research randomizer

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RESEARCH RANDOMIZER

Random sampling and random assignment made easy.

Research Randomizer is a free resource for researchers and students in need of a quick way to generate random numbers or assign participants to experimental conditions. This site can be used for a variety of purposes, including psychology experiments, medical trials, and survey research.

GENERATE NUMBERS

In some cases, you may wish to generate more than one set of numbers at a time (e.g., when randomly assigning people to experimental conditions in a "blocked" research design). If you wish to generate multiple sets of random numbers, simply enter the number of sets you want, and Research Randomizer will display all sets in the results.

Specify how many numbers you want Research Randomizer to generate in each set. For example, a request for 5 numbers might yield the following set of random numbers: 2, 17, 23, 42, 50.

Specify the lowest and highest value of the numbers you want to generate. For example, a range of 1 up to 50 would only generate random numbers between 1 and 50 (e.g., 2, 17, 23, 42, 50). Enter the lowest number you want in the "From" field and the highest number you want in the "To" field.

Selecting "Yes" means that any particular number will appear only once in a given set (e.g., 2, 17, 23, 42, 50). Selecting "No" means that numbers may repeat within a given set (e.g., 2, 17, 17, 42, 50). Please note: Numbers will remain unique only within a single set, not across multiple sets. If you request multiple sets, any particular number in Set 1 may still show up again in Set 2.

Sorting your numbers can be helpful if you are performing random sampling, but it is not desirable if you are performing random assignment. To learn more about the difference between random sampling and random assignment, please see the Research Randomizer Quick Tutorial.

Place Markers let you know where in the sequence a particular random number falls (by marking it with a small number immediately to the left). Examples: With Place Markers Off, your results will look something like this: Set #1: 2, 17, 23, 42, 50 Set #2: 5, 3, 42, 18, 20 This is the default layout Research Randomizer uses. With Place Markers Within, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p1=5, p2=3, p3=42, p4=18, p5=20 This layout allows you to know instantly that the number 23 is the third number in Set #1, whereas the number 18 is the fourth number in Set #2. Notice that with this option, the Place Markers begin again at p1 in each set. With Place Markers Across, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p6=5, p7=3, p8=42, p9=18, p10=20 This layout allows you to know that 23 is the third number in the sequence, and 18 is the ninth number over both sets. As discussed in the Quick Tutorial, this option is especially helpful for doing random assignment by blocks.

Please note: By using this service, you agree to abide by the SPN User Policy and to hold Research Randomizer and its staff harmless in the event that you experience a problem with the program or its results. Although every effort has been made to develop a useful means of generating random numbers, Research Randomizer and its staff do not guarantee the quality or randomness of numbers generated. Any use to which these numbers are put remains the sole responsibility of the user who generated them.

Note: By using Research Randomizer, you agree to its Terms of Service .

Simple, easy randomization for research studies and clinical trials.

Automate your trial randomization Automate your trial randomization

Study Randomizer Features

Easy to use.

Access study data and enroll participants from any web browser. No more paper envelopes or slow phone systems.

Set up multiple organizations and trials

You can set up multiple trials. Each trial is independent from other trials. Set up separate organizations administering separate trial groups.

How to use Study Randomizer

Powerful randomization options.

Use comprehensive randomization algorithms (permuted blocks, minimization, adaptive randomization, stratification, and more). Delegate study enrollment to multiple users.

Design and simulate your trial

Design your trial in the interactive design form. Test different parameters and trial designs. Simulate trial randomization. Use stratification on variables for multi-center and multi-site studies.

Study Randomization Information

Use live enrollment or pre-enrollment with coding for double-blind studies. You can use Study Randomizer in multiple locations with internet access.

Invite collaborators

Invite collaborators into the system. Use multi-user access controls to allow view, enroll, or edit privileges.

Data is encrypted, backed up, and protected. Transactions are logged and an auditable record can be provided.

Security Information

Free for small studies, significantly cheaper than an expensive CTMS or EDC system for large studies.

Integrate with HIPAA and GDPR requirements for data security and data residency. Study Randomizer does not store trial subject information and can work with your patient record system, whether it's on paper or digital.

Customizable

Full configuration of study arms & variables (text, number, group type). Choose between urn and block based randomization. Set up multi-site studies by stratifying using a variable for the trial site.

Register and design your trial

How Study Randomizer works

The problem.

You need to set up a trial with randomization. Simple usage is important.

Create an account at Study Randomizer and confirm your email.

Design and Simulate Your Trial

Make sure your trial design works. Simulate block allocation and trial imbalance. Test stratification for e.g. multi-center trials.

