models with marginally different numbers of lags in the error-sampling procedure of our projection of future damages. On the basis of the lag-selection procedure (the significance of lagged terms in Extended Data Fig. 1 and Extended Data Table 2 , as well as information criteria in Extended Data Fig. 3 ), we sample from models with eight to ten lags for temperature and four for precipitation (models shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). In summary, this empirical approach to constrain the persistence of climate impacts on economic growth rates is conservative by design in avoiding assumptions of infinite persistence, but nevertheless provides a lower bound on the extent of impact persistence that is robust to the numerous tests outlined above.

Committed damages until mid-century

We combine these empirical economic response functions (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) with an ensemble of 21 climate models (see Supplementary Table 5 ) from the Coupled Model Intercomparison Project Phase 6 (CMIP-6) 22 to project the macroeconomic damages from these components of physical climate change (see Methods for further details). Bias-adjusted climate models that provide a highly accurate reproduction of observed climatological patterns with limited uncertainty (Supplementary Table 6 ) are used to avoid introducing biases in the projections. Following a well-developed literature 2 , 3 , 19 , these projections do not aim to provide a prediction of future economic growth. Instead, they are a projection of the exogenous impact of future climate conditions on the economy relative to the baselines specified by socio-economic projections, based on the plausibly causal relationships inferred by the empirical models and assuming ceteris paribus. Other exogenous factors relevant for the prediction of economic output are purposefully assumed constant.

A Monte Carlo procedure that samples from climate model projections, empirical models with different numbers of lags and model parameter estimates (obtained by 1,000 block-bootstrap resamples of each of the regressions in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) is used to estimate the combined uncertainty from these sources. Given these uncertainty distributions, we find that projected global damages are statistically indistinguishable across the two most extreme emission scenarios until 2049 (at the 5% significance level; Fig. 1 ). As such, the climate damages occurring before this time constitute those to which the world is already committed owing to the combination of past emissions and the range of future emission scenarios that are considered socio-economically plausible 15 . These committed damages comprise a permanent income reduction of 19% on average globally (population-weighted average) in comparison with a baseline without climate-change impacts (with a likely range of 11–29%, following the likelihood classification adopted by the Intergovernmental Panel on Climate Change (IPCC); see caption of Fig. 1 ). Even though levels of income per capita generally still increase relative to those of today, this constitutes a permanent income reduction for most regions, including North America and Europe (each with median income reductions of approximately 11%) and with South Asia and Africa being the most strongly affected (each with median income reductions of approximately 22%; Fig. 1 ). Under a middle-of-the road scenario of future income development (SSP2, in which SSP stands for Shared Socio-economic Pathway), this corresponds to global annual damages in 2049 of 38 trillion in 2005 international dollars (likely range of 19–59 trillion 2005 international dollars). Compared with empirical specifications that assume pure growth or pure level effects, our preferred specification that provides a robust lower bound on the extent of climate impact persistence produces damages between these two extreme assumptions (Extended Data Fig. 3 ).

Estimates of the projected reduction in income per capita from changes in all climate variables based on empirical models of climate impacts on economic output with a robust lower bound on their persistence (Extended Data Fig. 1 ) under a low-emission scenario compatible with the 2 °C warming target and a high-emission scenario (SSP2-RCP2.6 and SSP5-RCP8.5, respectively) are shown in purple and orange, respectively. Shading represents the 34% and 10% confidence intervals reflecting the likely and very likely ranges, respectively (following the likelihood classification adopted by the IPCC), having estimated uncertainty from a Monte Carlo procedure, which samples the uncertainty from the choice of physical climate models, empirical models with different numbers of lags and bootstrapped estimates of the regression parameters shown in Supplementary Figs. 1 – 3 . Vertical dashed lines show the time at which the climate damages of the two emission scenarios diverge at the 5% and 1% significance levels based on the distribution of differences between emission scenarios arising from the uncertainty sampling discussed above. Note that uncertainty in the difference of the two scenarios is smaller than the combined uncertainty of the two respective scenarios because samples of the uncertainty (climate model and empirical model choice, as well as model parameter bootstrap) are consistent across the two emission scenarios, hence the divergence of damages occurs while the uncertainty bounds of the two separate damage scenarios still overlap. Estimates of global mitigation costs from the three IAMs that provide results for the SSP2 baseline and SSP2-RCP2.6 scenario are shown in light green in the top panel, with the median of these estimates shown in bold.

Damages already outweigh mitigation costs

We compare the damages to which the world is committed over the next 25 years to estimates of the mitigation costs required to achieve the Paris Climate Agreement. Taking estimates of mitigation costs from the three integrated assessment models (IAMs) in the IPCC AR6 database 23 that provide results under comparable scenarios (SSP2 baseline and SSP2-RCP2.6, in which RCP stands for Representative Concentration Pathway), we find that the median committed climate damages are larger than the median mitigation costs in 2050 (six trillion in 2005 international dollars) by a factor of approximately six (note that estimates of mitigation costs are only provided every 10 years by the IAMs and so a comparison in 2049 is not possible). This comparison simply aims to compare the magnitude of future damages against mitigation costs, rather than to conduct a formal cost–benefit analysis of transitioning from one emission path to another. Formal cost–benefit analyses typically find that the net benefits of mitigation only emerge after 2050 (ref.  5 ), which may lead some to conclude that physical damages from climate change are simply not large enough to outweigh mitigation costs until the second half of the century. Our simple comparison of their magnitudes makes clear that damages are actually already considerably larger than mitigation costs and the delayed emergence of net mitigation benefits results primarily from the fact that damages across different emission paths are indistinguishable until mid-century (Fig. 1 ).

Although these near-term damages constitute those to which the world is already committed, we note that damage estimates diverge strongly across emission scenarios after 2049, conveying the clear benefits of mitigation from a purely economic point of view that have been emphasized in previous studies 4 , 24 . As well as the uncertainties assessed in Fig. 1 , these conclusions are robust to structural choices, such as the timescale with which changes in the moderating variables of the empirical models are estimated (Supplementary Figs. 10 and 11 ), as well as the order in which one accounts for the intertemporal and international components of currency comparison (Supplementary Fig. 12 ; see Methods for further details).

Damages from variability and extremes

Committed damages primarily arise through changes in average temperature (Fig. 2 ). This reflects the fact that projected changes in average temperature are larger than those in other climate variables when expressed as a function of their historical interannual variability (Extended Data Fig. 4 ). Because the historical variability is that on which the empirical models are estimated, larger projected changes in comparison with this variability probably lead to larger future impacts in a purely statistical sense. From a mechanistic perspective, one may plausibly interpret this result as implying that future changes in average temperature are the most unprecedented from the perspective of the historical fluctuations to which the economy is accustomed and therefore will cause the most damage. This insight may prove useful in terms of guiding adaptation measures to the sources of greatest damage.

Estimates of the median projected reduction in sub-national income per capita across emission scenarios (SSP2-RCP2.6 and SSP2-RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ). a , Impacts arising from all climate variables. b – f , Impacts arising separately from changes in annual mean temperature ( b ), daily temperature variability ( c ), total annual precipitation ( d ), the annual number of wet days (>1 mm) ( e ) and extreme daily rainfall ( f ) (see Methods for further definitions). Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Nevertheless, future damages based on empirical models that consider changes in annual average temperature only and exclude the other climate variables constitute income reductions of only 13% in 2049 (Extended Data Fig. 5a , likely range 5–21%). This suggests that accounting for the other components of the distribution of temperature and precipitation raises net damages by nearly 50%. This increase arises through the further damages that these climatic components cause, but also because their inclusion reveals a stronger negative economic response to average temperatures (Extended Data Fig. 5b ). The latter finding is consistent with our Monte Carlo simulations, which suggest that the magnitude of the effect of average temperature on economic growth is underestimated unless accounting for the impacts of other correlated climate variables (Supplementary Fig. 7 ).

In terms of the relative contributions of the different climatic components to overall damages, we find that accounting for daily temperature variability causes the largest increase in overall damages relative to empirical frameworks that only consider changes in annual average temperature (4.9 percentage points, likely range 2.4–8.7 percentage points, equivalent to approximately 10 trillion international dollars). Accounting for precipitation causes smaller increases in overall damages, which are—nevertheless—equivalent to approximately 1.2 trillion international dollars: 0.01 percentage points (−0.37–0.33 percentage points), 0.34 percentage points (0.07–0.90 percentage points) and 0.36 percentage points (0.13–0.65 percentage points) from total annual precipitation, the number of wet days and extreme daily precipitation, respectively. Moreover, climate models seem to underestimate future changes in temperature variability 25 and extreme precipitation 26 , 27 in response to anthropogenic forcing as compared with that observed historically, suggesting that the true impacts from these variables may be larger.

The distribution of committed damages

The spatial distribution of committed damages (Fig. 2a ) reflects a complex interplay between the patterns of future change in several climatic components and those of historical economic vulnerability to changes in those variables. Damages resulting from increasing annual mean temperature (Fig. 2b ) are negative almost everywhere globally, and larger at lower latitudes in regions in which temperatures are already higher and economic vulnerability to temperature increases is greatest (see the response heterogeneity to mean temperature embodied in Extended Data Fig. 1a ). This occurs despite the amplified warming projected at higher latitudes 28 , suggesting that regional heterogeneity in economic vulnerability to temperature changes outweighs heterogeneity in the magnitude of future warming (Supplementary Fig. 13a ). Economic damages owing to daily temperature variability (Fig. 2c ) exhibit a strong latitudinal polarisation, primarily reflecting the physical response of daily variability to greenhouse forcing in which increases in variability across lower latitudes (and Europe) contrast decreases at high latitudes 25 (Supplementary Fig. 13b ). These two temperature terms are the dominant determinants of the pattern of overall damages (Fig. 2a ), which exhibits a strong polarity with damages across most of the globe except at the highest northern latitudes. Future changes in total annual precipitation mainly bring economic benefits except in regions of drying, such as the Mediterranean and central South America (Fig. 2d and Supplementary Fig. 13c ), but these benefits are opposed by changes in the number of wet days, which produce damages with a similar pattern of opposite sign (Fig. 2e and Supplementary Fig. 13d ). By contrast, changes in extreme daily rainfall produce damages in all regions, reflecting the intensification of daily rainfall extremes over global land areas 29 , 30 (Fig. 2f and Supplementary Fig. 13e ).

The spatial distribution of committed damages implies considerable injustice along two dimensions: culpability for the historical emissions that have caused climate change and pre-existing levels of socio-economic welfare. Spearman’s rank correlations indicate that committed damages are significantly larger in countries with smaller historical cumulative emissions, as well as in regions with lower current income per capita (Fig. 3 ). This implies that those countries that will suffer the most from the damages already committed are those that are least responsible for climate change and which also have the least resources to adapt to it.

Estimates of the median projected change in national income per capita across emission scenarios (RCP2.6 and RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ) are plotted against cumulative national emissions per capita in 2020 (from the Global Carbon Project) and coloured by national income per capita in 2020 (from the World Bank) in a and vice versa in b . In each panel, the size of each scatter point is weighted by the national population in 2020 (from the World Bank). Inset numbers indicate the Spearman’s rank correlation ρ and P -values for a hypothesis test whose null hypothesis is of no correlation, as well as the Spearman’s rank correlation weighted by national population.

To further quantify this heterogeneity, we assess the difference in committed damages between the upper and lower quartiles of regions when ranked by present income levels and historical cumulative emissions (using a population weighting to both define the quartiles and estimate the group averages). On average, the quartile of countries with lower income are committed to an income loss that is 8.9 percentage points (or 61%) greater than the upper quartile (Extended Data Fig. 6 ), with a likely range of 3.8–14.7 percentage points across the uncertainty sampling of our damage projections (following the likelihood classification adopted by the IPCC). Similarly, the quartile of countries with lower historical cumulative emissions are committed to an income loss that is 6.9 percentage points (or 40%) greater than the upper quartile, with a likely range of 0.27–12 percentage points. These patterns reemphasize the prevalence of injustice in climate impacts 31 , 32 , 33 in the context of the damages to which the world is already committed by historical emissions and socio-economic inertia.

Contextualizing the magnitude of damages

The magnitude of projected economic damages exceeds previous literature estimates 2 , 3 , arising from several developments made on previous approaches. Our estimates are larger than those of ref.  2 (see first row of Extended Data Table 3 ), primarily because of the facts that sub-national estimates typically show a steeper temperature response (see also refs.  3 , 34 ) and that accounting for other climatic components raises damage estimates (Extended Data Fig. 5 ). However, we note that our empirical approach using first-differenced climate variables is conservative compared with that of ref.  2 in regard to the persistence of climate impacts on growth (see introduction and Methods section ‘Empirical model specification: fixed-effects distributed lag models’), an important determinant of the magnitude of long-term damages 19 , 21 . Using a similar empirical specification to ref.  2 , which assumes infinite persistence while maintaining the rest of our approach (sub-national data and further climate variables), produces considerably larger damages (purple curve of Extended Data Fig. 3 ). Compared with studies that do take the first difference of climate variables 3 , 35 , our estimates are also larger (see second and third rows of Extended Data Table 3 ). The inclusion of further climate variables (Extended Data Fig. 5 ) and a sufficient number of lags to more adequately capture the extent of impact persistence (Extended Data Figs. 1 and 2 ) are the main sources of this difference, as is the use of specifications that capture nonlinearities in the temperature response when compared with ref.  35 . In summary, our estimates develop on previous studies by incorporating the latest data and empirical insights 7 , 8 , as well as in providing a robust empirical lower bound on the persistence of impacts on economic growth, which constitutes a middle ground between the extremes of the growth-versus-levels debate 19 , 21 (Extended Data Fig. 3 ).

Compared with the fraction of variance explained by the empirical models historically (<5%), the projection of reductions in income of 19% may seem large. This arises owing to the fact that projected changes in climatic conditions are much larger than those that were experienced historically, particularly for changes in average temperature (Extended Data Fig. 4 ). As such, any assessment of future climate-change impacts necessarily requires an extrapolation outside the range of the historical data on which the empirical impact models were evaluated. Nevertheless, these models constitute the most state-of-the-art methods for inference of plausibly causal climate impacts based on observed data. Moreover, we take explicit steps to limit out-of-sample extrapolation by capping the moderating variables of the interaction terms at the 95th percentile of the historical distribution (see Methods ). This avoids extrapolating the marginal effects outside what was observed historically. Given the nonlinear response of economic output to annual mean temperature (Extended Data Fig. 1 and Extended Data Table 2 ), this is a conservative choice that limits the magnitude of damages that we project. Furthermore, back-of-the-envelope calculations indicate that the projected damages are consistent with the magnitude and patterns of historical economic development (see Supplementary Discussion Section  5 ).

Missing impacts and spatial spillovers

Despite assessing several climatic components from which economic impacts have recently been identified 3 , 7 , 8 , this assessment of aggregate climate damages should not be considered comprehensive. Important channels such as impacts from heatwaves 31 , sea-level rise 36 , tropical cyclones 37 and tipping points 38 , 39 , as well as non-market damages such as those to ecosystems 40 and human health 41 , are not considered in these estimates. Sea-level rise is unlikely to be feasibly incorporated into empirical assessments such as this because historical sea-level variability is mostly small. Non-market damages are inherently intractable within our estimates of impacts on aggregate monetary output and estimates of these impacts could arguably be considered as extra to those identified here. Recent empirical work suggests that accounting for these channels would probably raise estimates of these committed damages, with larger damages continuing to arise in the global south 31 , 36 , 37 , 38 , 39 , 40 , 41 , 42 .

Moreover, our main empirical analysis does not explicitly evaluate the potential for impacts in local regions to produce effects that ‘spill over’ into other regions. Such effects may further mitigate or amplify the impacts we estimate, for example, if companies relocate production from one affected region to another or if impacts propagate along supply chains. The current literature indicates that trade plays a substantial role in propagating spillover effects 43 , 44 , making their assessment at the sub-national level challenging without available data on sub-national trade dependencies. Studies accounting for only spatially adjacent neighbours indicate that negative impacts in one region induce further negative impacts in neighbouring regions 45 , 46 , 47 , 48 , suggesting that our projected damages are probably conservative by excluding these effects. In Supplementary Fig. 14 , we assess spillovers from neighbouring regions using a spatial-lag model. For simplicity, this analysis excludes temporal lags, focusing only on contemporaneous effects. The results show that accounting for spatial spillovers can amplify the overall magnitude, and also the heterogeneity, of impacts. Consistent with previous literature, this indicates that the overall magnitude (Fig. 1 ) and heterogeneity (Fig. 3 ) of damages that we project in our main specification may be conservative without explicitly accounting for spillovers. We note that further analysis that addresses both spatially and trade-connected spillovers, while also accounting for delayed impacts using temporal lags, would be necessary to adequately address this question fully. These approaches offer fruitful avenues for further research but are beyond the scope of this manuscript, which primarily aims to explore the impacts of different climate conditions and their persistence.

Policy implications

We find that the economic damages resulting from climate change until 2049 are those to which the world economy is already committed and that these greatly outweigh the costs required to mitigate emissions in line with the 2 °C target of the Paris Climate Agreement (Fig. 1 ). This assessment is complementary to formal analyses of the net costs and benefits associated with moving from one emission path to another, which typically find that net benefits of mitigation only emerge in the second half of the century 5 . Our simple comparison of the magnitude of damages and mitigation costs makes clear that this is primarily because damages are indistinguishable across emissions scenarios—that is, committed—until mid-century (Fig. 1 ) and that they are actually already much larger than mitigation costs. For simplicity, and owing to the availability of data, we compare damages to mitigation costs at the global level. Regional estimates of mitigation costs may shed further light on the national incentives for mitigation to which our results already hint, of relevance for international climate policy. Although these damages are committed from a mitigation perspective, adaptation may provide an opportunity to reduce them. Moreover, the strong divergence of damages after mid-century reemphasizes the clear benefits of mitigation from a purely economic perspective, as highlighted in previous studies 1 , 4 , 6 , 24 .

Historical climate data

Historical daily 2-m temperature and precipitation totals (in mm) are obtained for the period 1979–2019 from the W5E5 database. The W5E5 dataset comes from ERA-5, a state-of-the-art reanalysis of historical observations, but has been bias-adjusted by applying version 2.0 of the WATCH Forcing Data to ERA-5 reanalysis data and precipitation data from version 2.3 of the Global Precipitation Climatology Project to better reflect ground-based measurements 49 , 50 , 51 . We obtain these data on a 0.5° × 0.5° grid from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) database. Notably, these historical data have been used to bias-adjust future climate projections from CMIP-6 (see the following section), ensuring consistency between the distribution of historical daily weather on which our empirical models were estimated and the climate projections used to estimate future damages. These data are publicly available from the ISIMIP database. See refs.  7 , 8 for robustness tests of the empirical models to the choice of climate data reanalysis products.

Future climate data

Daily 2-m temperature and precipitation totals (in mm) are taken from 21 climate models participating in CMIP-6 under a high (RCP8.5) and a low (RCP2.6) greenhouse gas emission scenario from 2015 to 2100. The data have been bias-adjusted and statistically downscaled to a common half-degree grid to reflect the historical distribution of daily temperature and precipitation of the W5E5 dataset using the trend-preserving method developed by the ISIMIP 50 , 52 . As such, the climate model data reproduce observed climatological patterns exceptionally well (Supplementary Table 5 ). Gridded data are publicly available from the ISIMIP database.

Historical economic data

Historical economic data come from the DOSE database of sub-national economic output 53 . We use a recent revision to the DOSE dataset that provides data across 83 countries, 1,660 sub-national regions with varying temporal coverage from 1960 to 2019. Sub-national units constitute the first administrative division below national, for example, states for the USA and provinces for China. Data come from measures of gross regional product per capita (GRPpc) or income per capita in local currencies, reflecting the values reported in national statistical agencies, yearbooks and, in some cases, academic literature. We follow previous literature 3 , 7 , 8 , 54 and assess real sub-national output per capita by first converting values from local currencies to US dollars to account for diverging national inflationary tendencies and then account for US inflation using a US deflator. Alternatively, one might first account for national inflation and then convert between currencies. Supplementary Fig. 12 demonstrates that our conclusions are consistent when accounting for price changes in the reversed order, although the magnitude of estimated damages varies. See the documentation of the DOSE dataset for further discussion of these choices. Conversions between currencies are conducted using exchange rates from the FRED database of the Federal Reserve Bank of St. Louis 55 and the national deflators from the World Bank 56 .

Future socio-economic data

Baseline gridded gross domestic product (GDP) and population data for the period 2015–2100 are taken from the middle-of-the-road scenario SSP2 (ref.  15 ). Population data have been downscaled to a half-degree grid by the ISIMIP following the methodologies of refs.  57 , 58 , which we then aggregate to the sub-national level of our economic data using the spatial aggregation procedure described below. Because current methodologies for downscaling the GDP of the SSPs use downscaled population to do so, per-capita estimates of GDP with a realistic distribution at the sub-national level are not readily available for the SSPs. We therefore use national-level GDP per capita (GDPpc) projections for all sub-national regions of a given country, assuming homogeneity within countries in terms of baseline GDPpc. Here we use projections that have been updated to account for the impact of the COVID-19 pandemic on the trajectory of future income, while remaining consistent with the long-term development of the SSPs 59 . The choice of baseline SSP alters the magnitude of projected climate damages in monetary terms, but when assessed in terms of percentage change from the baseline, the choice of socio-economic scenario is inconsequential. Gridded SSP population data and national-level GDPpc data are publicly available from the ISIMIP database. Sub-national estimates as used in this study are available in the code and data replication files.

Climate variables

Following recent literature 3 , 7 , 8 , we calculate an array of climate variables for which substantial impacts on macroeconomic output have been identified empirically, supported by further evidence at the micro level for plausible underlying mechanisms. See refs.  7 , 8 for an extensive motivation for the use of these particular climate variables and for detailed empirical tests on the nature and robustness of their effects on economic output. To summarize, these studies have found evidence for independent impacts on economic growth rates from annual average temperature, daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall. Assessments of daily temperature variability were motivated by evidence of impacts on agricultural output and human health, as well as macroeconomic literature on the impacts of volatility on growth when manifest in different dimensions, such as government spending, exchange rates and even output itself 7 . Assessments of precipitation impacts were motivated by evidence of impacts on agricultural productivity, metropolitan labour outcomes and conflict, as well as damages caused by flash flooding 8 . See Extended Data Table 1 for detailed references to empirical studies of these physical mechanisms. Marked impacts of daily temperature variability, total annual precipitation, the number of wet days and extreme daily rainfall on macroeconomic output were identified robustly across different climate datasets, spatial aggregation schemes, specifications of regional time trends and error-clustering approaches. They were also found to be robust to the consideration of temperature extremes 7 , 8 . Furthermore, these climate variables were identified as having independent effects on economic output 7 , 8 , which we further explain here using Monte Carlo simulations to demonstrate the robustness of the results to concerns of imperfect multicollinearity between climate variables (Supplementary Methods Section  2 ), as well as by using information criteria (Supplementary Table 1 ) to demonstrate that including several lagged climate variables provides a preferable trade-off between optimally describing the data and limiting the possibility of overfitting.

We calculate these variables from the distribution of daily, d , temperature, T x , d , and precipitation, P x , d , at the grid-cell, x , level for both the historical and future climate data. As well as annual mean temperature, \({\bar{T}}_{x,y}\) , and annual total precipitation, P x , y , we calculate annual, y , measures of daily temperature variability, \({\widetilde{T}}_{x,y}\) :

the number of wet days, Pwd x , y :

and extreme daily rainfall:

in which T x , d , m , y is the grid-cell-specific daily temperature in month m and year y , \({\bar{T}}_{x,m,{y}}\) is the year and grid-cell-specific monthly, m , mean temperature, D m and D y the number of days in a given month m or year y , respectively, H the Heaviside step function, 1 mm the threshold used to define wet days and P 99.9 x is the 99.9th percentile of historical (1979–2019) daily precipitation at the grid-cell level. Units of the climate measures are degrees Celsius for annual mean temperature and daily temperature variability, millimetres for total annual precipitation and extreme daily precipitation, and simply the number of days for the annual number of wet days.

We also calculated weighted standard deviations of monthly rainfall totals as also used in ref.  8 but do not include them in our projections as we find that, when accounting for delayed effects, their effect becomes statistically indistinct and is better captured by changes in total annual rainfall.

Spatial aggregation

We aggregate grid-cell-level historical and future climate measures, as well as grid-cell-level future GDPpc and population, to the level of the first administrative unit below national level of the GADM database, using an area-weighting algorithm that estimates the portion of each grid cell falling within an administrative boundary. We use this as our baseline specification following previous findings that the effect of area or population weighting at the sub-national level is negligible 7 , 8 .

Empirical model specification: fixed-effects distributed lag models

Following a wide range of climate econometric literature 16 , 60 , we use panel regression models with a selection of fixed effects and time trends to isolate plausibly exogenous variation with which to maximize confidence in a causal interpretation of the effects of climate on economic growth rates. The use of region fixed effects, μ r , accounts for unobserved time-invariant differences between regions, such as prevailing climatic norms and growth rates owing to historical and geopolitical factors. The use of yearly fixed effects, η y , accounts for regionally invariant annual shocks to the global climate or economy such as the El Niño–Southern Oscillation or global recessions. In our baseline specification, we also include region-specific linear time trends, k r y , to exclude the possibility of spurious correlations resulting from common slow-moving trends in climate and growth.

The persistence of climate impacts on economic growth rates is a key determinant of the long-term magnitude of damages. Methods for inferring the extent of persistence in impacts on growth rates have typically used lagged climate variables to evaluate the presence of delayed effects or catch-up dynamics 2 , 18 . For example, consider starting from a model in which a climate condition, C r , y , (for example, annual mean temperature) affects the growth rate, Δlgrp r , y (the first difference of the logarithm of gross regional product) of region r in year y :

which we refer to as a ‘pure growth effects’ model in the main text. Typically, further lags are included,

and the cumulative effect of all lagged terms is evaluated to assess the extent to which climate impacts on growth rates persist. Following ref.  18 , in the case that,

the implication is that impacts on the growth rate persist up to NL years after the initial shock (possibly to a weaker or a stronger extent), whereas if

then the initial impact on the growth rate is recovered after NL years and the effect is only one on the level of output. However, we note that such approaches are limited by the fact that, when including an insufficient number of lags to detect a recovery of the growth rates, one may find equation ( 6 ) to be satisfied and incorrectly assume that a change in climatic conditions affects the growth rate indefinitely. In practice, given a limited record of historical data, including too few lags to confidently conclude in an infinitely persistent impact on the growth rate is likely, particularly over the long timescales over which future climate damages are often projected 2 , 24 . To avoid this issue, we instead begin our analysis with a model for which the level of output, lgrp r , y , depends on the level of a climate variable, C r , y :

Given the non-stationarity of the level of output, we follow the literature 19 and estimate such an equation in first-differenced form as,

which we refer to as a model of ‘pure level effects’ in the main text. This model constitutes a baseline specification in which a permanent change in the climate variable produces an instantaneous impact on the growth rate and a permanent effect only on the level of output. By including lagged variables in this specification,

we are able to test whether the impacts on the growth rate persist any further than instantaneously by evaluating whether α L  > 0 are statistically significantly different from zero. Even though this framework is also limited by the possibility of including too few lags, the choice of a baseline model specification in which impacts on the growth rate do not persist means that, in the case of including too few lags, the framework reverts to the baseline specification of level effects. As such, this framework is conservative with respect to the persistence of impacts and the magnitude of future damages. It naturally avoids assumptions of infinite persistence and we are able to interpret any persistence that we identify with equation ( 9 ) as a lower bound on the extent of climate impact persistence on growth rates. See the main text for further discussion of this specification choice, in particular about its conservative nature compared with previous literature estimates, such as refs.  2 , 18 .

We allow the response to climatic changes to vary across regions, using interactions of the climate variables with historical average (1979–2019) climatic conditions reflecting heterogenous effects identified in previous work 7 , 8 . Following this previous work, the moderating variables of these interaction terms constitute the historical average of either the variable itself or of the seasonal temperature difference, \({\hat{T}}_{r}\) , or annual mean temperature, \({\bar{T}}_{r}\) , in the case of daily temperature variability 7 and extreme daily rainfall, respectively 8 .

The resulting regression equation with N and M lagged variables, respectively, reads:

in which Δlgrp r , y is the annual, regional GRPpc growth rate, measured as the first difference of the logarithm of real GRPpc, following previous work 2 , 3 , 7 , 8 , 18 , 19 . Fixed-effects regressions were run using the fixest package in R (ref.  61 ).

Estimates of the coefficients of interest α i , L are shown in Extended Data Fig. 1 for N  =  M  = 10 lags and for our preferred choice of the number of lags in Supplementary Figs. 1 – 3 . In Extended Data Fig. 1 , errors are shown clustered at the regional level, but for the construction of damage projections, we block-bootstrap the regressions by region 1,000 times to provide a range of parameter estimates with which to sample the projection uncertainty (following refs.  2 , 31 ).

Spatial-lag model

In Supplementary Fig. 14 , we present the results from a spatial-lag model that explores the potential for climate impacts to ‘spill over’ into spatially neighbouring regions. We measure the distance between centroids of each pair of sub-national regions and construct spatial lags that take the average of the first-differenced climate variables and their interaction terms over neighbouring regions that are at distances of 0–500, 500–1,000, 1,000–1,500 and 1,500–2000 km (spatial lags, ‘SL’, 1 to 4). For simplicity, we then assess a spatial-lag model without temporal lags to assess spatial spillovers of contemporaneous climate impacts. This model takes the form:

in which SL indicates the spatial lag of each climate variable and interaction term. In Supplementary Fig. 14 , we plot the cumulative marginal effect of each climate variable at different baseline climate conditions by summing the coefficients for each climate variable and interaction term, for example, for average temperature impacts as:

These cumulative marginal effects can be regarded as the overall spatially dependent impact to an individual region given a one-unit shock to a climate variable in that region and all neighbouring regions at a given value of the moderating variable of the interaction term.

Constructing projections of economic damage from future climate change

We construct projections of future climate damages by applying the coefficients estimated in equation ( 10 ) and shown in Supplementary Tables 2 – 4 (when including only lags with statistically significant effects in specifications that limit overfitting; see Supplementary Methods Section  1 ) to projections of future climate change from the CMIP-6 models. Year-on-year changes in each primary climate variable of interest are calculated to reflect the year-to-year variations used in the empirical models. 30-year moving averages of the moderating variables of the interaction terms are calculated to reflect the long-term average of climatic conditions that were used for the moderating variables in the empirical models. By using moving averages in the projections, we account for the changing vulnerability to climate shocks based on the evolving long-term conditions (Supplementary Figs. 10 and 11 show that the results are robust to the precise choice of the window of this moving average). Although these climate variables are not differenced, the fact that the bias-adjusted climate models reproduce observed climatological patterns across regions for these moderating variables very accurately (Supplementary Table 6 ) with limited spread across models (<3%) precludes the possibility that any considerable bias or uncertainty is introduced by this methodological choice. However, we impose caps on these moderating variables at the 95th percentile at which they were observed in the historical data to prevent extrapolation of the marginal effects outside the range in which the regressions were estimated. This is a conservative choice that limits the magnitude of our damage projections.

Time series of primary climate variables and moderating climate variables are then combined with estimates of the empirical model parameters to evaluate the regression coefficients in equation ( 10 ), producing a time series of annual GRPpc growth-rate reductions for a given emission scenario, climate model and set of empirical model parameters. The resulting time series of growth-rate impacts reflects those occurring owing to future climate change. By contrast, a future scenario with no climate change would be one in which climate variables do not change (other than with random year-to-year fluctuations) and hence the time-averaged evaluation of equation ( 10 ) would be zero. Our approach therefore implicitly compares the future climate-change scenario to this no-climate-change baseline scenario.

The time series of growth-rate impacts owing to future climate change in region r and year y , δ r , y , are then added to the future baseline growth rates, π r , y (in log-diff form), obtained from the SSP2 scenario to yield trajectories of damaged GRPpc growth rates, ρ r , y . These trajectories are aggregated over time to estimate the future trajectory of GRPpc with future climate impacts:

in which GRPpc r , y =2020 is the initial log level of GRPpc. We begin damage estimates in 2020 to reflect the damages occurring since the end of the period for which we estimate the empirical models (1979–2019) and to match the timing of mitigation-cost estimates from most IAMs (see below).

For each emission scenario, this procedure is repeated 1,000 times while randomly sampling from the selection of climate models, the selection of empirical models with different numbers of lags (shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) and bootstrapped estimates of the regression parameters. The result is an ensemble of future GRPpc trajectories that reflect uncertainty from both physical climate change and the structural and sampling uncertainty of the empirical models.

Estimates of mitigation costs

We obtain IPCC estimates of the aggregate costs of emission mitigation from the AR6 Scenario Explorer and Database hosted by IIASA 23 . Specifically, we search the AR6 Scenarios Database World v1.1 for IAMs that provided estimates of global GDP and population under both a SSP2 baseline and a SSP2-RCP2.6 scenario to maintain consistency with the socio-economic and emission scenarios of the climate damage projections. We find five IAMs that provide data for these scenarios, namely, MESSAGE-GLOBIOM 1.0, REMIND-MAgPIE 1.5, AIM/GCE 2.0, GCAM 4.2 and WITCH-GLOBIOM 3.1. Of these five IAMs, we use the results only from the first three that passed the IPCC vetting procedure for reproducing historical emission and climate trajectories. We then estimate global mitigation costs as the percentage difference in global per capita GDP between the SSP2 baseline and the SSP2-RCP2.6 emission scenario. In the case of one of these IAMs, estimates of mitigation costs begin in 2020, whereas in the case of two others, mitigation costs begin in 2010. The mitigation cost estimates before 2020 in these two IAMs are mostly negligible, and our choice to begin comparison with damage estimates in 2020 is conservative with respect to the relative weight of climate damages compared with mitigation costs for these two IAMs.

Data availability

Data on economic production and ERA-5 climate data are publicly available at https://doi.org/10.5281/zenodo.4681306 (ref. 62 ) and https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5 , respectively. Data on mitigation costs are publicly available at https://data.ene.iiasa.ac.at/ar6/#/downloads . Processed climate and economic data, as well as all other necessary data for reproduction of the results, are available at the public repository https://doi.org/10.5281/zenodo.10562951  (ref. 63 ).

Code availability

All code necessary for reproduction of the results is available at the public repository https://doi.org/10.5281/zenodo.10562951  (ref. 63 ).

Glanemann, N., Willner, S. N. & Levermann, A. Paris Climate Agreement passes the cost-benefit test. Nat. Commun. 11 , 110 (2020).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Burke, M., Hsiang, S. M. & Miguel, E. Global non-linear effect of temperature on economic production. Nature 527 , 235–239 (2015).

Article   ADS   CAS   PubMed   Google Scholar  

Kalkuhl, M. & Wenz, L. The impact of climate conditions on economic production. Evidence from a global panel of regions. J. Environ. Econ. Manag. 103 , 102360 (2020).

Article   Google Scholar  

Moore, F. C. & Diaz, D. B. Temperature impacts on economic growth warrant stringent mitigation policy. Nat. Clim. Change 5 , 127–131 (2015).

Article   ADS   Google Scholar  

Drouet, L., Bosetti, V. & Tavoni, M. Net economic benefits of well-below 2°C scenarios and associated uncertainties. Oxf. Open Clim. Change 2 , kgac003 (2022).

Ueckerdt, F. et al. The economically optimal warming limit of the planet. Earth Syst. Dyn. 10 , 741–763 (2019).

Kotz, M., Wenz, L., Stechemesser, A., Kalkuhl, M. & Levermann, A. Day-to-day temperature variability reduces economic growth. Nat. Clim. Change 11 , 319–325 (2021).

Kotz, M., Levermann, A. & Wenz, L. The effect of rainfall changes on economic production. Nature 601 , 223–227 (2022).

Kousky, C. Informing climate adaptation: a review of the economic costs of natural disasters. Energy Econ. 46 , 576–592 (2014).

Harlan, S. L. et al. in Climate Change and Society: Sociological Perspectives (eds Dunlap, R. E. & Brulle, R. J.) 127–163 (Oxford Univ. Press, 2015).

Bolton, P. et al. The Green Swan (BIS Books, 2020).

Alogoskoufis, S. et al. ECB Economy-wide Climate Stress Test: Methodology and Results European Central Bank, 2021).

Weber, E. U. What shapes perceptions of climate change? Wiley Interdiscip. Rev. Clim. Change 1 , 332–342 (2010).

Markowitz, E. M. & Shariff, A. F. Climate change and moral judgement. Nat. Clim. Change 2 , 243–247 (2012).

Riahi, K. et al. The shared socioeconomic pathways and their energy, land use, and greenhouse gas emissions implications: an overview. Glob. Environ. Change 42 , 153–168 (2017).

Auffhammer, M., Hsiang, S. M., Schlenker, W. & Sobel, A. Using weather data and climate model output in economic analyses of climate change. Rev. Environ. Econ. Policy 7 , 181–198 (2013).

Kolstad, C. D. & Moore, F. C. Estimating the economic impacts of climate change using weather observations. Rev. Environ. Econ. Policy 14 , 1–24 (2020).

Dell, M., Jones, B. F. & Olken, B. A. Temperature shocks and economic growth: evidence from the last half century. Am. Econ. J. Macroecon. 4 , 66–95 (2012).

Newell, R. G., Prest, B. C. & Sexton, S. E. The GDP-temperature relationship: implications for climate change damages. J. Environ. Econ. Manag. 108 , 102445 (2021).

Kikstra, J. S. et al. The social cost of carbon dioxide under climate-economy feedbacks and temperature variability. Environ. Res. Lett. 16 , 094037 (2021).

Article   ADS   CAS   Google Scholar  

Bastien-Olvera, B. & Moore, F. Persistent effect of temperature on GDP identified from lower frequency temperature variability. Environ. Res. Lett. 17 , 084038 (2022).

Eyring, V. et al. Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev. 9 , 1937–1958 (2016).

Byers, E. et al. AR6 scenarios database. Zenodo https://zenodo.org/records/7197970 (2022).

Burke, M., Davis, W. M. & Diffenbaugh, N. S. Large potential reduction in economic damages under UN mitigation targets. Nature 557 , 549–553 (2018).

Kotz, M., Wenz, L. & Levermann, A. Footprint of greenhouse forcing in daily temperature variability. Proc. Natl Acad. Sci. 118 , e2103294118 (2021).

Article   CAS   PubMed   PubMed Central   Google Scholar  

Myhre, G. et al. Frequency of extreme precipitation increases extensively with event rareness under global warming. Sci. Rep. 9 , 16063 (2019).

Min, S.-K., Zhang, X., Zwiers, F. W. & Hegerl, G. C. Human contribution to more-intense precipitation extremes. Nature 470 , 378–381 (2011).

England, M. R., Eisenman, I., Lutsko, N. J. & Wagner, T. J. The recent emergence of Arctic Amplification. Geophys. Res. Lett. 48 , e2021GL094086 (2021).

Fischer, E. M. & Knutti, R. Anthropogenic contribution to global occurrence of heavy-precipitation and high-temperature extremes. Nat. Clim. Change 5 , 560–564 (2015).

Pfahl, S., O’Gorman, P. A. & Fischer, E. M. Understanding the regional pattern of projected future changes in extreme precipitation. Nat. Clim. Change 7 , 423–427 (2017).