Make sure multiple people can enroll trial subjects. Give view-only access to administrative staff.

Start Trial Enrollment

Enroll trial subjects with the click of a button wherever you have access to internet.

Enrollment Records

You can print enrollment records for archiving or offline usage.

Study Randomizer Use Cases

Study Randomizer is used worldwide in trials. Partial list of studies where Study Randomizer is used: Study Randomizer Studies

Randomization software has many use cases such as:

Clinical Trials: Study Randomizer is used in many clinical trials world-wide. From helping with Covid-19 trial randomization to improve clinical outcomes for patients to supporting sleep studies to psychosis research.

Veterinary trials: Dose requirements for anesthesia in dogs.

Psychological trials: Simple randomization support for trial enrollment.

Food trials and research: Bioavailability and food ingredient influence on serum levels in the human body.

Economic research: Effects of mentoring on smaller companies.

Get started and design your trial

How to do Clinical Trial Randomization

Randomization is a key aspect of clinical trials that helps to ensure that the results of the study are the result of the treatment and unbiased. To perform randomization in a clinical trial, you first need to determine the number of participants in the study and the number of different groups (or "arms") that the participants will be assigned to. Then, you need to create a randomization schedule that specifies which participants will be assigned to which group. This can be done using a computer program like Studyrandomizer.com or by using randomization cards or tables. Once the randomization schedule has been created, the participants can be enrolled in the study and assigned to their respective groups according to the schedule. It is important to keep the randomization schedule confidential to avoid biasing the results of the study.

Get in touch. We’re happy to talk about your project’s specific needs. Contact us for additional requirements for Study Randomizer.

Email: 📨 contact@studyrandomizer.com ↗

Study Randomizer is made by: Phase Locked Software Wageningen The Netherlands

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• Knowledge Base

Methodology

• Simple Random Sampling | Definition, Steps & Examples

Simple Random Sampling | Definition, Steps & Examples

Published on August 28, 2020 by Lauren Thomas . Revised on December 18, 2023.

A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected.

This method is the most straightforward of all the probability sampling methods , since it only involves a single random selection and requires little advance knowledge about the population. Because it uses randomization, any research performed on this sample should have high internal and external validity, and be at a lower risk for research biases like sampling bias and selection bias .

Table of contents

When to use simple random sampling, how to perform simple random sampling, other interesting articles, frequently asked questions about simple random sampling.

Simple random sampling is used to make statistical inferences about a population. It helps ensure high internal validity : randomization is the best method to reduce the impact of potential confounding variables .

In addition, with a large enough sample size, a simple random sample has high external validity : it represents the characteristics of the larger population.

However, simple random sampling can be challenging to implement in practice. To use this method, there are some prerequisites:

• You have a complete list of every member of the population .
• You can contact or access each member of the population if they are selected.
• You have the time and resources to collect data from the necessary sample size.

Simple random sampling works best if you have a lot of time and resources to conduct your study, or if you are studying a limited population that can easily be sampled.

In some cases, it might be more appropriate to use a different type of probability sampling:

• Systematic sampling involves choosing your sample based on a regular interval, rather than a fully random selection. It can also be used when you don’t have a complete list of the population.
• Stratified sampling is appropriate when you want to ensure that specific characteristics are proportionally represented in the sample. You split your population into strata (for example, divided by gender or race), and then randomly select from each of these subgroups.
• Cluster sampling is appropriate when you are unable to sample from the entire population. You divide the sample into clusters that approximately reflect the whole population, and then choose your sample from a random selection of these clusters.

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There are 4 key steps to select a simple random sample.

Step 1: Define the population

Start by deciding on the population that you want to study.

It’s important to ensure that you have access to every individual member of the population, so that you can collect data from all those who are selected for the sample.

Step 2: Decide on the sample size

Next, you need to decide how large your sample size will be. Although larger samples provide more statistical certainty, they also cost more and require far more work.

There are several potential ways to decide upon the size of your sample, but one of the simplest involves using a formula with your desired confidence interval and confidence level , estimated size of the population you are working with, and the standard deviation of whatever you want to measure in your population.

The most common confidence interval and levels used are 0.05 and 0.95, respectively. Since you may not know the standard deviation of the population you are studying, you should choose a number high enough to account for a variety of possibilities (such as 0.5).

You can then use a sample size calculator to estimate the necessary sample size.

Step 3: Randomly select your sample

This can be done in one of two ways: the lottery or random number method.

In the lottery method , you choose the sample at random by “drawing from a hat” or by using a computer program that will simulate the same action.

In the random number method , you assign every individual a number. By using a random number generator or random number tables, you then randomly pick a subset of the population. You can also use the random number function (RAND) in Microsoft Excel to generate random numbers.