Callahan, C. W. & Mankin, J. S. Globally unequal effect of extreme heat on economic growth. Sci. Adv. 8 , eadd3726 (2022).

Diffenbaugh, N. S. & Burke, M. Global warming has increased global economic inequality. Proc. Natl Acad. Sci. 116 , 9808–9813 (2019).

Callahan, C. W. & Mankin, J. S. National attribution of historical climate damages. Clim. Change 172 , 40 (2022).

Burke, M. & Tanutama, V. Climatic constraints on aggregate economic output. National Bureau of Economic Research, Working Paper 25779. https://doi.org/10.3386/w25779 (2019).

Kahn, M. E. et al. Long-term macroeconomic effects of climate change: a cross-country analysis. Energy Econ. 104 , 105624 (2021).

Desmet, K. et al. Evaluating the economic cost of coastal flooding. National Bureau of Economic Research, Working Paper 24918. https://doi.org/10.3386/w24918 (2018).

Hsiang, S. M. & Jina, A. S. The causal effect of environmental catastrophe on long-run economic growth: evidence from 6,700 cyclones. National Bureau of Economic Research, Working Paper 20352. https://doi.org/10.3386/w2035 (2014).

Ritchie, P. D. et al. Shifts in national land use and food production in Great Britain after a climate tipping point. Nat. Food 1 , 76–83 (2020).

Dietz, S., Rising, J., Stoerk, T. & Wagner, G. Economic impacts of tipping points in the climate system. Proc. Natl Acad. Sci. 118 , e2103081118 (2021).

Bastien-Olvera, B. A. & Moore, F. C. Use and non-use value of nature and the social cost of carbon. Nat. Sustain. 4 , 101–108 (2021).

Carleton, T. et al. Valuing the global mortality consequences of climate change accounting for adaptation costs and benefits. Q. J. Econ. 137 , 2037–2105 (2022).

Bastien-Olvera, B. A. et al. Unequal climate impacts on global values of natural capital. Nature 625 , 722–727 (2024).

Malik, A. et al. Impacts of climate change and extreme weather on food supply chains cascade across sectors and regions in Australia. Nat. Food 3 , 631–643 (2022).

Article   ADS   PubMed   Google Scholar  

Kuhla, K., Willner, S. N., Otto, C., Geiger, T. & Levermann, A. Ripple resonance amplifies economic welfare loss from weather extremes. Environ. Res. Lett. 16 , 114010 (2021).

Schleypen, J. R., Mistry, M. N., Saeed, F. & Dasgupta, S. Sharing the burden: quantifying climate change spillovers in the European Union under the Paris Agreement. Spat. Econ. Anal. 17 , 67–82 (2022).

Dasgupta, S., Bosello, F., De Cian, E. & Mistry, M. Global temperature effects on economic activity and equity: a spatial analysis. European Institute on Economics and the Environment, Working Paper 22-1 (2022).

Neal, T. The importance of external weather effects in projecting the macroeconomic impacts of climate change. UNSW Economics Working Paper 2023-09 (2023).

Deryugina, T. & Hsiang, S. M. Does the environment still matter? Daily temperature and income in the United States. National Bureau of Economic Research, Working Paper 20750. https://doi.org/10.3386/w20750 (2014).

Hersbach, H. et al. The ERA5 global reanalysis. Q. J. R. Meteorol. Soc. 146 , 1999–2049 (2020).

Cucchi, M. et al. WFDE5: bias-adjusted ERA5 reanalysis data for impact studies. Earth Syst. Sci. Data 12 , 2097–2120 (2020).

Adler, R. et al. The New Version 2.3 of the Global Precipitation Climatology Project (GPCP) Monthly Analysis Product 1072–1084 (University of Maryland, 2016).

Lange, S. Trend-preserving bias adjustment and statistical downscaling with ISIMIP3BASD (v1.0). Geosci. Model Dev. 12 , 3055–3070 (2019).

Wenz, L., Carr, R. D., Kögel, N., Kotz, M. & Kalkuhl, M. DOSE – global data set of reported sub-national economic output. Sci. Data 10 , 425 (2023).

Article   PubMed   PubMed Central   Google Scholar  

Gennaioli, N., La Porta, R., Lopez De Silanes, F. & Shleifer, A. Growth in regions. J. Econ. Growth 19 , 259–309 (2014).

Board of Governors of the Federal Reserve System (US). U.S. dollars to euro spot exchange rate. https://fred.stlouisfed.org/series/AEXUSEU (2022).

World Bank. GDP deflator. https://data.worldbank.org/indicator/NY.GDP.DEFL.ZS (2022).

Jones, B. & O’Neill, B. C. Spatially explicit global population scenarios consistent with the Shared Socioeconomic Pathways. Environ. Res. Lett. 11 , 084003 (2016).

Murakami, D. & Yamagata, Y. Estimation of gridded population and GDP scenarios with spatially explicit statistical downscaling. Sustainability 11 , 2106 (2019).

Koch, J. & Leimbach, M. Update of SSP GDP projections: capturing recent changes in national accounting, PPP conversion and Covid 19 impacts. Ecol. Econ. 206 (2023).

Carleton, T. A. & Hsiang, S. M. Social and economic impacts of climate. Science 353 , aad9837 (2016).

Article   PubMed   Google Scholar  

Bergé, L. Efficient estimation of maximum likelihood models with multiple fixed-effects: the R package FENmlm. DEM Discussion Paper Series 18-13 (2018).

Kalkuhl, M., Kotz, M. & Wenz, L. DOSE - The MCC-PIK Database Of Subnational Economic output. Zenodo https://zenodo.org/doi/10.5281/zenodo.4681305 (2021).

Kotz, M., Wenz, L. & Levermann, A. Data and code for “The economic commitment of climate change”. Zenodo https://zenodo.org/doi/10.5281/zenodo.10562951 (2024).

Dasgupta, S. et al. Effects of climate change on combined labour productivity and supply: an empirical, multi-model study. Lancet Planet. Health 5 , e455–e465 (2021).

Lobell, D. B. et al. The critical role of extreme heat for maize production in the United States. Nat. Clim. Change 3 , 497–501 (2013).

Zhao, C. et al. Temperature increase reduces global yields of major crops in four independent estimates. Proc. Natl Acad. Sci. 114 , 9326–9331 (2017).

Wheeler, T. R., Craufurd, P. Q., Ellis, R. H., Porter, J. R. & Prasad, P. V. Temperature variability and the yield of annual crops. Agric. Ecosyst. Environ. 82 , 159–167 (2000).

Rowhani, P., Lobell, D. B., Linderman, M. & Ramankutty, N. Climate variability and crop production in Tanzania. Agric. For. Meteorol. 151 , 449–460 (2011).

Ceglar, A., Toreti, A., Lecerf, R., Van der Velde, M. & Dentener, F. Impact of meteorological drivers on regional inter-annual crop yield variability in France. Agric. For. Meteorol. 216 , 58–67 (2016).

Shi, L., Kloog, I., Zanobetti, A., Liu, P. & Schwartz, J. D. Impacts of temperature and its variability on mortality in New England. Nat. Clim. Change 5 , 988–991 (2015).

Xue, T., Zhu, T., Zheng, Y. & Zhang, Q. Declines in mental health associated with air pollution and temperature variability in China. Nat. Commun. 10 , 2165 (2019).

Article   ADS   PubMed   PubMed Central   Google Scholar  

Liang, X.-Z. et al. Determining climate effects on US total agricultural productivity. Proc. Natl Acad. Sci. 114 , E2285–E2292 (2017).

Desbureaux, S. & Rodella, A.-S. Drought in the city: the economic impact of water scarcity in Latin American metropolitan areas. World Dev. 114 , 13–27 (2019).

Damania, R. The economics of water scarcity and variability. Oxf. Rev. Econ. Policy 36 , 24–44 (2020).

Davenport, F. V., Burke, M. & Diffenbaugh, N. S. Contribution of historical precipitation change to US flood damages. Proc. Natl Acad. Sci. 118 , e2017524118 (2021).

Dave, R., Subramanian, S. S. & Bhatia, U. Extreme precipitation induced concurrent events trigger prolonged disruptions in regional road networks. Environ. Res. Lett. 16 , 104050 (2021).

Download references

Acknowledgements

We gratefully acknowledge financing from the Volkswagen Foundation and the Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH on behalf of the Government of the Federal Republic of Germany and Federal Ministry for Economic Cooperation and Development (BMZ).

Open access funding provided by Potsdam-Institut für Klimafolgenforschung (PIK) e.V.

Author information

Authors and affiliations.

Research Domain IV, Research Domain IV, Potsdam Institute for Climate Impact Research, Potsdam, Germany

Maximilian Kotz, Anders Levermann & Leonie Wenz

Institute of Physics, Potsdam University, Potsdam, Germany

Maximilian Kotz & Anders Levermann

Mercator Research Institute on Global Commons and Climate Change, Berlin, Germany

Leonie Wenz

You can also search for this author in PubMed   Google Scholar

Contributions

All authors contributed to the design of the analysis. M.K. conducted the analysis and produced the figures. All authors contributed to the interpretation and presentation of the results. M.K. and L.W. wrote the manuscript.

Corresponding author

Correspondence to Leonie Wenz .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Peer review

Peer review information.

Nature thanks Xin-Zhong Liang, Chad Thackeray and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended data fig. 1 constraining the persistence of historical climate impacts on economic growth rates..

The results of a panel-based fixed-effects distributed lag model for the effects of annual mean temperature ( a ), daily temperature variability ( b ), total annual precipitation ( c ), the number of wet days ( d ) and extreme daily precipitation ( e ) on sub-national economic growth rates. Point estimates show the effects of a 1 °C or one standard deviation increase (for temperature and precipitation variables, respectively) at the lower quartile, median and upper quartile of the relevant moderating variable (green, orange and purple, respectively) at different lagged periods after the initial shock (note that these are not cumulative effects). Climate variables are used in their first-differenced form (see main text for discussion) and the moderating climate variables are the annual mean temperature, seasonal temperature difference, total annual precipitation, number of wet days and annual mean temperature, respectively, in panels a – e (see Methods for further discussion). Error bars show the 95% confidence intervals having clustered standard errors by region. The within-region R 2 , Bayesian and Akaike information criteria for the model are shown at the top of the figure. This figure shows results with ten lags for each variable to demonstrate the observed levels of persistence, but our preferred specifications remove later lags based on the statistical significance of terms shown above and the information criteria shown in Extended Data Fig. 2 . The resulting models without later lags are shown in Supplementary Figs. 1 – 3 .

Extended Data Fig. 2 Incremental lag-selection procedure using information criteria and within-region R 2 .

Starting from a panel-based fixed-effects distributed lag model estimating the effects of climate on economic growth using the real historical data (as in equation ( 4 )) with ten lags for all climate variables (as shown in Extended Data Fig. 1 ), lags are incrementally removed for one climate variable at a time. The resulting Bayesian and Akaike information criteria are shown in a – e and f – j , respectively, and the within-region R 2 and number of observations in k – o and p – t , respectively. Different rows show the results when removing lags from different climate variables, ordered from top to bottom as annual mean temperature, daily temperature variability, total annual precipitation, the number of wet days and extreme annual precipitation. Information criteria show minima at approximately four lags for precipitation variables and ten to eight for temperature variables, indicating that including these numbers of lags does not lead to overfitting. See Supplementary Table 1 for an assessment using information criteria to determine whether including further climate variables causes overfitting.

Extended Data Fig. 3 Damages in our preferred specification that provides a robust lower bound on the persistence of climate impacts on economic growth versus damages in specifications of pure growth or pure level effects.

Estimates of future damages as shown in Fig. 1 but under the emission scenario RCP8.5 for three separate empirical specifications: in orange our preferred specification, which provides an empirical lower bound on the persistence of climate impacts on economic growth rates while avoiding assumptions of infinite persistence (see main text for further discussion); in purple a specification of ‘pure growth effects’ in which the first difference of climate variables is not taken and no lagged climate variables are included (the baseline specification of ref.  2 ); and in pink a specification of ‘pure level effects’ in which the first difference of climate variables is taken but no lagged terms are included.

Extended Data Fig. 4 Climate changes in different variables as a function of historical interannual variability.

Changes in each climate variable of interest from 1979–2019 to 2035–2065 under the high-emission scenario SSP5-RCP8.5, expressed as a percentage of the historical variability of each measure. Historical variability is estimated as the standard deviation of each detrended climate variable over the period 1979–2019 during which the empirical models were identified (detrending is appropriate because of the inclusion of region-specific linear time trends in the empirical models). See Supplementary Fig. 13 for changes expressed in standard units. Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Extended Data Fig. 5 Contribution of different climate variables to overall committed damages.

a , Climate damages in 2049 when using empirical models that account for all climate variables, changes in annual mean temperature only or changes in both annual mean temperature and one other climate variable (daily temperature variability, total annual precipitation, the number of wet days and extreme daily precipitation, respectively). b , The cumulative marginal effects of an increase in annual mean temperature of 1 °C, at different baseline temperatures, estimated from empirical models including all climate variables or annual mean temperature only. Estimates and uncertainty bars represent the median and 95% confidence intervals obtained from 1,000 block-bootstrap resamples from each of three different empirical models using eight, nine or ten lags of temperature terms.

Extended Data Fig. 6 The difference in committed damages between the upper and lower quartiles of countries when ranked by GDP and cumulative historical emissions.

Quartiles are defined using a population weighting, as are the average committed damages across each quartile group. The violin plots indicate the distribution of differences between quartiles across the two extreme emission scenarios (RCP2.6 and RCP8.5) and the uncertainty sampling procedure outlined in Methods , which accounts for uncertainty arising from the choice of lags in the empirical models, uncertainty in the empirical model parameter estimates, as well as the climate model projections. Bars indicate the median, as well as the 10th and 90th percentiles and upper and lower sixths of the distribution reflecting the very likely and likely ranges following the likelihood classification adopted by the IPCC.

Supplementary information

Supplementary information, peer review file, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Kotz, M., Levermann, A. & Wenz, L. The economic commitment of climate change. Nature 628 , 551–557 (2024). https://doi.org/10.1038/s41586-024-07219-0

Download citation

Received : 25 January 2023

Accepted : 21 February 2024

Published : 17 April 2024

Issue Date : 18 April 2024

DOI : https://doi.org/10.1038/s41586-024-07219-0

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

• Open access
• Published: 15 April 2024

Machine-learning analysis reveals an important role for negative selection in shaping cancer aneuploidy landscapes

• Juman Jubran 1   na1 ,
• Rachel Slutsky 2   na1 ,
• Nir Rozenblum 2 ,
• Lior Rokach 3 ,
• Uri Ben-David 2   na2 &
• Esti Yeger-Lotem   ORCID: orcid.org/0000-0002-8279-7898 1 , 4   na2  

Genome Biology volume  25 , Article number:  95 ( 2024 ) Cite this article

712 Accesses

10 Altmetric

Metrics details

Aneuploidy, an abnormal number of chromosomes within a cell, is a hallmark of cancer. Patterns of aneuploidy differ across cancers, yet are similar in cancers affecting closely related tissues. The selection pressures underlying aneuploidy patterns are not fully understood, hindering our understanding of cancer development and progression.

Here, we apply interpretable machine learning methods to study tissue-selective aneuploidy patterns. We define 20 types of features corresponding to genomic attributes of chromosome-arms, normal tissues, primary tumors, and cancer cell lines (CCLs), and use them to model gains and losses of chromosome arms in 24 cancer types. To reveal the factors that shape the tissue-specific cancer aneuploidy landscapes, we interpret the machine learning models by estimating the relative contribution of each feature to the models. While confirming known drivers of positive selection, our quantitative analysis highlights the importance of negative selection for shaping aneuploidy landscapes. This is exemplified by tumor suppressor gene density being a better predictor of gain patterns than oncogene density, and vice versa for loss patterns. We also identify the importance of tissue-selective features and demonstrate them experimentally, revealing KLF5 as an important driver for chr13q gain in colon cancer. Further supporting an important role for negative selection in shaping the aneuploidy landscapes, we find compensation by paralogs to be among the top predictors of chromosome arm loss prevalence and demonstrate this relationship for one paralog interaction. Similar factors shape aneuploidy patterns in human CCLs, demonstrating their relevance for aneuploidy research.

Conclusions

Our quantitative, interpretable machine learning models improve the understanding of the genomic properties that shape cancer aneuploidy landscapes.

Introduction

Aneuploidy, defined as an abnormal number of chromosomes or chromosome-arms within a cell, is a characteristic trait of human cancer [ 1 ]. Aneuploidy is associated with patient prognosis and with response to anticancer therapies [ 2 , 3 ], indicating that it can play a driving role in tumorigenesis. It is well established that the fitness advantage conferred by specific aneuploidies depends on the genomic, environmental, and developmental contexts [ 1 ]. One important cellular context is the cancer tissue of origin; aneuploidy patterns are cancer type-specific, and cancers that originate from related tissues tend to exhibit similar aneuploidy patterns [ 2 , 4 , 5 ]. Nonetheless, the selection pressures that shape the aneuploidy landscapes of human tumors are not fully understood, and it is not clear why some chromosome-arm gains and losses would recur in some tumor types but not in others.

Several non-mutually exclusive explanations have been previously provided in an attempt to explain the tissue selectivity of aneuploidy patterns. First, the densities of oncogenes (OGs) and tumor suppressor genes (TSGs) are enriched in chromosome-arms that tend to be gained or lost, respectively, potentially due to the cumulative effect of altering multiple such genes at the same time [ 6 ]. As cell proliferation is controlled in a tissue-dependent manner, the relative importance of OGs and TSGs varies across tissues, so that the density of tissue-specific driver genes can help predict aneuploidy patterns [ 7 ]. Second, some recurrent aneuploidies reflect the chromosome arm-wide gene expression patterns that characterize their normal tissue of origin, suggesting that chromosome-arm gains and losses may ‘hardwire’ pre-existing gene expression patterns [ 8 ]. Third, several strong cancer driver genes have been shown to underlie the recurrent aneuploidy of the chromosome-arms on which these genes reside; prominent examples are the tumor suppressors TP53 and PTEN , which have been shown to drive the recurrent loss of chromosome-arm 17p in leukemia and that of 10q in glioma, respectively [ 9 , 10 , 11 ]. Fourth, it has been recently proposed that somatic amplifications, including chromosome-arm gains, are positively selected in cancer evolution in order to buffer gene inactivation of haploinsufficient genes in mutation-prone regions [ 12 ].

Notably, each previous study focused on a separate aspect of tissue specificity; therefore, the relative contribution of each factor to shaping the overall aneuploidy landscape of human tumors is currently unknown. Furthermore, whether any additional tissue-specific traits could also play a major role in driving aneuploidy patterns remains an open question. Importantly, previous studies focused on the role of positive selection in driving the gain or the loss of specific chromosome-arms in specific tumor types. However, unlike point mutations in specific genes, aneuploidies come with a strong fitness cost [ 1 , 13 ]. Therefore, whereas positive selection greatly outweighs negative selection in shaping the landscape of point mutations in cancer, as evaluated by a refined version of the normalized ratio of non-synonymous to synonymous mutations [ 14 ], both positive selection and negative selection may be important for shaping the landscape of aneuploidy. Indeed, a recent study showed that negative selection could determine the boundaries of recurrent cancer copy number alterations [ 15 ]. It is therefore necessary to consider the balance between positive and negative selection in shaping the aneuploidy landscapes of human cancer.

Machine learning (ML) methods have been applied to study a variety of biological and medical questions where heterogeneous large-scale data are available [ 16 ]. In the context of cancer, supervised ML methods were applied to predict cancer driver genes [ 17 , 18 ], to distinguish between cancer types [ 19 , 20 ], and to predict gene dependency in tumors [ 21 ]. However, ML has not been applied to investigate the observed patterns of aneuploidy in human cancer. Whereas ML has been frequently used for prediction and often regarded as a black box, recent advancements have allowed more insight into the factors that underlie prediction. For example, Shapley Additive exPlanations algorithm (SHAP) [ 22 , 23 ] estimates the importance and relative contribution of each of the features utilized by the model to the model’s decisions.

Here, we present a novel ML approach to elucidate the factors that underlie the cancer type-specific patterns of aneuploidy. For this, we constructed separate ML models for chromosome-arm gain and loss, whereby each of 39 chromosome-arms within 24 cancer types was associated with 20 types of features corresponding to various genomic attributes of chromosome-arms, normal tissues, primary tumors, and cancer cell lines (CCLs). Our approach is focused on interpretation rather than prediction of aneuploidy recurrence patterns. Interpretation of the gain and loss models for aneuploidy in primary tumors captured known genomic features that had been previously reported to shape aneuploidy landscapes, supporting the models’ validity. Furthermore, these analyses suggested that negative selection played a greater role than positive selection in this process and revealed paralog compensation as an important contributor to cancer type-specific aneuploidy patterns, in both primary tumors and CCLs. Lastly, we experimentally validated a specific aneuploidy driver using genetically engineered isogenic human cells.

Constructing machine learning models to classify cancer aneuploidy patterns

To create a supervised classification ML model that predicts the recurrence pattern of aneuploidy across cancer types, we built a large‐scale dataset consisting of labels and features per instance of chromosome-arm and cancer type. For each instance, the label indicated whether the chromosome-arm was recurrently gained, lost, or remained neutral in that cancer. Labels were determined according to Genomic Identification of Significant Targets in Cancer (GISTIC2.0) [ 24 ]. We focused on 24 cancer types for which transcriptomic data of normal tissues of origin was available from the Genotype-Tissue Expression Consortium (GTEx) ([ 25 ] ( Methods ). In total, 199 instances of chromosome-arm and cancer type were labeled as gained, 307 were labeled as lost, and 430 were labeled as neutral (Fig.  1 A).

A machine learning (ML) approach for predicting aneuploidy in cancer. A Schematic view of the ML model construction. Labels represent aneuploidy status of each chromosome arm in 24 cancer types (abbreviation of cancer types detailed in Additional file 2 : Table S1), classified as gained (red, n  = 199), lost (blue, n  = 307), or neutral (white, n  = 430). Features consist of 20 types of features pertaining to chromosome-arms, normal tissues and cancer tissues (see B ). Two separate ML models were constructed to predict gained and lost chromosome-arms (gain model and loss model). Each model was analyzed to estimate the contribution of the features to the predicted outcome. B The features analyzed by the ML model. The inner layer shows feature categories: chromosome arms (purple), cancer tissues (primary tumors and CCLs, blue), and normal tissues (green). The middle layer shows the sub-categories of the features. Chromosome-arm features include essentiality and driver genes features. Cancer-tissue features include transcriptomics and essentiality features. Normal-tissue features include protein–protein interactions (PPIs), transcriptomics, paralogs, eQTL, tissue-specific (TS) genes, development, and GO processes features. The outer layer represents all 20 feature types that were analyzed by the model. Numbers in parentheses indicate the number of tissues, organs, or cell lines from which cancer and normal tissue features were derived, or the number of chromosome-arms from which chromosome-arm features were derived. C The performance of the ML models as evaluated by the area under the receiver-operating characteristic curve (auROC, left) and the precision recall curve (auPRC, right) using tenfold cross-validation. Gain model (gradient boosting): auROC = 74% and auPRC = 63% (expected 32%). Loss model (XGBoost): auROC = 70% and auPRC = 63% (expected 42%)

Next, we defined three categories of features (Fig.  1 B; Methods ). The first category, denoted ‘chromosome-arms’, contained features of chromosome-arms that are independent of cancer type. Chromosome-arm features included the density of OGs, the density of TSGs [ 6 ], and the density of essential genes [ 26 ] per chromosome-arm. The second category, denoted ‘cancer tissues’, contained features pertaining to chromosome-arms in primary tumors and CCLs. It included features pertaining to expression of genes in primary tumors and essentiality of genes in CCLs. Expression levels of genes in each chromosome-arm per cancer type were obtained from The Cancer Genome Atlas (TCGA, https://www.cancer.gov/tcga ). Gene essentiality scores were obtained from the Cancer Dependency Map (DepMap) [ 27 ]. In total, this category included 103 omics-based readouts ( Methods ). The third category, denoted ‘normal tissues’, contained features pertaining to chromosome-arms in normal tissues from which cancer types originated (e.g., colon tissue was matched with colon adenocarcinoma, Additional file 2 : Table S1). Features of normal tissues included expression levels of genes located on each chromosome-arm in the respective normal tissue, their tissue protein–protein interactions (PPIs) [ 28 , 29 ], and their tissue-specific biological process activities [ 30 ]. It also included tissue-specific dosage relationships between paralogous genes, denoted ‘paralog compensation’ [ 31 , 32 ]. In total, this category included 447 tissue-based properties ( Methods ). To enhance our understanding of cancer and tissue selectivity, feature values of cancer and normal tissues were transformed from absolute to relative; for example, instead of indicating the absolute expression level of a gene in a given normal tissue, the expression feature was set to the expression level of the gene in the given tissue relative to its expression levels in all tissues (Additional file 1 : Fig. S1). Each chromosome-arm was then assigned with a feature value that was inferred from the values of its genes ( Methods , Additional file 1 : Fig. S2).

To fit the features dataset and the labels dataset, we further transformed the features dataset, such that each instance of chromosome-arm and cancer type was associated with features corresponding to the chromosome-arm, cancer type, and matching normal tissue ( Methods ). In total, the dataset included 20 types of features per chromosome-arm and cancer type: 3 in the chromosome-arm category, 4 in the cancer tissues category, and 13 in the normal tissues category (Fig.  1 B). We assessed the similarity between every pair of features using Spearman correlation (Additional file 1 : Fig. S3A). Most features did not correlate with each other (Additional file 1 : Fig. S3B). Among the correlated feature pairs were PPI-related features and expression in normal adult and developing tissues features (Additional file 1 : Fig. S3A). Lastly, we assessed the similarity between instances of chromosome-arm and cancer type by their feature values using principal component analysis (PCA) (Additional file 1 : Fig. S3C). Instances did not cluster by their aneuploidy pattern (gain/loss/neutral), suggesting that a more complex model is needed to classify the different patterns.

With these labels and features of each chromosome-arm and cancer type, we set out to construct two separate ML models to predict chromosome-arm gain and loss patterns across cancer types (denoted as the ‘gain model’ and the ‘loss model’, respectively; Fig.  1 A). Each model was trained and tested on data of gained (or lost) chromosome-arms versus neutral chromosome-arms. We employed five different ML methods ( Methods ) and assessed the performance of each method by using tenfold cross-validation and calculating average area under the receiver operating characteristic (auROC) and average area under the precision-recall curve (auPRC) (Additional file 1 : Fig. S4A,B). Logistic regression showed similar results to a random prediction, with auROC of 54% for each model (Additional file 1 : Fig. S4), indicating that the relationships between features and labels are non-linear. Decision tree methods that can capture such relationships [ 33 , 34 ], including gradient boosting, XGBoost, and random forest, performed better than logistic regression and similarly to each other (Additional file 1 : Fig. S4). Best performance in the gain model was achieved by gradient boosting method, with auROC of 74% and auPRC of 63% (expected: 32%) (Fig.  1 C). Best performance in the loss model was achieved by XGBoost, with auROC of 70% and auPRC of 63% (expected: 42%) (Fig.  1 C).

Revealing the top contributors to cancer aneuploidy patterns

The main purpose of our models was to identify the features that contribute the most to the recurrence patterns of aneuploidy observed in human cancer, which could illuminate the factors at play. To this aim, we used the SHAP (Shapley Additive exPlanations) algorithm [ 22 , 23 ], which estimates the importance and relative contribution of each feature to the model’s decision and ranks them accordingly. We applied SHAP separately to the gain model and to the loss model ( Methods ).

In the gain model, the topmost features were TSG density and OG density (Fig.  2 A,B). As expected, these features showed opposite directions: TSG density was low in gained chromosome-arms, whereas OG density was high, in line with previous observations [ 6 , 7 ] (Fig.  2 B). Importantly, this analysis revealed that the impact of TSGs on the gain model’s decision was twice larger than that of OGs (Fig.  2 A), highlighting the importance of negative selection for shaping cancer aneuploidy patterns. The third most important feature was TCGA expression, which quantified the expression of arm-residing genes in the given cancer type relative to their expression in other cancers. Notably, expression levels were obtained only from samples where the chromosome-arm was not gained or lost ( Methods ). This analysis revealed that, across cancer types, chromosome-arms that tend to be gained exhibit higher expression of genes even in neutral cases, consistent with a previous recent study [ 8 ]. This confirms that the genes on gained chromosome-arms are preferentially important for the specific cancer types in which these gains are recurrent. Congruently, PPIs and normal tissue expression—features of normal tissues—were also among the ten top-contributing features (Fig.  2 A). The estimated importance of all features in the gain model is shown in Additional file 1 : Fig. S5A.

Quantitative views into the ten topmost contributing features of the gain and loss models. Features are ordered from bottom to top by their increased average absolute contribution to the model, as calculated by SHAP. A The average absolute contribution of each feature to the gain model. The directionality of the feature (i.e., whether high feature values correspond to gain or neutral) is represented by an arrow. B A detailed view of the contribution of each feature to the gain model. Per feature, each dot represents the contribution per instance of a chromosome-arm and cancer type pair. The dots are spread based on whether they were classified as neutral (left) or gain (right) by the model. Instances are colored by the feature value (green-to-orange scale denotes low-to-high value). The order (height) of each feature is the same as in A . C Same as panel A for the loss model. D  Same as panel B for the loss model. E The correlations between top contributing features and the frequencies of chromosome-arm gains and losses, as measured by Spearman correlation. P -values were adjusted for multiple hypothesis testing using Benjamini–Hochberg procedure. Negative correlation between TSG density and gain frequency ( ρ  = − 0.52, adjusted p  = 0.006). Positive correlation between TSG density and loss frequency ( ρ  = 0.3, adjusted p  = 0.17). Positive correlation between OG density and gain frequency ( ρ  = 0.25, adjusted p  = 0.18). Negative correlation between OG density and loss frequency ( ρ  = − 0.47, adjusted p  = 0.01). Positive correlation between TCGA expression and gain frequency ( ρ  = 0.29, adjusted p  = 0.14). Negative correlation between TCGA expression and loss frequency ( ρ  = − 0.33, adjusted p  = 0.12). Positive correlation between essential gene density and gain frequency ( ρ  = 0.16, adjusted p  = 0.37). Negative correlation between essential gene density and loss frequency ( ρ  = − 0.1, adjusted p  = 0.5)

The loss model shared the same top three features, yet with opposite directions and different ranks (Fig.  2 C,D). OG density ranked first, was low in lost chromosome-arms, whereas TSG density ranked third, was high (Fig.  2 D), in line with previous observations [ 6 , 7 ]. In contrast to the gain model, in the loss model, the impact of OG density on the model’s decision was larger than that of TSG density, again in line with negative selection as an important force in cancer aneuploidy evolution. TCGA expression (computed from samples where the chromosome-arm was not lost or gained, see Methods ) ranked second: chromosome-arms with highly-expressed genes tended not to be recurrently lost, in line with negative selection. Another top feature that showed opposite directions between the gain and loss model was essential gene density [ 26 ]. As expected, essential gene density was low in lost chromosome-arms, in line with negative selection against losing copies of essential genes [ 26 , 27 , 35 ]. The estimated importance of all features in the loss model is shown in Additional file 1 : Fig. S5B.

To examine the direct relationships between high-ranking features and aneuploidy recurrence patterns, we assessed the correlations between these features and aneuploidy prevalence ( Methods ). In accordance with the SHAP analysis, the negative correlation between TSG density and chromosome-arm gain ( ρ  = − 0.52, adjusted p  = 0.0006, Spearman correlation; Fig.  2 E) was much stronger and more significant than the positive correlation between OG density and chromosome-arm gain ( ρ  = 0.25, adjusted p  = 0.12, Spearman correlation; Fig.  2 E). Similarly, the negative correlation between OG density and chromosome-arm loss ( ρ  = − 0.47, adjusted p  = 0.003, Spearman correlation; Fig.  2 E) was much stronger and more significant than the positive correlation between TSG density and chromosome-arm loss ( ρ  = 0.3, adjusted p  = 0.067, Spearman correlation; Fig.  2 E). TCGA expression and essential gene density were correlated with chromosome-arm gain, and anticorrelated with chromosome-arm loss, albeit to a lesser extent (Fig.  2 E, Additional file 1 : Fig. S6). Also showing positive correlations with gains and negative correlations with losses were features derived from expression levels in normal adult and developing tissues, certain PPI-related features, and additional essentiality features (Additional file 1 : Fig. S6). However, these correlations were weaker than the correlations described above. Altogether, correlation analyses supported the relationships between top features of each model and aneuploidy patterns.

The robust impact of top contributors to cancer aneuploidy patterns

Next, we asked if the above results were sensitive to our model construction schemes. We first tested the robustness of the models to internal parameters used to generate the features ( Methods ). We therefore recreated features upon modifying internal parameters and repeated model construction and interpretation ( Methods ). We found that feature importance was robust to these changes (Additional file 1 : Fig. S7, Additional file 3 : Table S2). Second, we tested the robustness of the results upon tuning the hyperparameters of each model ( Methods , Additional file 1 : Fig. S8). The top contributing features of each model were retained following hyperparameter tuning, supporting their reliability (Additional file 1 : Fig. S8C). We also checked whether the same top features would be recognized upon modeling one type of chromosome-arm event versus all other events. Applying the same approaches, we constructed two additional ML models. One model classified chromosome-arm gain versus no-gain (i.e., chromosome-arm loss or neutrality). Another model classified chromosome-arm loss versus no-loss (i.e., chromosome-arm gain or neutral). These additional models performed similarly to their respective models (Additional file 1 : Fig. S9). SHAP analysis of the two additional models revealed that feature importance was very similar between these models and the original models, which compared gained and lost chromosome-arms only to neutral chromosome-arms (Additional file 1 : Fig. S9).

We next tested whether the results were driven by a small subset of chromosome-arm and cancer type instances. For that, per model, we identified chromosome-arm and cancer type instances with the top contributions to the five topmost important features ( Methods , Additional file 4 : Table S3A,B, Additional file 5 : Table S4A,B). Most instances contributed to at least one of these features, and none of the instances contributed to all five (Additional file 5 : Table S4C). Next, we focused on chromosome-arm and cancer type instances that were top contributors to at least three of the five features (4.3% and 1.9% of the pairs in the gain and loss models, respectively). We tested their impact on the model by excluding them from the dataset and repeating the construction and interpretation of each model without them. The revised gain model retained its five topmost important features, though their ranking slightly changed (the third and fifth features switched). The revised loss model retained its four topmost important features (the fifth and seventh features switched) (Additional file 1 : Fig. S10). This suggests that the general effect of the features was not driven by a small subset of instances.

Lastly, we expanded our analyses to address whole-chromosome gains and losses. For this, we updated the features dataset to refer to whole-chromosome and cancer type instances ( Methods ). For example, the feature TSG density was updated to refer to the entire chromosome. Likewise, we updated the aneuploidy status of whole-chromosome and cancer type instances using data from GISTIC ( Methods ). This resulted in a dataset of 78 whole-chromosome gains, 151 whole-chromosome loss, and 299 neutral cases. Next, we used these data to train a whole-chromosome gain (trisomy) model and a whole-chromosome loss (monosomy) model. Model training and assessment were similar to the chromosome-arm gain and loss models. Specifically, we employed five different ML methods and assessed their performance using fivefold cross-validation. Best performance for the trisomy model was achieved by random forest, with auROC of 69% and auPRC of 47% (expected 21%; Additional file 1 : Fig. S11A). Best performance for the monosomy model was achieved by XGBoost, with auROC of 71% and auPRC of 59% (expected 34%; Additional file 1 : Fig. S11D). Performances were somewhat weaker than the chromosome-arm models, in accordance with the training data being almost twofold smaller. Lastly, we interpreted each model using SHAP. In the trisomy model, the topmost feature was TSG density and its impact was over twofold larger than the impact of other features, similarly to the chromosome-arm gain model (Additional file 1 : Fig. S11B,C). Other strong features of the chromosome-arm gain model, TCGA expression and OG density, ranked fifth and sixth, yet preserved their directionality. In the monosomy model, top features included OG density, TCGA expression, and paralogs compensation, fitting with the chromosome-arm loss model (Additional file 1 : Fig. S11E,F). The feature TSG density was ranked eight, yet preserved its directionality, similarly to the remaining features. Altogether, these results suggest that negative selection is an important factor in shaping both chromosome-arm and whole-chromosome aneuploidy patterns.

Similar features shape aneuploidy patterns in human cancer cell lines and in human tumors

Next, we aimed to test whether similar features also shape aneuploidy patterns in CCLs. We collected data of aneuploidy patterns of all chromosome-arms in CCLs [ 36 ] and analyzed 10 cancer types with matched normal tissue data from GTEx [ 25 ] ( Methods ). Similar to the analysis of cancer tissues, we labeled each instance of chromosome-arm and CCL as recurrently gained (59 instances), recurrently lost (45 instances), or neutral (286 instances) and updated the features associated with cancer types according to the CCL data ( Methods ). We then applied the gain and loss ML models, which were trained on primary tumor data, to identify determinants of aneuploidy patterns of CCLs ( Methods ). The performance of the models was at least as good as for primary tumors (gain model: auROC = 83% and auPRC = 49% (expected 15%); loss model: auROC = 76% and auPRC = 45% (expected 11%), Fig.  3 A). These results indicate that similar factors affect aneuploidy in cancers and in CCLs, consistent with the highly similar aneuploidy patterns observed in tumors and in CCLs [ 36 , 37 ].

Aneuploidy patterns in CCLs and primary tumors are shaped by similar features. A The ML scheme for analysis of aneuploidy patterns in CCLs. The gain and loss models that were trained on aneuploidy patterns in primary tumors were applied to aneuploidy patterns in CCLs. Performance was measured using tenfold cross-validation. Gain model (gradient boosting): auROC = 83%, auPRC = 49% (expected 15%). Loss model (XGBoost): auROC = 76%, auPRC = 45% (expected 11%). B The average absolute contribution of the ten topmost features to the gain model (see legend of Fig.  2 A). The order and directionality of the features generally agree with the gain model in primary tumors. C A detailed view of the contribution of the ten topmost features to the gain model (see legend of Fig.  2 B). D Same as B for the loss model. The order and directionality of the features generally agree with the loss model in primary tumors. E Same as panel C for the loss model. F The correlations between top contributing features and the frequencies of chromosome-arm gains and losses, as measured by Spearman correlation. p -values were adjusted for multiple hypothesis testing using Benjamini–Hochberg procedure. Negative correlation between TSG density and gain frequency ( ρ  = − 0.37, adjusted p  = 0.04). Positive correlation between TSG density and loss frequency ( ρ  = 0.17, adjusted p  = 0.32). Positive correlation between OG density and gain frequency ( ρ  = 0.44, adjusted p  = 0.012). Negative correlation between OG density and loss frequency ( ρ  = − 0.28, adjusted p  = 0.13). Positive correlation between CCL expression and gain frequency ( ρ  = 0.53, adjusted p  = 0.002). Negative correlation between CCL expression and loss frequency ( ρ  = − 0.6, adjusted p  = 0.0006). Positive correlation between essential gene density and gain frequency ( ρ  = 0.18, adjusted p  = 0.33). Negative correlation between essential gene density and loss frequency ( ρ  = − 0.17, adjusted p  = 0.32)

We next used SHAP to assess the contribution of each feature to each of the models. TSG density and OG density remained the top contributing features for the gain model. Consistent with our results in primary tumors, the contribution of TSG density was much stronger than that of OG density, confirming the role of negative selection (Fig.  3 B,C). In the loss model, the ranking of top features was slightly different than in primary tumors (Fig.  3 D). Expression in CCL was the top feature, such that recurrently lost chromosome-arms were associated with lower gene expression in neutral cases. OG density was one of the strongest contributing features for the loss model whereas TSG density had weaker contribution, again in line with negative selection playing an important role in shaping cancer aneuploidy landscapes (Fig.  3 D,E). Certain features of normal tissues were also highly ranked. The contribution of essential gene density was also consistent with its impact in primary tumors (Fig.  3 B,C).