Step 4: Collect data from your sample

Finally, you should collect data from your sample.

To ensure the validity of your findings, you need to make sure every individual selected actually participates in your study. If some drop out or do not participate for reasons associated with the question that you’re studying, this could bias your findings.

For example, if young participants are systematically less likely to participate in your study, your findings might not be valid due to the underrepresentation of this group.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Prospective cohort study

Research bias

• Implicit bias
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic
• Social desirability bias

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.

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Article Contents

What is randomisation, why do we randomise, choosing a randomisation method, implementing the chosen randomisation method.

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Randomisation: What, Why and How?

• Article contents
• Figures & tables
• Supplementary Data

Zoë Hoare, Randomisation: What, Why and How?, Significance , Volume 7, Issue 3, September 2010, Pages 136–138, https://doi.org/10.1111/j.1740-9713.2010.00443.x

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Randomisation is a fundamental aspect of randomised controlled trials, but how many researchers fully understand what randomisation entails or what needs to be taken into consideration to implement it effectively and correctly? Here, for students or for those about to embark on setting up a trial, Zoë Hoare gives a basic introduction to help approach randomisation from a more informed direction.

Most trials of new medical treatments, and most other trials for that matter, now implement some form of randomisation. The idea sounds so simple that defining it becomes almost a joke: randomisation is “putting participants into the treatment groups randomly”. If only it were that simple. Randomisation can be a minefield, and not everyone understands what exactly it is or why they are doing it.

A key feature of a randomised controlled trial is that it is genuinely not known whether the new treatment is better than what is currently offered. The researchers should be in a state of equipoise; although they may hope that the new treatment is better, there is no definitive evidence to back this hypothesis up. This evidence is what the trial is trying to provide.

You will have, at its simplest, two groups: patients who are getting the new treatment, and those getting the control or placebo. You do not hand-select which patient goes into which group, because that would introduce selection bias. Instead you allocate your patients randomly. In its simplest form this can be done by the tossing of a fair coin: heads, the patient gets the trial treatment; tails, he gets the control. Simple randomisation is a fair way of ensuring that any differences that occur between the treatment groups arise completely by chance. But – and this is the first but of many here – simple randomisation can lead to unbalanced groups, that is, groups of unequal size. This is particularly true if the trial is only small. For example, tossing a fair coin 10 times will only result in five heads and five tails about 25% of the time. We would have a 66% chance of getting 6 heads and 4 tails, 5 and 5, or 4 and 6; 33% of the time we would get an even larger imbalance, with 7, 8, 9 or even all 10 patients in one group and the other group correspondingly undersized.

The impact of an imbalance like this is far greater for a small trial than for a larger trial. Tossing a fair coin 100 times will result in imbalance larger than 60–40 less than 1% of the time. One important part of the trial design process is the statement of intention of using randomisation; then we need to establish which method to use, when it will be used, and whether or not it is in fact random.

Randomisation needs to be controlled: You would not want all the males under 30 to be in one trial group and all the women over 70 in the other

It is partly true to say that we do it because we have to. The Consolidated Standards of Reporting Trials (CONSORT) 1 , to which we should all adhere, tells us: “Ideally, participants should be assigned to comparison groups in the trial on the basis of a chance (random) process characterized by unpredictability.” The requirement is there for a reason. Randomisation of the participants is crucial because it allows the principles of statistical theory to stand and as such allows a thorough analysis of the trial data without bias. The exact method of randomisation can have an impact on the trial analyses, and this needs to be taken into account when writing the statistical analysis plan.

Ideally, simple randomisation would always be the preferred option. However, in practice there often needs to be some control of the allocations to avoid severe imbalances within treatments or within categories of patient. You would not want, for example, all the males under 30 to be in one group and all the females over 70 in the other. This is where restricted or stratified randomisation comes in.

Restricted randomisation relates to using any method to control the split of allocations to each of the treatment groups based on certain criteria. This can be as simple as generating a random list, such as AAABBBABABAABB …, and allocating each participant as they arrive to the next treatment on the list. At certain points within the allocations we know that the groups will be balanced in numbers – here at the sixth, eighth, tenth and 14th participants – and we can control the maximum imbalance at any one time.

Stratified randomisation sets out to control the balance in certain baseline characteristics of the participants – such as sex or age. This can be thought of as producing an individual randomisation list for each of the characteristics concerned.

© iStockphoto.com/dra_schwartz

Stratification variables are the baseline characteristics that you think might influence the outcome your trial is trying to measure. For example, if you thought gender was going to have an effect on the efficacy of the treatment then you would use it as one of your stratification variables. A stratified randomisation procedure would aim to ensure a balance of the two gender groups between the two treatment groups.