As with the primary tumors, correlation analyses supported the contributions of the different features. CCL expression was highly correlated with chromosome-arm gain and anticorrelated with chromosome-arm loss ( ρ  = 0.54, adjusted p  = 0.02, and ρ  = − 0.6, adjusted p  = 0.0006, respectively; Fig.  3 F). Negative correlations were also observed between TSG density and gain frequency ( ρ  = − 0.37, adjusted p  = 0.04, Spearman correlation; Fig.  3 F) and between OG density and loss frequency ( ρ  = − 0.28, adjusted p  = 0.1, Spearman correlation; Fig.  3 F). Altogether, these results indicate that despite the continuous evolution of aneuploidy throughout CCL culture propagation [ 38 ], similar features drive aneuploidy recurrence patterns in primary tumors and in CCLs.

Chromosome 13q aneuploidy patterns are tissue-specific, and KLF5 is a driver of 13q gain in colorectal cancer

In human cancer, a chromosome-arm is either recurrently gained across cancer types or it is recurrently lost across cancer types, but rarely is a chromosome-arm both gained in some cancer types and lost in others [ 4 , 5 ]. An intriguing exception is chr13q. Of all chromosome-arms, chr13q is the chromosome-arm with the highest density of tumor suppressor genes (Fig.  2 E). It is therefore not surprising that chr13q is recurrently lost across multiple cancer types (with a median of 30% of the tumors losing one copy of 13q across cancer types) [ 4 , 5 ]. Interestingly, however, chr13q is recurrently gained in human colorectal cancer (in 58% of the samples), suggesting that it can confer a selection advantage to colorectal cells in a tissue-specific manner. Indeed, when comparing colorectal tumors and colorectal cancer cell lines against all other cancer types, chr13q was the top differentially affected chromosome-arm (Fig.  4 A,B). We therefore set out to study the basis for this unique tissue-specific aneuploidy pattern.

KLF5 is a potential driver of chromosome 13q gain in human colorectal cancer. A Comparison of the prevalence of chromosome-arm aneuploidies in colorectal tumors against all other tumors (left) and colorectal cancer cell lines against all other cancer cell lines (right). On the right side are the aneuploidies that are more common in colorectal cancer, and on the left side are the ones that are less common in colorectal cancer. Chromosome-arm 13q (in red) is the top differential aneuploidy in colorectal cancer. B Comparison of the prevalence of 13q aneuploidy between colorectal tumors and all other tumors (left) and between colorectal cancer cell lines and all other cancer cell lines (right). ****, p  < 0.0001 and ****, p  < 0.0001; Chi-square test. C Genome-wide comparison of differentially essential genes between colorectal cancer cell lines ( n  = 85) and all other cancer cell lines ( n  = 1407). On the right side are the genes that are more essential in other cancer cell lines, and on the left side are those that are more essential in colorectal cancer, based on a genome-wide CRISPR/Cas9 knockout screens [ 39 ]. The x -axis presents the effect size (i.e., the differential response between colorectal cell lines and other cell lines), and the y -axis presents the significance of the difference (-log10( p -value)). KLF5 (in red) is the second most differentially essential gene in colorectal cancer cell lines. D Comparison of the sensitivity to CRISPR knockout of KLF5 between colorectal cancer cell lines ( n  = 59) and all other cancer cell lines ( n  = 1041). ****, p  < 0.0001; two-tailed Mann–Whitney test. E Genome-wide comparison of differentially expressed genes between colorectal tumors ( n  = 434) and all other tumors (on the left, n  = 11,060) and between colorectal cancer cell lines ( n  = 85) and all other cancer cell lines (on the right, n = 1407). On the right side are the genes that are over-expressed in colorectal cancer and on the left side are those that are over-expressed in other cell lines. KLF5 (in red) significantly over-expressed in colorectal cancer. F Comparison of KLF5 mRNA levels between colorectal tumors ( n  = 434) and all other tumors on the left ( n  = 11,060) and between colorectal cancer cell lines ( n  = 85) and all other cancer cell lines (on the right, n  = 1407). ****, p  < 0.0001; two-tailed Mann–Whitney test. G Correlation between KLF5 mRNA expression and the sensitivity to KLF5 knockdown, showing that higher KLF5 expression is associated with increased sensitivity to its RNAi-mediated knockdown. ρ  = − 0.39, p  = 0.01; Spearman correlation. H Comparison of KLF5 mRNA levels between DLD1-WT (without trisomy of chromosome 13) and DLD1-Ts13 (with trisomy of chromosome 13) colorectal cancer cells. **, p  = 0.0025; one-sample t -test. I Representative images of DLD1-WT and DLD1-Ts13 cells treated with siRNA against KLF5 . DLD1-Ts13 cells proliferated more slowly, as previously reported, but were more sensitive to the knockdown after accounting for their basal proliferation rate. Cell masking (shown in yellow) was performed using live cell imaging (IncuCyte) following 72 h of treatment. Scale bar 400µm. J Quantification of the relative response to KLF5 knockdown between DLD1-WT and DLD1-Ts13, as evaluated by quantifying cell viability in cells treated with siRNA against KLF5 versus a control siRNA for 72 h. n  = 3 independent experiments. *, p  = 0.0346; one-sided paired t -test

We performed a genome-wide comparison of differentially essential genes between colorectal cell lines and all other cell lines. The two top genes, which are much more essential in colorectal cancer cells than in other cancer types, were CTNNB1 and KLF5 (Fig.  4 C). Of particular interest is KLF5 , which is located on chr13q and colorectal cancer cell lines are significantly more sensitive to its knockout (Fig.  4 D). KLF5 was reported to be tumor-suppressive in the context of several cancer types, such as breast and prostate [ 40 , 41 ]. In colon cancer, however, not only is KLF5 important for tissue identity [ 42 ], but it was also reported to be haploinsufficient [ 43 ], potentially explaining why loss of chr13q is so rare in colorectal cancer. In line with a potential driving role in the recurrence of chr13q gain in colorectal cancer, KLF5 was among the most significantly overexpressed genes in colorectal tumors and in colorectal cell lines versus all other cancer types (Fig.  4 E,F). Furthermore, KLF5 expression levels correlated with the cells’ sensitivity to its knockdown (Fig.  4 G). To confirm the association between chr13q gain and KLF5 expression and dependency, we next turned to an isogenic system of human colon cancer cells (DLD1) into which trisomy 13 had been introduced (DLD1-Ts13) [ 44 ]. Using this unique experimental system, we confirmed that trisomy 13 results in overexpression of KLF5 (Fig.  4 H) and increased sensitivity to its siRNA-mediated genetic depletion (Fig.  4 I,J and Additional file 1 : Fig. S12, Additional file 1 : Fig. S13). This differential response was specific to KLF5 , as the trisomy did not affect the sensitivity of the cells to a control siRNA (Additional file 1 : Fig. S14), to knockdown of an unrelated gene residing on chr13q ( NEK3 ; Additional file 1 : Fig. S15), or to knockdown of another transcription factor that plays a role in colon development and is located on another chromosome ( TTC7A , located on chr2p; Additional file 1 : Fig. S16). We, therefore, propose that KLF5 contributes to the uniquely variable pattern of chr13q aneuploidy across cancer types.

Paralog compensation is an important feature shaping tissue-specific aneuploidy patterns

One of the topmost contributing features to the chromosome-arm loss model in primary tumors and in CCLs, as well as to the whole-chromosome loss model, was paralog compensation. It was previously shown that while loss of genes with paralogs was less detrimental than loss of singleton genes [ 45 ], the impact of gene loss in a specific condition depends on the expression level of its paralog [ 46 ]. The paralog compensation feature was therefore designed to quantify the expression ratio between two paralogs. Specifically, higher values of this feature for a given gene correspond to a higher expression of the paralog relative to the gene ( Methods ). Previous studies of hereditary disease genes showed that lower paralog compensation in a tissue was associated with disease manifestation in that tissue [ 31 , 32 ]. Paralog compensation was also shown in cancer tissues: In CCLs, essentiality of a gene was decreased with an increased expression of its paralog [ 27 , 46 , 47 ]. In primary tumors, paralog compensation was shown to be associated with increased prevalence of non-synonymous mutations [ 48 ] and to correlate with the prevalence of homozygous gene deletion [ 49 ]. However, the contribution of paralog compensation to aneuploidy has not been studied to date.

Paralog compensation ranked fourth and sixth in the loss models of primary tumors and CCLs, respectively (Fig.  2 C, Fig.  3 D). In both, chromosome-arm loss was associated with higher paralog compensation, suggesting that loss is facilitated by higher relative expression of paralogs (Fig.  2 D, Fig.  3 E). We also analyzed the correlations between the frequency of chromosome-arm loss and paralog compensation ( Methods , Fig.  5 A). Indeed, the frequency of chromosome-arm loss was positively correlated with paralog compensation in both primary tumors and in CCLs ( ρ  = 0.26 and ρ  = 0.46, respectively, Spearman correlation; Fig.  5 A).

Paralog compensation is an important feature shaping tissue-specific aneuploidy patterns. A The correlation between paralog compensation values and loss frequency of chromosome arms in primary tumors (left, ρ  = 0.26, adjusted p  = 0.18, Spearman correlation) and in CCLs (right, ρ  = 0.46, adjusted p  = 0.01, Spearman correlation). B A view into the aneuploidy patterns of paralogs of recurrently lost genes. Recurrently lost genes were divided into essential, intermediate, and non-essential groups. Paralogs of essential genes were more frequently gained, whereas paralogs of non-essential genes were more frequently lost. C Genome-wide comparison of differentially essential genes in colorectal cell lines with chr13q gain ( n  = 39) versus chr13q-WT colorectal cell lines ( n  = 25). On the right side are the genes that are more essential in chr13q-WT cells, and on the left side those that are more essential in chr13q-gain cells, based on a genome-wide CRISPR/Cas9 knockout screens [ 39 ]. The x -axis presents the effect size (i.e., the differential response between chr1q-WT and chr13q-gain colorectal cell lines) and the y -axis presents the significance of the difference (-log10(p-value)). UCHL1 (in red) is one of the top genes identified to be more essential in chr13q-WT cells. D Comparison of the sensitivity to CRISPR knockout of UCHL1 between colorectal cell lines with ( n  = 28) and without chr13q gain ( n  = 16). ***, p  = 0.0003; two-tailed Mann–Whitney test. E Comparison of UCHL3 mRNA expression between colorectal cell lines with ( n  = 34) and without chr13q gain ( n  = 23). ****, p  < 0.0001; two-tailed Mann–Whitney test. F Correlation between UCHL3 mRNA expression and the sensitivity to UCHL1 knockout, showing that higher UCHL3 mRNA levels are associated with reduced sensitivity to UCHL1 knockout. ρ  = 0.28, p  = 0.041; Spearman correlation. G Comparison of the prevalence of chr4p loss between human primary colorectal tumors with and without chr13q gain. ****, p  < 0.0001, Chi-square test. H Comparison of the prevalence of chr4p loss between human colorectal cancer cell lines with and without chr13q gain. ****, p  < 0.0001, Chi-square test

Next, we tested whether paralog compensation, namely gain or overexpression of paralogs, could indeed facilitate chromosome-arm loss. We started by grouping genes in recurrently lost chromosome-arms into essential, intermediate, or non-essential, according to their essentiality in CCLs [ 27 ] ( Methods ). We then associated each gene with the aneuploidy status of the chromosome-arm of its paralog, namely whether the chromosome-arm of the paralog was gained, lost, or remained neutral in the corresponding CCL ( Methods , Additional file 1 : Fig. S17A). The fraction of genes with paralogs on neutral chromosome-arms was similar in all essentiality groups (Fig.  5 B). In contrast, the fraction of gained paralogs was highest in the group of essential genes and lowest in the group of non-essential genes. This suggests that the loss of essential genes is more likely accompanied by the gain of their paralogs. Likewise, the fraction of lost paralogs was lowest in the group of essential genes and highest in the group of non-essential genes ( p  = 2.38e − 24, Chi-square test; Fig.  5 B). This suggests that the loss of essential genes is less likely to be accompanied by the loss of their paralog. The same trend was shown upon comparing the distribution of essentiality scores between genes with gained paralogs versus genes with lost paralogs ( p  = 9.2e − 16, KS test; Additional file 1 : Fig. S17B). Hence, paralog compensation can facilitate chromosome-arm loss.

Next, we decided to identify a specific example. In human colon cancer, the long arm of chromosome 13 (chr13q) is commonly gained, as described above, whereas the short arm of chromosome 4 (chr4p) is commonly lost [ 5 , 37 ]. We analyzed the association between chr13q-residing genes and the essentiality of their paralogs, revealing UCHL3 (chr13q)- UCHL1 (chr 4p) as the most significant correlation (Additional file 6 : Table S5 and Fig.  5 C). Human colon cancer cell lines with chr13q gain were less sensitive to CRISPR/Cas9-mediated knockout of UCHL1 (Fig.  5 D). Consistently, chr13q-gained cell lines had significantly higher mRNA levels of UCHL3 (Fig.  5 E), and the expression of UCHL3 was significantly correlated with the essentiality of UCHL1 (Fig.  5 F). We hypothesized that the relationship between these paralogs may affect the co-occurrence patterns of the chromosome-arms on which they reside. Indeed, both in primary human colon cancer and in colon cancer cell lines, loss of chr4p was significantly more prevalent when chr13q was gained (Fig.  5 G,H). Together, these results demonstrate that paralog compensation can be affected by—and contribute to the shaping of—aneuploidy patterns.

Recurrent aneuploidy patterns are an intriguing phenomenon that is only partly understood. Several previous studies characterized the unique patterns of aneuploidy in cancer [ 4 , 5 , 50 ] or attempted to identify the driving role of a specific aberration in a specific cancer context [ 9 , 51 , 52 , 53 , 54 ]. Attempts to explain copy number patterns in cancer focused on specific pre-defined aspects, such as the specific boundaries of the alterations [ 15 ], the densities of OGs and TSGs on the aberrant chromosomes [ 6 , 7 ] or the gene expression changes that they induce [ 8 ], and these aspects were interrogated using statistical methods and correlation analyses. Here, in contrast, we studied this phenomenon using an unbiased ML-based approach. As with other ML applications, it allowed us to study multiple aspects simultaneously. Yet, unlike classical ML-based studies that mainly aim to improve prediction, for example by using deep learning to predict gene dependency in tumors [ 21 ], our focus was on interpretability. In fact, we built chromosome-arm gains and loss models only to then identify factors that shape aneuploidy patterns. Interpretable ML was recently applied to reveal genetic attributes that contribute to the manifestation of Mendelian diseases [ 55 ]. In this study, we applied interpretable ML for the first time in the context of aneuploidy and at chromosome-arm resolution.

The capability of ML to concurrently assess multiple features opened the door for assessing the relevance of features that have not been rigorously studied to date, such as paralog compensation. Yet, ML has its limitations. Mainly, the number of features that could be analyzed depends on the size of the labeled dataset [ 56 ], which, in aneuploidy, was restricted by the number of chromosome-arms and cancer types. We therefore analyzed 20 types of features and tested linear regression and tree-based ML methods, which, unlike deep learning, are suitable for this size of data. Following prediction, our main goal was to assess the relative contribution of each feature to the model’s decision and its directionality using SHAP. Nevertheless, SHAP results should be interpreted with caution. First, SHAP assumes feature independence, although features could be correlated with each other or confounded. Importantly, we found that only a small subset of features correlated with each other, and they did not include the topmost contributing features (Additional file 1 : Fig. S3A). Second, the top contributing factors could be correlated with prediction strength, rather than being causal. Lastly, due to the hierarchical nature of decision trees, features that are located low in the decision tree explain only a small fraction of the cases. To estimate feature contribution and directionality more broadly, we explicitly correlated feature values with chromosome-arm gain and loss frequency, finding support for their broad relevance (Fig.  2 E, Additional file 1 : Fig. S6). We also conducted multiple analyses that tested the robustness of the results to the models’ construction schemes (Additional file 1 : Fig. S7, S8), the modeled events (one event versus rest, Additional file 1 : Fig. S9; whole-chromosome, Additional file 1 : Fig. S11), or to a subset of the chromosome-arm and cancer type instances (Additional file 1 : Fig. S10). The different analyses repeatedly revealed the same factors at play, supporting the reliability of our results.

The features that we studied included known and previously underexplored attributes of chromosome-arms, healthy tissues and cancer cells (Fig.  1 A,B). OG and TSG densities, which have previously been observed to be enriched on gained and lost chromosome-arms, respectively [ 6 , 7 ], were top contributing features in both models, thereby supporting the validity of our approach (Fig.  2 A,C). In the gain model in particular, their contribution was over 2.6 and 5 times stronger, respectively, than any other feature (Fig.  2 A). As our TSG and OG features were cancer-independent, their importance may explain the observation that certain chromosome-arms tend to be either gained or lost across multiple cancer types [ 4 , 5 ]. Their relative contribution, however, was surprising. In both models, negative associations were much stronger than positive associations: OG density contributed to chromosome-arm loss more than TSG density, implying that it was more important to maintain OGs than to lose TSG (Fig.  2 B,D). The reciprocal relationship was true for chromosome-arm gain, as it was more important to maintain TSGs than to gain OGs (Fig.  2 A,C). These results were validated using correlation analyses (Fig.  2 E) and were recapitulated in CCLs (Fig.  3 ) and in the analysis of whole-chromosome gains and losses (Additional file 1 : Fig. S11). Together, they highlight the importance of negative selection for shaping cancer aneuploidy landscapes [ 1 , 15 ].

A known factor that contributed to both models was gene expression in primary tumors (TCGA expression, Fig.  2 ) and in CCLs (CCL expression, Fig.  3 ). This result suggests that cancers tend to gain chromosome-arms that are enriched for highly-expressed genes and tend to lose chromosome-arms that are enriched for lowly expressed genes. A Similar trend was shown recently for gene expression in normal tissues [ 8 ]. Our approach was capable of comparing the relative contributions of both features. We found that the contribution of gene expression in normal tissue was lower than that in cancer tissues, as also evident by its lower correlation with the frequencies of chromosome-arm gains and losses (Additional file 1 : Fig. S6). Nevertheless, other features that were derived from gene expression in normal tissues ranked highly, such as the number of PPIs in the gain model and paralog compensation in the loss model, and hence expression in normal tissues is also important (Fig.  2 ).

A previously under-explored feature that we considered was paralog compensation. Paralog compensation was shown to play a role in the manifestation of Mendelian and complex diseases [ 31 , 32 ] and in the dispensability of genes in tumors [ 48 , 49 ] and CCLs [ 27 , 46 , 47 ], but was not studied in the context of aneuploidy. Here, paralog compensation was among the top contributors to the loss model (Fig.  2 C, Fig.  3 D). The directionality of this feature and correlation analyses showed that, relative to genes located on neutral chromosome-arms, genes located on lost chromosome-arms tend to have higher compensation by paralogs (Fig.  5 A). This suggests that chromosome-arm loss is facilitated, or better tolerated, through paralogs’ expression. We also showed that the more essential recurrently lost genes are, the more likely they are to be associated with gains of paralog-bearing chromosome-arms (Fig.  5 B). We further demonstrated this for a specific example (the UCHL3 - UCHL1 paralog pair; Fig.  5 ). Overall, our analysis reveals that compensation between paralogs through expression or chromosome-arm gain plays an important role in shaping the landscape of chromosome-arm loss.

Combining the different results, our models reveal a previously under-appreciated role for negative selection in driving human cancer aneuploidy. This was evident by the tendency not to lose chromosome arms with high OG density, high frequency of essential genes, or low compensation by paralogs, and not to gain chromosome arms with high TSG density (Fig.  6 ). Previous studies have shown that positive selection outweighs negative selection in shaping the point mutation landscape of human tumors [ 14 ]. However, the strong fitness cost associated with aneuploidy suggests that the aneuploidy landscape of tumors might be strongly affected by negative selection as well (reviewed in [ 1 ]). Interestingly, evidence for the involvement of negative selection in shaping the copy number alteration (CNA) landscapes of tumors has been proposed in a recent study that analyzed CNA length distributions across human tumors [ 15 ]. Our study thus lends further independent support to the importance of negative selection in shaping the landscape of aneuploidy across human cancers (Fig.  6 ).

A schematic presentation of the results of the study. Cancer evolution is shaped by negative and positive selection leading to enrichment or depletion of cells with distinct aneuploidy patterns. In the gain model (left), main contributors to positive selection of gained chromosome arms are: (1) high oncogene density, (2) high expression of genes in the cancer tissue, and (3) high essential gene density. A major contributor to negative selection is high tumor suppressor gene density. Importantly, the density of TSGs is more important than the density of OGs for predicting chromosome-arm gains. In the loss model (right), a main contributor to positive selection of lost chromosome arms is high tumor suppressor gene density. Major contributors to negative selection are high oncogene density, high expression of genes in the cancer tissue, low compensation by paralogs, and high density of essential genes. In both models, the features associated with negative selection have higher overall contribution than features associated with positive selection. The thickness of the borders of the boxes reflects the relative contribution of the features to the model

Our genome-wide analysis could be expanded in future studies in several ways: (1) While we focused on the top-contributing features, other features, such as PPIs that contributed to both gain and loss models, are also relevant and remain to be studied in depth. (2) It will be interesting to consider additional types of aneuploidy, such as tetrasomies, and explore how whole-genome doubling affects the importance of the features in shaping the aneuploidy landscapes of tumors. (3) Tumors often exhibit heterogeneous (mosaic) aneuploidy patterns [ 57 , 58 , 59 , 60 ]. Our analyses were entirely based on bulk-population data, and our results therefore describe the selection pressures that shape the landscape of clonal aneuploidies. As more single-cell omics data becomes available, it will be interesting to also study the selection pressures that shape subclonal aneuploidy patterns. (4) Aneuploidies do not always arise independently, so that chromosome-arm events can co-occur or be mutually exclusive [ 37 ]. We show that only a small fraction of chromosome-arm events co-occur (Additional file 7 : Table S6), suggesting that their effect on our models would likely be small. Nonetheless, considering co-occurrence patterns could further refine the models.

Lastly, we explored one example of a unique aneuploidy pattern (chr13q) that is recurrently altered in opposite directions in different cancer types. In line with tumor suppressors and oncogenes being a major feature explaining aneuploidy patterns, we identified KLF5 as a colorectal-specific dependency gene. Using an isogenic system of colorectal cancer cells with/without gain of chr13, we experimentally demonstrated that this aneuploidy is associated with increased expression and increased essentiality of KLF5 . The finding that colorectal cells with trisomy 13 are more sensitive to KLF5 depletion suggests positive selection for its gain, on top of a potential negative selection against a deleterious loss. We therefore propose that KLF5 might explain why chr13q is commonly gained and rarely lost in colorectal cancer, unlike its recurrent loss across multiple other cancer types.

Overall, our study provides novel insights into the forces that shape the tissue-specific patterns of aneuploidy observed in human cancer and demonstrates the value of applying ML approaches to dissect this complicated question. Our results suggest that aneuploidy patterns are shaped by a combination of tissue-specific and non-tissue-specific factors. Negative selection in general and paralog compensation in particular play a major role in shaping the aneuploidy landscapes of human cancer and should therefore be computationally modeled and experimentally studied in the research of cancer aneuploidy.

Chromosome-arm aneuploidy patterns per cancer

Chromosome-arm events per cancer were defined according to GISTIC2.0 [ 24 ] for all (39) chromosome-arms in 24 cancer types for which data of the normal tissue of origin was available from GTEx [ 25 ]. GISTIC2.0 computed the probability of chromosome-arm events by comparing the observed frequency to the expected rate, while considering chromosome-arm length and other parameters [ 61 ]. A chromosome-arm was considered as gained or lost in a specific cancer if the q -value of its amplification or deletion, respectively, was lower than 0.05. Otherwise, the chromosome-arm was considered as neutral. In case the q -value of both amplification and deletion was lower than 0.05, decision was made based on the lower q -value. In case of a tie, the more frequent event was selected. GISTIC2.0 data, including q -values and frequencies, were downloaded from ref. [ 62 ]. Lastly, we analyzed co-incidence probabilities of chromosome-arm events per cancer. Co-incidence probabilities for chromosome-arms and cancers in our dataset were obtained from [ 37 ].The median fraction of chromosome-arm pairs with significant co-incidence per cancer was 2.05% (Additional file 7 : Table S6). Hence, the impact of co-incidence on the models is expected to be small.

We also carried separate analyses of gain and loss of whole-chromosomes. A whole-chromosome was considered as gained if the q -value of the amplification of its two arms was lower than 0.05. Likewise, a whole-chromosome was considered as lost if the q -value of the deletion of its two arms was lower than 0.05.

Construction of a features dataset of instances of chromosome-arm and cancer type pairs

For each chromosome-arm and cancer, we created features that were inferred from data of chromosome-arms, genes, cancer tissues and CCLs, and normal tissues (Fig.  1 B, Additional file 2 : Table S1). A schematic pipeline of the dataset construction appears in Additional file 1 : Fig. S1. The different types of features are described below.

Features of chromosome-arms

Each chromosome-arm was associated with three types of features, including oncogene density, tumor suppressor gene density, and essential gene density. Oncogene density and tumor suppressor gene density per chromosome-arm were obtained from Davoli et al. [ 6 ]. Data of essential genes was obtained from Nichols et al. [ 26 ], where a gene was considered essential if its essentiality probability was > 0.8. The density of essential genes per chromosome-arm was calculated as the fraction of essential genes out of the protein-coding genes on that chromosome-arm. Next, we associated each instance of chromosome-arm and cancer type with features of that chromosome-arm.

Features of cancer tissues

Each instance of chromosome-arm and cancer type was associated with four types of cancer-related features, including transcriptomics, essentiality by CRISPR or RNAi in CCLs, and cancer-specific density of essential genes. Transcriptomics was based on transcriptomic profiles of 33 cancer types from TCGA [ 63 ] that were obtained from GDC Xena Hub v18.0 (updated 2019–08-28). Per cancer, we associated each gene with its median expression level in samples of that cancer. To avoid expression bias due to chromosome-arm gain or loss, the median expression of each gene was computed from samples where the chromosome-arm harboring the gene was neutral according to Taylor et al. [ 5 ]. Essentiality by CRISPR was based on CRISPR screens of 24 CCLs from the DepMap portal version 21Q1. Essentiality by RNAi was based on RNAi data of 20 CCLs from DepMap [ 27 ]. In each of these datasets, the score of each gene indicated the change, relative to control, in the growth rate of the cell line upon gene inactivation via CRISPR or RNAi. Accordingly, genes with negative scores were essential for the growth of the respective cell line. We associated each gene with its median essentiality score based on either CRISPR or RNAi per cell line. To reflect gene essentiality more intuitively, we reversed the direction of the scores (multiplied them by − 1), so that more essential genes had higher scores. To avoid bias due to chromosome-arm gain or loss, the median essentially of each gene was computed from samples where the chromosome-arm harboring the gene was neutral [ 5 ]. Cancer-specific density of essential genes was calculated as the fraction of essential genes (CRISPR-based essentiality score > 0.5) in a given CCL out of the protein-coding genes residing on that chromosome-arm.

Features of normal tissues

Each instance of chromosome-arm and cancer type was associated with 13 types of features that were derived from [ 55 ]. We associated each cancer type with the normal tissue in which it originates (Additional file 2 : Table S1).

Transcriptomics

Data of normal tissues included transcriptomic profiles of 54 adult human tissues measured via RNA-sequencing from GTEx v8 [ 25 ]. Each gene was associated with its median expression in each adult human tissue. Genes with median TPM > 1 in a tissue were considered as expressed in that tissue.

Tissue-specific genes

Per gene, we measured its expression in a given tissue relative to other tissues using z -score calculation. Genes with z -score > 2 were considered tissue-specific. Lastly, we associated each chromosome-arm and tissue with the density of tissue-specific genes.

PPI features

Each gene was associated with the set of its PPI partners. We included only partners with experimentally detected interactions that were obtained from MyProteinNet web-tool [ 64 ]. Per each tissue, we associated each gene with four PPI-related features:

“Number PPIs” was set to the number of PPI partners that were expressed in that tissue.

“Number elevated PPIs” relied on preferential expression scores computed according to [ 28 ] and was set to the number of PPI partners that were preferentially expressed in that tissue (preferential expression > 2, [ 65 ].

“Number tissue-specific PPIs” was set to the number of PPI partners that were expressed in that tissue and in at most 20% of the tissues.

“Differential PPIs” relied on differential PPI scores per tissue from The DifferentialNet Database [ 28 ] and was set to gene’s median differential PPI score per tissue. If the gene was not expressed in a given tissue, its feature values in that tissue were set to 0.

Differential process activity features

Differential process activity scores per gene and tissue were obtained from [ 30 ]. The score of a gene in a given tissue was set to the median differential activity of the Gene Ontology (GO) processes involving that gene. The differential activity was relative to the activity of the same processes in other tissues.

eQTL features

eQTLs per gene and tissue were obtained from GTEx [ 25 ]. Each gene was associated with the p -value its eGene in that tissue.

Paralog compensation features

Each gene was associated with its best matching paralog according to Ensembl-BioMart. Per tissue, the gene score was set to the median expression ratio of the gene and its paralog, as described in [ 31 , 32 ]. Accordingly, high values mark genes with low paralog compensation.

Development features

Transcriptomic data of seven human organs measured at several time points during development were obtained from [ 66 ]. We united time points into time periods including fetal (4–20 weeks post-conception), childhood (newborn, infant, and toddler), and young (school, teenager and young adult). Per organ, we associated each gene with its median expression level per period. Next, we created an additional feature that reflected the expression variability of each gene across periods.

Transforming gene features into chromosome-arm features

Some of the features described above referred to genes. To create chromosome-arm-based features, we grouped together genes that were located on the same chromosome-arm [ 67 ]. Next, to highlight differences between tissues, for each feature, we associated a gene with its value in that tissue relative to other tissues. Features that were already tissue-relative, including “Differential PPIs” and “Differential process activity,” were maintained. Other features were converted into tissue-relative values via a z -score calculation (see Eq.  1 ). Lastly, per feature, we ranked genes by their tissue-relative score and associated each chromosome-arm with the median score of the genes ranking at the top 10% (Additional file 1 : Fig. S2). Transcriptomic features in the testis and whole blood were highly distinct from other tissues; we normalized all transcriptomic features per tissue. To reflect paralog compensation more intuitively, we reversed the direction of the resulting features (multiplied them by − 1), so that genes with higher compensation had higher scores.

T denotes the set of tissues, G denotes the set of genes, v denotes the value of the feature, and σ denotes the standard deviation.

Construction of the final dataset

The features described above referred to chromosome-arms in cancers, CCLs, and normal tissues. To create chromosome-arm features per cancer, we associated each cancer with the chromosome-arm features of its tissue of origin and CCL (Additional file 2 : Table S1). For features of normal tissues where multiple sub-regions were sampled (e.g., skin sun-exposed and not sun-exposed, or brain sub-regions), we set the chromosome-arm values to their median across sub-regions. The final dataset contained features for all 936 instances of 39 chromosome-arms and 24 cancers for which the cancer’s normal tissue of origin was available in GTEx [ 25 ] (Additional file 2 : Table S1). We assessed the similarity between every pair of features using Spearman correlation (Additional file 1 : Fig. S3A). We assessed whether chromosome-arm and cancer type instances had similar feature values using PCA (Additional file 1 : Fig. S3C).

ML application to model chromosome-arm and cancer aneuploidy

Below we describe the ML method used for aneuploidy classification and the SHAP (SHapley Additive exPlanations) analysis of feature importance that was used to interpret the resulting models.

Aneuploidy ML classification models

We constructed two ML models: a gain model that compared between gained and unchanged (neutral) chromosome-arms and a loss model that compared between lost and unchanged (neutral) chromosome-arm.

ML comparison and implementation

Per model, we tested several ML methods, including logistic regression, XGBoost, gradient boosting, random forest, and bagging. All ML methods were implemented using the Scikit-learn python package [ 68 ], except for XGB, which was implemented using the Scikit-learn API of the XGBoost package [ 69 ]. To assess the performance of each model, we used tenfold cross-validation. Then, we calculated the au-ROC and the au-PRC. Each point on the curve corresponded to a particular cutoff that represented a trade-off between sensitivity and specificity and between precision and recall, respectively.

SHAP analysis of feature importance

To measure the contribution and importance of the different features, we used SHAP algorithm [ 70 ]. SHAP is a game-theoretic approach to explain the output of ML models: for each feature, SHAP assigns a contribution value to each instance of chromosome-arm and cancer type. It then estimates the contribution of that feature to the model by the average absolute SHAP values of all instances. Per model, we created the SHAP plots corresponding to feature contribution and directionality. In both, features were ordered by their importance to the model (top meaning most contributing). We also visualized the directionality of each feature using arrows in the SHAP bar plot. The direction of the arrow showed whether the highest values of that feature (top 50%) corresponded to a chromosome-arm event (gain or loss, right) or to neutrality (left).

Robustness analyses

We analyzed the robustness of the models and their interpretation with respect to internal parameters used to generate the features and the hyperparameters of the ML models. For feature generation, we used top 10% of genes with highest values to calculate each gene-based chromosome-arm feature. We therefore reconstructed features by also using the top 1%, 5%, 15%, and 20% of the genes. We then assessed the performance of each method using tenfold cross-validation. In all cases, method performance was similar (Additional file 3 : Table S2). SHAP analysis of the best performing method per case showed similar results with respect to the topmost contributing features and their directionality (Additional file 1 : Fig. S7). For robustness to parameter choices, we tuned the hyperparameters per ML method separately for the gain model and for the loss model, and repeated model construction and interpretation. Tuning was optimized for precision and performed using the “RandomizedSearch” function of sklearn python package, with number of sampled parameters (iterations, n_iter) set to 200 and tenfold cross-validation. Best parameters per method and model and their performance appear in Additional file 1 : Fig. S8A,B. Performance was only slightly improved, and interpretation of the best performing models revealed similar results (Additional file 1 : Fig. S8C).

Lastly, we tested if the most important features per model were driven by a small subset of chromosome-arm and cancer type instances. For that, per model, we focused on the five most important features and identified instances with the top contributions to these features. An instance was considered a top contributor if its SHAP value for that feature that was among the 10% positive SHAP values (i.e., was a potential driver of the gain or loss) or the 10% negative SHAP values (i.e., was a potential driver of neutrality). The SHAP value for each instance and feature appears in Additional file 4 : Table S3. The list of instances and the features that they contributed to appears in Additional file 5 : Table S4. We then associated each instance with the number of features in which it was a top contributor. Next, we tested the impact of the strongest potential driver instances on the five most important features of the model. This was done by excluding from the dataset chromosome-arm and cancer type instances that were top contributors to at least three of the five features and repeating the construction and interpretation of each model using the revised dataset.

Correlation analysis

We correlated between feature values and the frequency of chromosome-arm gain or loss. The frequency of chromosome-arm gain/loss in cancers was obtained from GISTIC2.0 [ 24 ]. The frequency of chromosome-arm gain/loss in CCLs were obtained from [ 37 ]. Per chromosome-arm, its gain (loss) frequency was set to the median gain (loss) across cancers or CCLs. The feature value was set to median across cancers or CCLs. We used Spearman correlation, and p -values were adjusted using Benjamini–Hochberg procedure [ 71 ].

Paralog compensation analysis

For each cancer type and chromosome-arm, we considered all paralog pairs in which one of the genes resides on that chromosome-arm. We focused on recurrently lost genes per cancer type as defined by GISTIC2.0 [ 24 ]. We divided those genes by their minimal CRISPR essentiality score in CCLs that match the same cancer type (Additional file 2 : Table S1). Genes with a score ≤ − 0.5 were considered essential, and genes with a score ≥ − 0.3 were considered non-essential. Other genes were considered intermediate. Per gene, we checked whether its paralog was recurrently gained, lost, or neutral, in the same cancer, as detailed in Additional file 1 : Fig. S17A.

Chromosome-arm aneuploidy patterns in CCLs

Aneuploidy patterns were available for all (39) chromosome-arms in 14 CCLs from [ 37 ]. A chromosome-arm was considered as gained or lost in a CCL if the q -value of its amplification or deletion, respectively, was smaller than 0.15 (in case of ties, decision was made based on the lower q -value). In case of equal significant q -values, a chromosome-arm was considered as gained or lost based on their frequencies. Otherwise, the chromosome-arm was considered as neutral.

Construction of a feature dataset of instances of chromosome-arm and CCL pairs

The features dataset was similar to the dataset created for cancers, with the following exceptions. In features of cancer tissues, we replaced the transcriptomic features of cancers with transcriptomic features of CCLs. We obtained transcriptomic data of 25 CCLs from DepMap [ 27 ] and constructed the feature values per chromosome-arm and CCL as described above per chromosome-arm and cancer. Development features were removed since only a small number of CCLs had a matching organ. The final dataset contained features for all instances of 39 chromosome-arms and 10 CCLs for which the cancer’s normal tissue of origin was available in GTEx.

Cell culture

DLD1-WT cells and DLD1-Ts13 cells were cultured in RPMI-1640 (Life Technologies) with 10% fetal bovine serum (Sigma-Aldrich) and 1% penicillin–streptomycin-glutamine (Life Technologies). Cells were incubated at 37 °C with 5% CO2 and passaged twice a week using Trypsin–EDTA (0.25%) (Life Technologies). Cells were tested for mycoplasma contamination using the MycoAlert Mycoplasma Detection Kit (Lonza), according to the manufacturer’s instructions.

Cells were harvested using Bio-TRI® (Bio-Lab) and RNA was extracted following manufacturer’s protocol. cDNA was amplified using GoScript™ Reverse Transcription System (Promega) following manufacturer’s protocol. qRT-PCR was performed using Sybr® green, and quantification was performed using the ΔCT method. The following primer sequences were used: human KLF5 , forward, 5' ACACCAGACCGCAGCTCCA 3' and reverse 5' TCCATTGCTGCTGTCTGATTTGTAG 3', human NEK3 , forward, 5’ TACCCAAATGTGCCTTGGAG 3’, reverse 5’ ATCGGATTGGAGAGAAGACG 3’, human TTC7A , forward 5’ CTCGTGACCTGCAGACAAG 3’, reverse 5’ GGCTCCTAAAGTCTCCCAGC 3’.

siRNA transfection

For siRNA experiments, cells were plated in 96-well plates at 6000 cells per well and treated with compounds 24 h later. The cells were transfected with 15 nM siRNA against KLF5 (ONTARGETplus SMART-POOL®, Dharmacon) or with a control siRNA at the respective concentration (ONTARGETplus SMART-POOL®, Dharmacon) using Lipofectamine® RNAiMAX (Invitrogen) following the manufacturer’s protocol. Alternatively, for siRNA experiments against NEK3 and TTC7A , and for additional KLF5 experiments, cells were plated in 6-well plates at 400,000 cells per well and treated with compounds 24 h later. The cells were transfected with 30 nM against NEK3 and TTC7A or with 5 nM and 10 nM against KLF5 ; 48 h post seeding, the cells were split and plated in 96-wells at 10,000 cells per well. The effect of the knockdown against KLF5 , NEK3 , or TTC7A on cell viability/proliferation was measured by live cell imaging using Incucyte® (Satorius) or by the MTT assay (Sigma M2128) at 72 h (or at the indicated time point) post-transfection; 500 µg/mL MTT salt was diluted in complete medium and incubated at 37°C for 2 h. Formazan crystals were extracted using 10% Triton X-100 and 0.1 N HCl in isopropanol, and color absorption was quantified at 570 nm and 630 nm (Alliance Q9, Uvitec).