If you also thought age would be affecting the treatment then you could also stratify by age (young/old) with some sensible limits on what old and young are. Once you start stratifying by age and by gender, you have to start taking care. You will need to use a stratified randomisation process that balances at the stratum level (i.e. at the level of those characteristics) to ensure that all four strata (male/young, male/old, female/young and female/old) have equivalent numbers of each of the treatment groups represented.

“Great”, you might think. “I'll just stratify by all my baseline characteristics!” Better not. Stop and consider what this would mean. As the number of stratification variables increases linearly, the number of strata increases exponentially. This reduces the number of participants that would appear in each stratum. In our example above, with our two stratification variables of age and sex we had four strata; if we added, say “blue-eyed” and “overweight” to our criteria to give four stratification variables each with just two levels we would get 16 represented strata. How likely is it that each of those strata will be represented in the population targeted by the trial? In other words, will we be sure of finding a blue-eyed young male who is also overweight among our patients? And would one such overweight possible Adonis be statistically enough? It becomes evident that implementing pre-generated lists within each stratification level or stratum and maintaining an overall balance of group sizes becomes much more complicated with many stratification variables and the uncertainty of what type of participant will walk through the door next.

Does it matter? There are a wide variety of methods for randomisation, and which one you choose does actually matter. It needs to be able to do everything that is required of it. Ask yourself these questions, and others:

Can the method accommodate enough treatment groups? Some methods are limited to two treatment groups; many trials involve three or more.

What type of randomness, if any, is injected into the method? The level of randomness dictates how predictable a method is.

A deterministic method has no randomness, meaning that with all the previous information you can tell in advance which group the next patient to appear will be allocated to. Allocating alternate participants to the two treatments using ABABABABAB … would be an example.

A static random element means that each allocation is made with a pre-defined probability. The coin-toss method does this.

With a dynamic element the probability of allocation is always changing in relation to the information received, meaning that the probability of allocation can only be worked out with knowledge of the algorithm together with all its settings. A biased coin toss does this where the bias is recalculated for each participant.

Can the method accommodate stratification variables, and if so how many? Not all of them can. And can it cope with continuous stratification variables? Most variables are divided into mutually exclusive categories (e.g. male or female), but sometimes it may be necessary (or preferable) to use a continuous scale of the variable – such as weight, or body mass index.

Can the method use an unequal allocation ratio? Not all trials require equal-sized treatment groups. There are many reasons why it might be wise to have more patients receiving treatment A than treatment B 2 . However, an allocation ratio being something other than 1:1 does impact on the study design and on the calculation of the sample size, so is not something to be changing mid-trial. Not all allocation methods can cope with this inequality.

Is thresholding used in the method? Thresholding handles imbalances in allocation. A threshold is set and if the imbalance becomes greater than the threshold then the allocation becomes deterministic to reduce the imbalance back below the threshold.

Can the method be implemented sequentially? In other words, does it require that the total number of participants be known at the beginning of the allocations? Some methods generate lists requiring exactly N participants to be recruited in order to be effective – and recruiting participants is often one of the more problematic parts of a trial.

Is the method complex? If so, then its practical implementation becomes an issue for the day-to-day running of the trial.

Is the method suitable to apply to a cluster randomisation? Cluster randomisations are used when randomising groups of individuals to a treatment rather than the individuals themselves. This can be due to the nature of the treatment, such as a new teaching method for schools or a dietary intervention for families. Using clusters is a big part of the trial design and the randomisation needs to be handled slightly differently.

Should a response-adaptive method be considered? If there is some evidence that one treatment is better than another, then a response-adaptive method works by taking into account the outcomes of previous allocations and works to minimise the number of participants on the “wrong” treatment.

For multi-centred trials, how to handle the randomisations across the centres should be considered at this point. Do all centres need to be completely balanced? Are all centres the same size? Considering the various centres as stratification variables is one way of dealing with more than one centre.

Once the method of randomisation has been established the next important step is to consider how to implement it. The recommended way is to enlist the services of a central randomisation office that can offer robust, validated techniques with the security and back-up needed to implement many of the methods proposed today. How the method is implemented must be as clearly reported as the method chosen. As part of the implementation it is important to keep the allocations concealed, both those already done and any future ones, from as many people as possible. This helps prevent selection bias: a clinician may withhold a participant if he believes that based on previous allocations the next allocations would not be the “preferred” ones – see the section below on subversion.

Part of the trial design will be to note exactly who should know what about how each participant has been allocated. Researchers and participants may be equally blinded, but that is not always the case.

For example, in a blinded trial there may be researchers who do not know which group the participants have been allocated to. This enables them to conduct the assessments without any bias for the allocation. They may, however, start to guess, on the basis of the results they see. A measure of blinding may be incorporated for the researchers to indicate whether they have remained blind to the treatment allocated. This can be in the form of a simple scale tool for the researcher to indicate how confident they are in knowing which allocated group the participant is in by the end of an assessment. With psychosocial interventions it is often impossible to hide from the participants, let alone the clinicians, which treatment group they have been allocated to.

In a drug trial where a placebo can be prescribed a coded system can ensure that neither patients nor researchers know which group is which until after the analysis stage.

With any level of blinding there may be a requirement to unblind participants or clinicians at any point in the trial, and there should be a documented procedure drawn up on how to unblind a particular participant without risking the unblinding of a trial. For drug trials in particular, the methods for unblinding a participant must be stated in the trial protocol. Wherever possible the data analysts and statisticians should remain blind to the allocation until after the main analysis has taken place.

Blinding should not be confused with allocation concealment. Blinding prevents performance and ascertainment bias within a trial, while allocation concealment prevents selection bias. Bias introduced by poor allocation concealment may be thought of as a predictive bias, trying to influence the results from the outset, while the biases introduced by non-blinding can be thought of as a reactive bias, creating causal links in outcomes because of being in possession of information about the treatment group.

In the literature on randomisation there are numerous tales of how allocation schemes have been subverted by clinicians trying to do the best for the trial or for their patient or both. This includes anecdotal tales of clinicians holding sealed envelopes containing the allocations up to X-ray lights and confessing to breaking into locked filing cabinets to get at the codes 3 . This type of behaviour has many explanations and reasons, but does raise the question whether these clinicians were in a state of equipoise with regard to the trial, and whether therefore they should really have been involved with the trial. Randomisation schemes and their implications must be signed up to by the whole team and are not something that only the participants need to consent to.

Clinicians have been known to X-ray sealed allocation envelopes to try to get their patients into the preferred group in a trial

The 2010 CONSORT statement can be found at http://www.consort-statement.org/consort-statement/ .

Dumville , J. C. , Hahn , S. , Miles , J. N. V. and Torgerson , D. J. ( 2006 ) The use of unequal randomisation ratios in clinical trials: A review . Contemporary Clinical Trials , 27 , 1 – 12 .

Google Scholar

Shulz , K. F. ( 1995 ) Subverting randomisation in controlled trials . Journal of the American Medical Association , 274 , 1456 – 1458 .

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Clinical Trial Randomization Tool

• For clinical trials, educational purposes, or just for your own interest.
• Uses MTI randomization to generate the allocation sequence.
• Default values are provided below. You may adjust these as you require or prefer.
• When you click “Request Confirmation Email,” your request will be sent to a server. You will receive an email when your download is ready (typically in a few minutes).
• For more detailed instructions, you may view the Tool Instructions page.

Basic Trial Info

A simple trial design is used by default. For more complex trials, change the trial settings below to customize arms and/or stratification.

You have selected maximal as the randomization method. This method is supported only for two-arm trials with an arm allocation ratio of 1:1.

These ratio values will be simplified to 1:1 when you save this section.

The MTI must be at least double the largest arm ratio value, which is 1 , so the MTI will be increased to 2 when you save this section.

Confirm reset

Based on the number of categories for your 1 stratification variables , your trial will have 1 strata . For each stratum, you will receive one worksheet containing 1,000 assignments .

Your results will use the following names for each stratum's sequence worksheet. Due to length restrictions in Microsoft Excel, category names may be truncated.

Algorithm Parameters

The following parameters should work well for most trials, but can be further customized.

Select a method to use for randomization. All methods shown use MTI randomization and are suitable for use. For more information about these different methods, consult the Learn About Randomization page.

The most under-assigned arms are always favored by a balance-forcing probability that varies based on the current degree of imbalance.

Neither arm is favored until the MTI threshold is reached — each arm's probability of assignment is always 0%, 50%, or 100%, based on the current imbalance. The Big Stick method is a special case of Chen's procedure where the balance-forcing probability is 50%.

This method is supported only for two-arm trials with an arm allocation ratio of 1:1.

The under-assigned arm is always favored by a preset balance-forcing probability, e.g., 60%. Chen's procedure is a generalized version of Big Stick where the balance-forcing probability can be greater than 50%.

At any point in the randomization process, for any stratification group, no trial arm will be assigned more than this many participants than any other arm.

The MTI can be any integer between twice the largest allocation ratio and 20 .