Cancer cell line and tumor data analysis

mRNA gene expression values, arm-level CNAs, CRISPR, and RNAi dependency scores (Chronos and DEMETER2 scores, respectively) were obtained from DepMap 22Q4 release ( www.depmap.org ). Effect size, p -values, and q -values (Fig.  4 A,C,E, Fig.  5 C) were taken directly from DepMap and were calculated as described in Tsherniak et al. TCGA mRNA gene expression values were obtained using the Xena browser [ 63 ]. Tumor arm-level alterations were retrieved from Taylor et al. 2018, Cancer Cell. Effect size, Spearman’s R and p -values in Fig.  4 G and Fig.  5 F were calculated using R functions. All colorectal cancer cell lines ( n  = 85) and colorectal tumors ( n  = 434) were included in the analyses.

The analyses that led to our choice of the paralog pair UCHL3 - UCHL1 are summarized in Additional file 6 : Table S5. In the left column are the paralogs that reside on chr-13q, which is frequently gained; in the adjacent column are the respective paralogs that reside on commonly lost chromosomes. The following columns describe the Spearman correlation between each paralog pair and the respective p -value. The right-hand columns describe the effect size of chr-13q paralogs’ gene expression between CRC cell lines with and without chr13q gain. Our criteria for finding appropriate paralog pairs for further analysis were as follows: firstly, to have a high expression of the chr-13q paralogs in CRC cell lines. Secondly, we aimed to reach a significant correlation between chr13q-residing genes and the essentiality of their paralogs.

Statistical analyses

Statistical analysis was performed using GraphPad PRISM® 9.1 software. Details of the statistical tests were reported in figure legends. Error bars represent SD. All experiments were performed in at least three biological replicates.

Availability of data and materials

The code for all the analyses is available on GitHub [ 72 ]. The datasets that were processed to build the dataset for the ML methods are available on Zenodo [ 73 ]. This includes features of normal tissues that were extracted from TRACE [ 74 ], TCGA expression data of the different cancer types that were obtained from Xena [ 75 ], and CRISPR and RNAi datasets that were obtained from DepMap [ 76 ].

Ben-David U, Amon A. Context is everything: aneuploidy in cancer. Nat Rev Genet. 2020;21(1):44–62.

Article   CAS   PubMed   Google Scholar  

Shukla A, Nguyen THM, Moka SB, Ellis JJ, Grady JP, Oey H, et al. Chromosome arm aneuploidies shape tumour evolution and drug response. Nat Commun. 2020;11(1):449.

Article   CAS   PubMed   PubMed Central   Google Scholar  

Vasudevan A, Baruah PS, Smith JC, Wang Z, Sayles NM, Andrews P, et al. Single-Chromosomal gains can function as metastasis suppressors and promoters in colon cancer. Dev Cell. 2020;52(4):413–28 e6.

Ben-David U, Ha G, Tseng YY, Greenwald NF, Oh C, Shih J, et al. Patient-derived xenografts undergo mouse-specific tumor evolution. Nat Genet. 2017;49(11):1567–75.

Taylor AM, Shih J, Ha G, Gao GF, Zhang X, Berger AC, et al. Genomic and functional approaches to understanding cancer aneuploidy. Cancer Cell. 2018;33(4):676–89 e3.

Davoli T, Xu AW, Mengwasser KE, Sack LM, Yoon JC, Park PJ, et al. Cumulative haploinsufficiency and triplosensitivity drive aneuploidy patterns and shape the cancer genome. Cell. 2013;155(4):948–62.

Sack LM, Davoli T, Li MZ, Li Y, Xu Q, Naxerova K, et al. Profound tissue specificity in proliferation control underlies cancer drivers and aneuploidy patterns. Cell. 2018;173(2):499–514 e23.

Patkar S, Heselmeyer-Haddad K, Auslander N, Hirsch D, Camps J, Bronder D, et al. Hard wiring of normal tissue-specific chromosome-wide gene expression levels is an additional factor driving cancer type-specific aneuploidies. Genome Med. 2021;13(1):93.

Liu Y, Chen C, Xu Z, Scuoppo C, Rillahan CD, Gao J, et al. Deletions linked to TP53 loss drive cancer through p53-independent mechanisms. Nature. 2016;531(7595):471–5.

Zhou XP, Li YJ, Hoang-Xuan K, Laurent-Puig P, Mokhtari K, Longy M, et al. Mutational analysis of the PTEN gene in gliomas: molecular and pathological correlations. Int J Cancer. 1999;84(2):150–4.

Verhaak RG, Hoadley KA, Purdom E, Wang V, Qi Y, Wilkerson MD, et al. Integrated genomic analysis identifies clinically relevant subtypes of glioblastoma characterized by abnormalities in PDGFRA, IDH1, EGFR, and NF1. Cancer Cell. 2010;17(1):98–110.

Alfieri F, Caravagna G, Schaefer MH. Cancer genomes tolerate deleterious coding mutations through somatic copy number amplifications of wild-type regions. Nat Commun. 2023;14(1):3594.

Sheltzer JM, Amon A. The aneuploidy paradox: costs and benefits of an incorrect karyotype. Trends Genet. 2011;27(11):446–53.

Martincorena I, Raine KM, Gerstung M, Dawson KJ, Haase K, Van Loo P, et al. Universal patterns of selection in cancer and somatic tissues. Cell. 2017;171(5):1029–41 e21.

Shih J, Sarmashghi S, Zhakula-Kostadinova N, Zhang S, Georgis Y, Hoyt SH, et al. Cancer aneuploidies are shaped primarily by effects on tumour fitness. Nature. 2023;619(7971):793–800.

Zitnik M, Nguyen F, Wang B, Leskovec J, Goldenberg A, Hoffman MM. Machine learning for integrating data in biology and medicine: principles, practice, and opportunities. Inf Fusion. 2019;50:71–91.

Article   PubMed   Google Scholar  

Han Y, Yang J, Qian X, Cheng WC, Liu SH, Hua X, et al. DriverML: a machine learning algorithm for identifying driver genes in cancer sequencing studies. Nucleic Acids Res. 2019;47(8): e45.

Luo P, Ding Y, Lei X, Wu FX. deepDriver: predicting cancer driver genes based on somatic mutations using deep convolutional neural networks. Front Genet. 2019;10:13.

Mostavi M, Chiu YC, Chen Y, Huang Y. CancerSiamese: one-shot learning for predicting primary and metastatic tumor types unseen during model training. BMC Bioinformatics. 2021;22(1):244.

Article   PubMed   PubMed Central   Google Scholar  

Ramirez R, Chiu YC, Hererra A, Mostavi M, Ramirez J, Chen Y, et al. Classification of cancer types using graph convolutional neural networks. Front Phys. 2020;8:203.

Chiu Y-C, Zheng S, Wang L-J, Iskra BS, Rao MK, Houghton PJ, et al. Predicting and characterizing a cancer dependency map of tumors with deep learning. Science Advances. 2021;7(34):eabh1275.

Lundberg SM, Lee S-I. A unified approach to interpreting model predictions. Adv Neural Inf Process Syst. 2017;30(9):4768–77.

Google Scholar  

Rodriguez-Perez R, Bajorath J. Interpretation of compound activity predictions from complex machine learning models using local approximations and Shapley values. J Med Chem. 2020;63(16):8761–77.

Mermel CH, Schumacher SE, Hill B, Meyerson ML, Beroukhim R, Getz G. GISTIC2.0 facilitates sensitive and confident localization of the targets of focal somatic copy-number alteration in human cancers. Genome Biol. 2011;12(4):R41.

GTEx Consortium. The GTEx Consortium atlas of genetic regulatory effects across human tissues. Science. 2020;369(6509):1318–30.

Article   Google Scholar  

Nichols CA, Gibson WJ, Brown MS, Kosmicki JA, Busanovich JP, Wei H, et al. Loss of heterozygosity of essential genes represents a widespread class of potential cancer vulnerabilities. Nat Commun. 2020;11(1):2517.

Tsherniak A, Vazquez F, Montgomery PG, Weir BA, Kryukov G, Cowley GS, et al. Defining a cancer dependency map. Cell. 2017;170(3):564–76 e16.

Basha O, Argov CM, Artzy R, Zoabi Y, Hekselman I, Alfandari L, et al. Differential network analysis of multiple human tissue interactomes highlights tissue-selective processes and genetic disorder genes. Bioinformatics. 2020;36(9):2821–8.

Greene CS, Krishnan A, Wong AK, Ricciotti E, Zelaya RA, Himmelstein DS, et al. Understanding multicellular function and disease with human tissue-specific networks. Nat Genet. 2015;47(6):569–76.

Sharon M, Vinogradov E, Argov CM, Lazarescu O, Zoabi Y, Hekselman I, et al. The differential activity of biological processes in tissues and cell subsets can illuminate disease-related processes and cell-type identities. Bioinformatics. 2022;38(6):1584–92.

Barshir R, Hekselman I, Shemesh N, Sharon M, Novack L, Yeger-Lotem E. Role of duplicate genes in determining the tissue-selectivity of hereditary diseases. PLoS Genet. 2018;14(5): e1007327.

Jubran J, Hekselman I, Novack L, Yeger-Lotem E. Dosage-sensitive molecular mechanisms are associated with the tissue-specificity of traits and diseases. Comput Struct Biotechnol J. 2020;18:4024–32.

Kingsford C, Salzberg SL. What are decision trees? Nat Biotechnol. 2008;26(9):1011–3.

Kotsiantis SB. Decision trees: a recent overview. Artif Intell Rev. 2013;39:261–83.

McFarland JM, Ho ZV, Kugener G, Dempster JM, Montgomery PG, Bryan JG, et al. Improved estimation of cancer dependencies from large-scale RNAi screens using model-based normalization and data integration. Nat Commun. 2018;9(1):4610.

Cohen-Sharir Y, McFarland JM, Abdusamad M, Marquis C, Bernhard SV, Kazachkova M, et al. Aneuploidy renders cancer cells vulnerable to mitotic checkpoint inhibition. Nature. 2021;590(7846):486–91.

Prasad K, Bloomfield M, Levi H, Keuper K, Bernhard SV, Baudoin NC, et al. Whole-genome duplication shapes the aneuploidy landscape of human cancers. Cancer Res. 2022;82(9):1736–52.

Ben-David U, Siranosian B, Ha G, Tang H, Oren Y, Hinohara K, et al. Genetic and transcriptional evolution alters cancer cell line drug response. Nature. 2018;560(7718):325–30.

Dempster JM, Boyle I, Vazquez F, Root DE, Boehm JS, Hahn WC, et al. Chronos: a cell population dynamics model of CRISPR experiments that improves inference of gene fitness effects. Genome Biol. 2021;22(1):343.

Chen C, Bhalala HV, Qiao H, Dong JT. A possible tumor suppressor role of the KLF5 transcription factor in human breast cancer. Oncogene. 2002;21(43):6567–72.

Ma J-B, Bai J-Y, Zhang H-B, Jia J, Shi Q, Yang C, et al. KLF5 inhibits STAT3 activity and tumor metastasis in prostate cancer by suppressing IGF1 transcription cooperatively with HDAC1. Cell Death Dis. 2020;11(6):466.

Luo Y, Chen C. The roles and regulation of the KLF5 transcription factor in cancers. Cancer Sci. 2021;112(6):2097–117.

McConnell BB, Bialkowska AB, Nandan MO, Ghaleb AM, Gordon FJ, Yang VW. Haploinsufficiency of Kruppel-like factor 5 rescues the tumor-initiating effect of the Apc(Min) mutation in the intestine. Cancer Res. 2009;69(10):4125–33.

Rutledge SD, Douglas TA, Nicholson JM, Vila-Casadesus M, Kantzler CL, Wangsa D, et al. Selective advantage of trisomic human cells cultured in non-standard conditions. Sci Rep. 2016;6:22828.

Chen WH, Zhao XM, van Noort V, Bork P. Human monogenic disease genes have frequently functionally redundant paralogs. PLoS Comput Biol. 2013;9(5): e1003073.

Wang T, Birsoy K, Hughes NW, Krupczak KM, Post Y, Wei JJ, et al. Identification and characterization of essential genes in the human genome. Science. 2015;350(6264):1096–101.

Ito T, Young MJ, Li R, Jain S, Wernitznig A, Krill-Burger JM, et al. Paralog knockout profiling identifies DUSP4 and DUSP6 as a digenic dependence in MAPK pathway-driven cancers. Nat Genet. 2021;53(12):1664–72.

Zapata L, Pich O, Serrano L, Kondrashov FA, Ossowski S, Schaefer MH. Negative selection in tumor genome evolution acts on essential cellular functions and the immunopeptidome. Genome Biol. 2018;19(1):1–17.

de Kegel B, Ryan CJ. Paralog dispensability shapes homozygous deletion patterns in tumor genomes. Mol Syst Biol. 2023;19(12):e11987. https://doi.org/10.15252/msb.202311987 .

Zack TI, Schumacher SE, Carter SL, Cherniack AD, Saksena G, Tabak B, et al. Pan-cancer patterns of somatic copy number alteration. Nat Genet. 2013;45(10):1134–40.

Cai Y, Crowther J, Pastor T, Abbasi Asbagh L, Baietti MF, De Troyer M, et al. Loss of chromosome 8p governs tumor progression and drug response by altering lipid metabolism. Cancer Cell. 2016;29(5):751–66.

Girish V, Lakhani AA, Thompson SL, Scaduto CM, Brown LM, Hagenson RA, et al. Oncogene-like addiction to aneuploidy in human cancers. Science. 2023;381(6660):eadg4521.

Zhao X, Cohen EEW, William WN Jr, Bianchi JJ, Abraham JP, Magee D, et al. Somatic 9p24.1 alterations in HPV(-) head and neck squamous cancer dictate immune microenvironment and anti-PD-1 checkpoint inhibitor activity. Proc Natl Acad Sci U S A. 2022;119(47):e2213835119.

Ben-David U, Ha G, Khadka P, Jin X, Wong B, Franke L, et al. The landscape of chromosomal aberrations in breast cancer mouse models reveals driver-specific routes to tumorigenesis. Nat Commun. 2016;7:12160.

Simonovsky E, Sharon M, Ziv M, Mauer O, Hekselman I, Jubran J, et al. Predicting molecular mechanisms of hereditary diseases by using their tissue-selective manifestation. Mol Syst Biol. 2023;19(8):e11407. https://doi.org/10.15252/msb.202211407 .

Hua J, Xiong Z, Lowey J, Suh E, Dougherty ER. Optimal number of features as a function of sample size for various classification rules. Bioinformatics. 2005;21(8):1509–15.

Bakker B, Taudt A, Belderbos ME, Porubsky D, Spierings DC, de Jong TV, et al. Single-cell sequencing reveals karyotype heterogeneity in murine and human malignancies. Genome Biol. 2016;17(1):115.

Gao R, Bai S, Henderson YC, Lin Y, Schalck A, Yan Y, et al. Delineating copy number and clonal substructure in human tumors from single-cell transcriptomes. Nat Biotechnol. 2021;39(5):599–608.

Gao R, Davis A, McDonald TO, Sei E, Shi X, Wang Y, et al. Punctuated copy number evolution and clonal stasis in triple-negative breast cancer. Nat Genet. 2016;48(10):1119–30.

Gavish A, Tyler M, Greenwald AC, Hoefflin R, Simkin D, Tschernichovsky R, et al. Hallmarks of transcriptional intratumour heterogeneity across a thousand tumours. Nature. 2023;618(7965):598–606.

Beroukhim R, Getz G, Nghiemphu L, Barretina J, Hsueh T, Linhart D, et al. Assessing the significance of chromosomal aberrations in cancer: methodology and application to glioma. Proc Natl Acad Sci U S A. 2007;104(50):20007–12.

Center BITGDA. SNP6 copy number analysis (GISTIC2). Broad Institute of MIT and Harvard. 2016. https://gdac.broadinstitute.org/runs/analyses__latest/reports/cancer/STAD-TP/CopyNumber_Gistic2/nozzle.html .

Goldman MJ, Craft B, Hastie M, Repecka K, McDade F, Kamath A, et al. Visualizing and interpreting cancer genomics data via the Xena platform. Nat Biotechnol. 2020;38(6):675–8.

Basha O, Flom D, Barshir R, Smoly I, Tirman S, Yeger-Lotem E. MyProteinNet: build up-to-date protein interaction networks for organisms, tissues and user-defined contexts. Nucleic Acids Res. 2015;43(W1):W258–63.

Sonawane AR, Platig J, Fagny M, Chen C-Y, Paulson JN, Lopes-Ramos CM, et al. Understanding tissue-specific gene regulation. Cell Rep. 2017;21(4):1077–88.

Cardoso-Moreira M, Halbert J, Valloton D, Velten B, Chen C, Shao Y, et al. Gene expression across mammalian organ development. Nature. 2019;571(7766):505–9.

Cunningham F, Allen JE, Allen J, Alvarez-Jarreta J, Amode MR, Armean IM, et al. Ensembl 2022. Nucleic Acids Res. 2022;50(D1):D988–95.

Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, et al. Scikit-learn: machine learning in Python. The Journal of machine Learning research. 2011;12:2825–30.

Chen T, Guestrin C, editors. Xgboost: a scalable tree boosting system. Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining; 2016. p. 785–94. https://doi.org/10.1145/2939672.2939785 .

Lundberg SM, Erion G, Chen H, DeGrave A, Prutkin JM, Nair B, et al. From local explanations to global understanding with explainable AI for trees. Nat Mach Intell. 2020;2(1):56–67.

Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J Roy Stat Soc: Ser B (Methodol). 1995;57(1):289–300.

Jubran J, Yeger-Lotem E. Machine-learning analysis of factors that shape cancer aneuploidy landscapes reveals an important role for negative selection. GitHub https://github.com/JumanJubran/AneuploidyML .

Jubran J, Yeger-Lotem E. Machine-learning analysis of factors that shape cancer aneuploidy landscapes reveals an important role for negative selection. Zenodo. https://zenodo.org/records/8199048 .

Simonovsky E, Yeger-Lotem E. Predicting molecular mechanisms of hereditary diseases by using their tissue-selective manifestation. Datasets. Zenodo. https://zenodo.org/records/10115922 .

Goldman MJ, Craft B, Hastie M, Repecka K, McDade F, Kamath A, et al. Visualizing and interpreting cancer genomics data via the Xena platform. Datasets. Xena. https://xenabrowser.net/datapages/?hub=https://gdc.xenahubs.net:443 .

Tsherniak A, Vazquez F, Montgomery P, Weir B, Kryukov G, Cowley G. Defining a cancer dependency map. Datasets. DepMap. https://depmap.org/portal/download/all/ .

Download references

Acknowledgements

The authors would like to thank Jason Sheltzer for providing DLD1-WT and DLD1 Ts13 cell lines.

J.J. wishes to thank the Baroness Ariane de Rothschild Women Doctoral Program.