At any point when the arms are imbalanced, this is the percent probability that the next enrollment goes to the arm that currently has fewer enrollments. When both arms have equal number of enrollments, the probability is 50% to each arm. If assignment to the larger arm would violate the MTI, the probability is 100% and the next enrollment goes to the smaller arm.

Contact Info

The Clinical Trial Randomization Tool is a web application developed by the National Cancer Institute (NCI) and the National Institutes of Health (NIH) to help researchers generate randomization sequences for their clinical trials.

A study statistician should be consulted in conjunction with the design and implementation of your randomization scheme to ensure it is appropriate for your clinical trial. NCI and NIH are not responsible for how any randomization sequence is used in a clinical setting.

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• v.1(1); Jan-Apr 2011

An Overview of Randomization and Minimization Programs for Randomized Clinical Trials

Mahmoud saghaei.

Department of Anesthesiology, Medical Image and Signal Processing Research Center, Department of Anesthesia, Isfahan University of Medical Sciences, Isfahan, Iran

Randomization is an essential component of sound clinical trials, which prevents selection biases and helps in blinding the allocations. Randomization is a process by which subsequent subjects are enrolled into trial groups only by chance, which essentially eliminates selection biases. A serious consequence of randomization is severe imbalance among the treatment groups with respect to some prognostic factors, which invalidate the trial results or necessitate complex and usually unreliable secondary analysis to eradicate the source of imbalances. Minimization on the other hand tends to allocate in such a way as to minimize the differences among groups, with respect to prognostic factors. Pure minimization is therefore completely deterministic, that is, one can predict the allocation of the next subject by knowing the factor levels of a previously enrolled subject and having the properties of the next subject. To eliminate the predictability of randomization, it is necessary to include some elements of randomness in the minimization algorithms. In this article brief descriptions of randomization and minimization are presented followed by introducing selected randomization and minimization programs.

INTRODUCTION

As stated in the Consolidated Standards of Reporting Trials,[ 1 ] a clear description of the method used to enroll subjects into different arms of a trial is necessary. This, way the reporter declares that no selection bias was present in the trial, and therefore, the trial results are valid.[ 2 ] Subjects must be allocated to trial groups randomly. The main purpose of random allocation is to prevent selection biases. In this article different aspects of randomization and minimization are presented, followed by a brief introduction of some common allocation programs.

RANDOMIZATION

Randomization or random allocation is usually performed by generating a random list of subject allocations prior to the start of a trial. Randomization is usually associated with trial blindness. That is, during randomization each subject will be given a unique identification code (numeral or alpha), which after the completion of the study will be decoded to the actual subject group. Traditional methods of subject allocation to treatment groups, such as, allocating every other subject to each group (alternating allocation) is not considered random allocation. Randomization may be simple or blocked.[ 3 ] In simple randomization we construct a randomized list of all the subjects who are going to be enrolled into the trial. Although it is effective to randomize subjects into trial arms, simple randomization may accidentally result in clusters of subjects being given the same treatment in certain periods during the trial. Also it tends to be inefficient with respect to the available resources, which is a problem when the trial involves preparation and blind labeling of drugs prior to the intervention. Block randomization can overcome the problem of subject sequestration and resource inefficiency by dividing the whole set of randomized subjects into smaller blocks. In this manner, after completion of a block, an equal number of subjects will be enrolled in each group. Also the researchers have to prepare and label the drugs for only one block at a time. The main usage of block randomization is for controlling the systematic factors, such as, time and location, which otherwise may affect the outcome of the trial. For example, in multi-center trials, each center may receive a whole block of subjects. Unfortunately, block randomization increases the predictability of subject enrollment near the end of the block boundary, especially when the allocations of already enrolled subjects are known and the blocks have an equal number of subjects from each group. Thus, one may guess the group of the next subject, especially if this is the last subject in the block. To overcome this problem we may use variable, but predefined block sizes, with blinding of researchers about the block boundaries. This way the block sizes are different from one another, which reduce the probability of predicting subject membership. Block sizes and numbers can be totally in random, that is the number of blocks and the size of each block can be varied randomly. This is random permuted block randomization.

To allocate subjects to treatment groups randomly, we can use the table of random numbers, tossing a coin, drawing sealed envelopes, and using computer software. Supervising the overall aspects of randomization and keeping records of different allocations, with their labels, is a difficult and error-prone task, which necessitates using advance computer software. Randomization software has the capability to control different aspects of randomization, such as, the type of randomization, generating unique identification codes for each participant and implementation of trial blindness. The typical randomization software has functions and control for selecting the type of randomization from among simple, equal blocks, random fixed permuted blocks, and total permuted blocks. In addition these software offer control over a generation of unique identifier strings to select alpha, numeric or mixed types of unique identifiers in sequential or random orders.

During the last decade many randomization programs have been developed. Some of these programs are downloadable and run on a personal computer (PC), others are used as web services. Although many of these randomization programs are free, a majoritiy of them are not open sources, which prevents close inspection of their algorithm and program functions. In this article some of these softwares are introduced. The selection is based on the availability of service, download, and documentation. This must in no way be considered as an exhaustive list of randomization programs, and the selection is only on availability and ease of use. A comprehensive list of randomization programs is available at the Directory of Randomization Software and Services.[ 4 ]

Clinstat is a free, closed source, interactive, multi-module MS-DOS statistical software for carrying out basic statistical analysis, in addition to performing randomization.[ 5 ] As it is old, running MS-DOS programs is tricky. Appendix A provides the basic instruction for running an MS-DOS program under the Windows operating system. Upon execution in a DOS console, the program displays a menu for various statistical analyses [ Figure 1 ]. Apart from different statistical modules, there is a randomization module for random number generation, sampling, and allocation of tasks, which can be selected as the eighth option in the main Clinstat menu (under ‘miscellaneous calculations’). In this program the trial groups are unlimited and it randomly allocates up to 1000 subjects into any number of treatment groups. The program support both equal and unequal group sizes. Block randomization (fixed and random sizes) is also supported. Group names or labels cannot be specified, and the subjects are allocated into groups with numeric indicators (that is group 1, 2, 3, …). Further documentation about the software is available on the program's website.

Clinstat program. A – The first screen of the Clinstat program showing different statistical utilities. To perform randomization, select option 8 ‘miscellaneous calculations’ from this menu. B – Upon selection of option 8 from the main menu, this menu will be displayed in the Clinstat program. For randomization select ‘random sampling and allocation’ (option 1). C – Different randomization procedures in the Clinstat program. D – An output from the program after selecting ‘random allocation in fixed blocks’ (menu option 6), showing two blocks of the output

Randomization.com

Randomization.com is an online, closed-source, free web service for obtaining randomized lists.[ 6 ] This program supports up to 20 groups each, with a unique label. Sequentially each subject is given an ID number, which by default starts from one, but it is possible to specify a different starting point. It consists of three generators. The first generator produces random permuted blocks with specified block sizes. Up to four block sizes may be used, and for each block a repeat factor can be specified, which defaults to one [ Figure 2 ]. The second generator is for cross-over studies, where each subject must receive all the treatments in random order. The output determines the order of receiving treatments for each subject. Up to six treatment labels may be entered [ Figure 3 ]. Orders may be produced in random permutations in which some orders may occur more frequently than others, or at balanced permutations, in which different orders occur at the same time. The last generator is for random sampling from a population source. The only thing this generator does is to permute a sequence of integers. In other words it shuffles the sequence in a random way. Separate documentations are available on the service website for each of three generators.

First generator of Randomization.com for random permuted blocks of determined sizes and numbers. Up to 20 group names may be entered. A maximum of four block sizes together with the number of blocks with each size may be specified

Second generator of Randomization.com for randomizing the order of treatment in cross-over trials. Up to six treatment labels may be specified

GraphPad QuickCalcs

GraphPad QuickCalcs is a closed-source, free, online limited randomization service for allocating subjects to a number of groups, with repeated block defaults at one.[ 7 ] It can also produce a shuffled list of numbers for each group. No documentation is available for this randomization service.

Research Randomizer

Research Randomizer is also a closed-source, free, randomization web service.[ 8 ] It can be used for random sampling, random assignment to treatment groups, and block randomization. It does not support group labels. This randomization service has an excellent tutorial with five sample randomization scenarios for random sampling, random assignment, random block assignment, generating random numbers in a specified range, and random ordering of a set of items.

Random Allocation Software and Service: The Random Allocation Software is a closed, source-free, desktop software, running on the MS-Windows operating system.[ 9 ] The Random Allocation Software is also available as a free open source web service.[ 10 , 11 ] Both have different settings for simple and blocked randomizations; length, format, and ordering of generated unique identifiers; type and format of program output; and saving sessions for future use. It permits complete control over the randomization protocol. However, it does not support randomization for cross-over trials or adapted randomization. Complete documentation of the program is published in the BMC Medical Research Methodology.[ 12 ]

Adaptive Randomization

This is a closed-source, free desktop software, available for download and running, on the MS-Windows operating system, under the dot net framework.[ 13 ] This program supports a specific type of randomization in which the randomization probabilities are affected in favor of those treatments with better outcomes. Two kinds of outcome measures can be fed into the program, which is a binary and time-to-event program. It has a limit of up to ten treatment groups. Also this program supports interim measures and stops rules for terminating a trial when certain criteria are met. It has adaptation factors. The more the adaptation factors, the more will be the probability of their assignment to treatments with better outcomes. The zero of this adaptation factor (no adaptation) means complete randomization. This program is a desktop software, running under the Windows operating system and requires pre-installation of the dot net framework.