Peer review information

Andrew Cosgrove was the primary editor of this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

Review history

The review history is available as Additional File 8 .

This study was funded by the Israel Science Foundation [401/22 to E.Y.-L.] and by a Ben-Gurion University grant [to E.Y.-L.]. Work in the Ben-David lab is supported by the European Research Council Starting Grant (grant #945674 to U.B.-D.), the Israel Science Foundation (grant #1805/21 to U.B.-D.), the Israel Cancer Research Fund (Project Grant to U.B.-D.), and the BSF Project Grant (grant #2019228 to U.B.-D.), and by the EMBO Young Investigator Program (to U.B.-D.).

Author information

Juman Jubran and Rachel Slutsky are equally contributing first authors.

Uri Ben-David and Esti Yeger-Lotem are equally contributing last authors.

Authors and Affiliations

Department of Clinical Biochemistry and Pharmacology, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

Juman Jubran & Esti Yeger-Lotem

Department of Human Molecular Genetics and Biochemistry, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel

Rachel Slutsky, Nir Rozenblum & Uri Ben-David

Department of Software & Information Systems Engineering, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

Lior Rokach

The National Institute for Biotechnology in the Negev, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

Esti Yeger-Lotem

You can also search for this author in PubMed   Google Scholar

Contributions

U.B.-D. and E.Y.-L. conceived and oversaw the study. J.J. designed and performed the computational analyses and developed and interpreted the ML models. R.S. designed and performed the UCHL1 and KLF5 DepMap data analyses and the in vitro experiments. N.R. assisted with the in vitro experiments. L.R. advised on the ML analyses. J.J., R.S., U.B.-D., and E.Y.-L. analyzed and interpreted the data and wrote the manuscript. All authors reviewed and approved the manuscript.

Authors’ Twitter handles

Twitter handles: @yegerlotemlab (Esti Yeger-Lotem), @BenDavidLab (Uri Ben-David).

Corresponding authors

Correspondence to Uri Ben-David or Esti Yeger-Lotem .

Ethics declarations

Ethics approval and consent to participate.

Ethics approval is not applicable.

Competing interests

The authors declare that they have no competing interests.

Additional information

Publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Additional file 1: supplementary figures..

This file contains Supplementary Figures S1-S17.

Additional file 2: Table S1.

Association of TCGA cancer types with normal tissues-of-origin and matching cell lines.

Additional file 3: Table S2.

The auROC and auPRC performance of ML models whose features were calculated using distinct percentages of genes.

Additional file 4: Table S3.

SHAP value per feature of each instance of chromosome-arm and tumor type in the gain and loss models.

Additional file 5: Table S4.

Potential driver instances of each feature in the gain and loss models, and their frequencies.

Additional file 6: Table S5.

Correlations between chr-13q residing genes and the essentiality of their paralogs.

Additional file 7: Table S6.

Co-incidence of arm-level events in the different cancer types, and their frequencies.

Additional file 8.

Rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and permissions

About this article

Cite this article.

Jubran, J., Slutsky, R., Rozenblum, N. et al. Machine-learning analysis reveals an important role for negative selection in shaping cancer aneuploidy landscapes. Genome Biol 25 , 95 (2024). https://doi.org/10.1186/s13059-024-03225-7

Download citation

Received : 05 July 2023

Accepted : 26 March 2024

Published : 15 April 2024

DOI : https://doi.org/10.1186/s13059-024-03225-7

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Genome Biology

ISSN: 1474-760X

• Submission enquiries: [email protected]
• General enquiries: [email protected]

AI Index Report

Welcome to the seventh edition of the AI Index report. The 2024 Index is our most comprehensive to date and arrives at an important moment when AI’s influence on society has never been more pronounced. This year, we have broadened our scope to more extensively cover essential trends such as technical advancements in AI, public perceptions of the technology, and the geopolitical dynamics surrounding its development. Featuring more original data than ever before, this edition introduces new estimates on AI training costs, detailed analyses of the responsible AI landscape, and an entirely new chapter dedicated to AI’s impact on science and medicine.

Read the 2024 AI Index Report

The AI Index report tracks, collates, distills, and visualizes data related to artificial intelligence (AI). Our mission is to provide unbiased, rigorously vetted, broadly sourced data in order for policymakers, researchers, executives, journalists, and the general public to develop a more thorough and nuanced understanding of the complex field of AI.

The AI Index is recognized globally as one of the most credible and authoritative sources for data and insights on artificial intelligence. Previous editions have been cited in major newspapers, including the The New York Times, Bloomberg, and The Guardian, have amassed hundreds of academic citations, and been referenced by high-level policymakers in the United States, the United Kingdom, and the European Union, among other places. This year’s edition surpasses all previous ones in size, scale, and scope, reflecting the growing significance that AI is coming to hold in all of our lives.

Steering Committee Co-Directors

Ray Perrault

Steering committee members.

Erik Brynjolfsson

John Etchemendy

Katrina Ligett

Terah Lyons

James Manyika

Juan Carlos Niebles

Vanessa Parli

Yoav Shoham

Russell Wald

Staff members.

Loredana Fattorini

Nestor Maslej

Letter from the co-directors.

A decade ago, the best AI systems in the world were unable to classify objects in images at a human level. AI struggled with language comprehension and could not solve math problems. Today, AI systems routinely exceed human performance on standard benchmarks.

Progress accelerated in 2023. New state-of-the-art systems like GPT-4, Gemini, and Claude 3 are impressively multimodal: They can generate fluent text in dozens of languages, process audio, and even explain memes. As AI has improved, it has increasingly forced its way into our lives. Companies are racing to build AI-based products, and AI is increasingly being used by the general public. But current AI technology still has significant problems. It cannot reliably deal with facts, perform complex reasoning, or explain its conclusions.

AI faces two interrelated futures. First, technology continues to improve and is increasingly used, having major consequences for productivity and employment. It can be put to both good and bad uses. In the second future, the adoption of AI is constrained by the limitations of the technology. Regardless of which future unfolds, governments are increasingly concerned. They are stepping in to encourage the upside, such as funding university R&D and incentivizing private investment. Governments are also aiming to manage the potential downsides, such as impacts on employment, privacy concerns, misinformation, and intellectual property rights.

As AI rapidly evolves, the AI Index aims to help the AI community, policymakers, business leaders, journalists, and the general public navigate this complex landscape. It provides ongoing, objective snapshots tracking several key areas: technical progress in AI capabilities, the community and investments driving AI development and deployment, public opinion on current and potential future impacts, and policy measures taken to stimulate AI innovation while managing its risks and challenges. By comprehensively monitoring the AI ecosystem, the Index serves as an important resource for understanding this transformative technological force.

On the technical front, this year’s AI Index reports that the number of new large language models released worldwide in 2023 doubled over the previous year. Two-thirds were open-source, but the highest-performing models came from industry players with closed systems. Gemini Ultra became the first LLM to reach human-level performance on the Massive Multitask Language Understanding (MMLU) benchmark; performance on the benchmark has improved by 15 percentage points since last year. Additionally, GPT-4 achieved an impressive 0.97 mean win rate score on the comprehensive Holistic Evaluation of Language Models (HELM) benchmark, which includes MMLU among other evaluations.

Although global private investment in AI decreased for the second consecutive year, investment in generative AI skyrocketed. More Fortune 500 earnings calls mentioned AI than ever before, and new studies show that AI tangibly boosts worker productivity. On the policymaking front, global mentions of AI in legislative proceedings have never been higher. U.S. regulators passed more AI-related regulations in 2023 than ever before. Still, many expressed concerns about AI’s ability to generate deepfakes and impact elections. The public became more aware of AI, and studies suggest that they responded with nervousness.

Ray Perrault Co-director, AI Index

Our Supporting Partners

Analytics & Research Partners

Stay up to date on the AI Index by subscribing to the  Stanford HAI newsletter.

• Download PDF
• Share X Facebook Email LinkedIn
• Permissions

Fatal Traffic Risks With a Total Solar Eclipse in the US

• 1 Department of Medicine, University of Toronto, Toronto, Ontario, Canada
• 2 Evaluative Clinical Science Platform, Sunnybrook Research Institute, Toronto, Ontario, Canada
• 3 Institute for Clinical Evaluative Sciences, Toronto, Ontario, Canada
• 4 Division of General Internal Medicine, Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada
• 5 Center for Leading Injury Prevention Practice Education & Research, Toronto, Ontario, Canada
• 6 Department of Medicine, University of British Columbia, Vancouver, British Columbia, Canada
• 7 Centre for Clinical Epidemiology & Evaluation, University of British Columbia, Vancouver, British Columbia, Canada

A total solar eclipse occurs when the moon temporarily obscures the sun and casts a dark shadow across the earth. This astronomical spectacle has been described for more than 3 millennia and can be predicted with high precision. Eclipse-related solar retinopathy (vision loss from staring at the sun) is an established medical complication; however, other medical outcomes have received little attention. 1

Read More About

Redelmeier DA , Staples JA. Fatal Traffic Risks With a Total Solar Eclipse in the US. JAMA Intern Med. Published online March 25, 2024. doi:10.1001/jamainternmed.2023.5234

Manage citations:

© 2024

Artificial Intelligence Resource Center

Best of JAMA Network 2022

Browse and subscribe to JAMA Network podcasts!

Others Also Liked

Select your interests.

Customize your JAMA Network experience by selecting one or more topics from the list below.

• Academic Medicine
• Acid Base, Electrolytes, Fluids
• Allergy and Clinical Immunology
• American Indian or Alaska Natives
• Anesthesiology
• Anticoagulation
• Art and Images in Psychiatry
• Artificial Intelligence
• Assisted Reproduction
• Bleeding and Transfusion
• Caring for the Critically Ill Patient
• Challenges in Clinical Electrocardiography
• Climate and Health
• Climate Change
• Clinical Challenge
• Clinical Decision Support
• Clinical Implications of Basic Neuroscience
• Clinical Pharmacy and Pharmacology
• Complementary and Alternative Medicine
• Consensus Statements
• Coronavirus (COVID-19)
• Critical Care Medicine
• Cultural Competency
• Dental Medicine
• Dermatology
• Diabetes and Endocrinology
• Diagnostic Test Interpretation
• Drug Development
• Electronic Health Records
• Emergency Medicine
• End of Life, Hospice, Palliative Care
• Environmental Health
• Equity, Diversity, and Inclusion
• Facial Plastic Surgery
• Gastroenterology and Hepatology
• Genetics and Genomics
• Genomics and Precision Health
• Global Health
• Guide to Statistics and Methods
• Hair Disorders
• Health Care Delivery Models
• Health Care Economics, Insurance, Payment
• Health Care Quality
• Health Care Reform
• Health Care Safety
• Health Care Workforce
• Health Disparities
• Health Inequities
• Health Policy
• Health Systems Science
• History of Medicine
• Hypertension
• Images in Neurology
• Implementation Science
• Infectious Diseases
• Innovations in Health Care Delivery
• JAMA Infographic
• Law and Medicine
• Leading Change
• Less is More
• LGBTQIA Medicine
• Lifestyle Behaviors
• Medical Coding
• Medical Devices and Equipment
• Medical Education
• Medical Education and Training
• Medical Journals and Publishing
• Mobile Health and Telemedicine
• Narrative Medicine
• Neuroscience and Psychiatry
• Notable Notes
• Nutrition, Obesity, Exercise
• Obstetrics and Gynecology
• Occupational Health
• Ophthalmology
• Orthopedics
• Otolaryngology
• Pain Medicine
• Palliative Care
• Pathology and Laboratory Medicine
• Patient Care
• Patient Information
• Performance Improvement
• Performance Measures
• Perioperative Care and Consultation
• Pharmacoeconomics
• Pharmacoepidemiology
• Pharmacogenetics
• Pharmacy and Clinical Pharmacology
• Physical Medicine and Rehabilitation
• Physical Therapy
• Physician Leadership
• Population Health
• Primary Care
• Professional Well-being
• Professionalism
• Psychiatry and Behavioral Health
• Public Health
• Pulmonary Medicine
• Regulatory Agencies
• Reproductive Health
• Research, Methods, Statistics
• Resuscitation
• Rheumatology
• Risk Management
• Scientific Discovery and the Future of Medicine
• Shared Decision Making and Communication
• Sleep Medicine
• Sports Medicine
• Stem Cell Transplantation
• Substance Use and Addiction Medicine
• Surgical Innovation
• Surgical Pearls
• Teachable Moment
• Technology and Finance
• The Art of JAMA
• The Arts and Medicine
• The Rational Clinical Examination
• Tobacco and e-Cigarettes
• Translational Medicine
• Trauma and Injury
• Treatment Adherence
• Ultrasonography
• Users' Guide to the Medical Literature
• Vaccination
• Venous Thromboembolism
• Veterans Health
• Women's Health
• Workflow and Process
• Wound Care, Infection, Healing
• Register for email alerts with links to free full-text articles
• Access PDFs of free articles
• Manage your interests
• Save searches and receive search alerts

Numbers, Facts and Trends Shaping Your World

Read our research on:

Full Topic List

Regions & Countries

• Publications
• Our Methods
• Short Reads
• Tools & Resources

Read Our Research On:

About 1 in 5 U.S. teens who’ve heard of ChatGPT have used it for schoolwork

Roughly one-in-five teenagers who have heard of ChatGPT say they have used it to help them do their schoolwork, according to a new Pew Research Center survey of U.S. teens ages 13 to 17. With a majority of teens having heard of ChatGPT, that amounts to 13% of all U.S. teens who have used the generative artificial intelligence (AI) chatbot in their schoolwork.

Teens in higher grade levels are particularly likely to have used the chatbot to help them with schoolwork. About one-quarter of 11th and 12th graders who have heard of ChatGPT say they have done this. This share drops to 17% among 9th and 10th graders and 12% among 7th and 8th graders.

There is no significant difference between teen boys and girls who have used ChatGPT in this way.

The introduction of ChatGPT last year has led to much discussion about its role in schools , especially whether schools should integrate the new technology into the classroom or ban it .

Pew Research Center conducted this analysis to understand American teens’ use and understanding of ChatGPT in the school setting.

The Center conducted an online survey of 1,453 U.S. teens from Sept. 26 to Oct. 23, 2023, via Ipsos. Ipsos recruited the teens via their parents, who were part of its KnowledgePanel . The KnowledgePanel is a probability-based web panel recruited primarily through national, random sampling of residential addresses. The survey was weighted to be representative of U.S. teens ages 13 to 17 who live with their parents by age, gender, race and ethnicity, household income, and other categories.

This research was reviewed and approved by an external institutional review board (IRB), Advarra, an independent committee of experts specializing in helping to protect the rights of research participants.

Here are the  questions used for this analysis , along with responses, and its  methodology .

Teens’ awareness of ChatGPT

Overall, two-thirds of U.S. teens say they have heard of ChatGPT, including 23% who have heard a lot about it. But awareness varies by race and ethnicity, as well as by household income:

• 72% of White teens say they’ve heard at least a little about ChatGPT, compared with 63% of Hispanic teens and 56% of Black teens.
• 75% of teens living in households that make $75,000 or more annually have heard of ChatGPT. Much smaller shares in households with incomes between $30,000 and $74,999 (58%) and less than $30,000 (41%) say the same.

Teens who are more aware of ChatGPT are more likely to use it for schoolwork. Roughly a third of teens who have heard a lot about ChatGPT (36%) have used it for schoolwork, far higher than the 10% among those who have heard a little about it.

When do teens think it’s OK for students to use ChatGPT?

For teens, whether it is – or is not – acceptable for students to use ChatGPT depends on what it is being used for.

There is a fair amount of support for using the chatbot to explore a topic. Roughly seven-in-ten teens who have heard of ChatGPT say it’s acceptable to use when they are researching something new, while 13% say it is not acceptable.

However, there is much less support for using ChatGPT to do the work itself. Just one-in-five teens who have heard of ChatGPT say it’s acceptable to use it to write essays, while 57% say it is not acceptable. And 39% say it’s acceptable to use ChatGPT to solve math problems, while a similar share of teens (36%) say it’s not acceptable.

Some teens are uncertain about whether it’s acceptable to use ChatGPT for these tasks. Between 18% and 24% say they aren’t sure whether these are acceptable use cases for ChatGPT.

Those who have heard a lot about ChatGPT are more likely than those who have only heard a little about it to say it’s acceptable to use the chatbot to research topics, solve math problems and write essays. For instance, 54% of teens who have heard a lot about ChatGPT say it’s acceptable to use it to solve math problems, compared with 32% among those who have heard a little about it.

Note: Here are the  questions used for this analysis , along with responses, and its  methodology .

• Artificial Intelligence
• Technology Adoption
• Teens & Tech

Many Americans think generative AI programs should credit the sources they rely on

Americans’ use of chatgpt is ticking up, but few trust its election information, q&a: how we used large language models to identify guests on popular podcasts, striking findings from 2023, what the data says about americans’ views of artificial intelligence, most popular.

1615 L St. NW, Suite 800 Washington, DC 20036 USA (+1) 202-419-4300 | Main (+1) 202-857-8562 | Fax (+1) 202-419-4372 |  Media Inquiries

Research Topics

• Age & Generations
• Coronavirus (COVID-19)
• Economy & Work
• Family & Relationships
• Gender & LGBTQ
• Immigration & Migration
• International Affairs
• Internet & Technology
• Methodological Research
• News Habits & Media
• Non-U.S. Governments
• Other Topics
• Politics & Policy
• Race & Ethnicity
• Email Newsletters

ABOUT PEW RESEARCH CENTER  Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of  The Pew Charitable Trusts .

Copyright 2024 Pew Research Center

Terms & Conditions

Privacy Policy

Cookie Settings

Reprints, Permissions & Use Policy

• Skip to main content
• Skip to FDA Search
• Skip to in this section menu
• Skip to footer links

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

U.S. Food and Drug Administration

•   Search
•   Menu
• Science & Research
• About Science & Research at FDA
• The FDA Science Forum

Dynamic headspace GC-MS method to detect volatile extractables from medical device materials

2023 FDA Science Forum

Volatile extractables, released from medical devices during use, are a concern as they may expose patients to harmful levels of toxic compounds.  According to ISO 10993-18:2020, the Analytical Evaluation Threshold (AET) is used to determine the analytical sensitivity required to detect extractables from medical devices. Compounds, at or above the AET, need to be reported for toxicological risk assessment. Currently, volatile analysis by static headspaces is used as a supplementary technique for medical device or material extracts. Variation of signal response in static headspace led to undefined AET for the volatile analysis method. Therefore, investigating new technologies that generate reproducible data for volatile quantification is needed for improved hazards identification. This study was designed to evaluate the performance of dynamic headspace (DHS) gas chromatography-mass spectrometric (GC-MS) analysis to achieve the sensitivity levels suitable for proper toxicological risk assessment for volatiles extracted from medical devices.  DHS method development was conducted using residual solvents class 3 - mix A standard and the initial method development and analyses were done using GERSTEL MPS attached to Agilent GC-MS system. Two different methods were designed to address both volatile and semi volatile compounds. The efficiency of DHS extraction was optimized based on incubation temperature, trapping volume/ time, adsorbent type (Carbopack B/ Carbopack X (Carbopack B/X) and Tenax TA), and drying time for low volume samples. Method performance was compared with commonly used static headspace GC-MS analysis. To further improve the headspace concentration of more water-soluble compounds such as alcohols, and ketones, the effect of surfactants addition to the sample matrix was also investigated. Application of developed methods were tested using saline extracts of various medical device materials such as ABS, Buna and PVC.  Preliminary results showed improved efficiency in detecting volatile extractable in ABS material extracts with semi volatile method with increased peak area responses compared to the volatile method. This sensitive dynamic headspace GC-MS method may facilitate improved toxicological risk assessment for the volatiles detected in medical devices. 

Download the Poster (PDF; 2.24 MB)