MINIMIZATION

The most important drawback of the randomization software is the problem of unmatched groups. In the process of randomization it is probable that the treatment groups develop significant differences in some prognostic factors, especially when the sample size is relatively small (<200).[ 14 , 15 ] If these factors have important effects on the primary or secondary outcomes of the study, any important difference in the levels of these factors invalidate the trial results, and necessitate complicated statistical analysis with unreliable results. Various methods have been used to overcome the problem of unmatched trial groups including minimization and stratification, with minimization providing more acceptable results.[ 16 ] Taves,[ 17 ] in 1974, and Pocock and Simon,[ 18 ] in 1975, independently described the method of minimization. With minimization the first subjects are enrolled randomly into one of groups. The subsequent subjects will be allocated to treatment groups after hypothetical allocation of each subject to every group, and then calculating an imbalance score. Using these imbalance scores, we can decide to which group the new subject must be allocated, to have the minimum amount of imbalance, in terms of prognostic factors. Pure minimization is indeed completely deterministic, that is, we can predict which group the next subject will be enrolled in, provided the factor levels of the new subject are known. This may invalidate the principle of trial blindness and introduce some bias into the trial. To overcome this shortcoming some elements of randomness are incorporated into the minimization algorithm, to make the prediction unlikely. Unfortunately the whole process of minimization is well beyond the skill of a typical clinical researcher, especially when the problem of unequal group allocations has to be taken into account. The difficulty in computation has resulted in a relatively less frequent use of minimization methods, in randomized clinical trials. The computer software can perform excellently in these situations, especially when the implementation has been logical. In the following sections, the aspects of two minimization programs are presented. Again the selection of these programs is based on the availability and ease of use.

Minim is a free, but closed-source, MS-DOS program, for minimizing subjects into the arms of a clinical trial.[ 19 ] This program must be run under the DOS or Windows operation system. Appendix A provides the basic instruction for running an MS-DOS program under the Windows operating system. Minim is an interactive program, which means it prompts for user input, one at a time, then displays the next prompt, and asks for another input. Upon execution it prompts for the data file name, which is the file containing the minimization settings for a trial, together with the already allocated subjects’ data if there are any. Therefore, if one has already defined a trial by this program and previously saved it, they can enter its name to load it. Otherwise the name will be used as also the name of the new trial settings. When defining a new trial, the program asks for trial information and the different trial settings. Appendix B is a typical minim program session, which displays the questions the program asks and sample answers to the questions.

To the best of our knowledge this program does not support setting the method and the amount of probability used for allocation of subjects to trial groups. Also it does not allow changing the distance measure.

MagMin is an online, closed-source, private minimization service, for blind allocation of subjects to multi-center clinical trials. As this is not a public service, its properties cannot be fully evaluated. However, in an article presenting this program it has been described as a minimization program using the Pocock and Simon's minimization method,[ 18 ] using standard deviation as the distance measure.[ 20 ] MagMin seems to have limited choice over different aspects of minimization, such as, the choice of distance measure. Anyhow, due to its unavailability it cannot be elucidated for certainty of its full potential. A demo website is available, which shows active allocation.[ 21 ] This demo has been previously set up, and in its present form is a running minimization service, which shows allocation of a new subject into the trial without displaying the details of the minimization setting. In the running demo it is possible to add subjects by minimization to an already defined trial. The demo asks for different properties of new subjects and enrolls it into the trial and returns the numerical blind code of the enrolled subject.

MinimPy is a free, open-source, desktop minimization program, which allocates subjects to treatment groups in a clinical trial.[ 22 ] With this program nearly all aspects of a minimization model can be configured. Of special note is the ability to choose distance measure and the probability method. In addition this program supports the biased coin minimization as the probability method, which has not been used in previous programs. MinimPy is produced using the python programming language,[ 23 ] which is very strong and efficient for computational purposes, and it is one of the most readable programming languages. MinimPy requires python to be installed, with gtk libraries, for support of graphic user interface. This program has different windows for such things as minimization settings, variables, groups, allocations, and balance [ Figure 4 ]. It also supports pre-loading an already allocated sample into a trial.

MinimPy program showing different tabs for settings, variables, groups, allocations, table and balance. In this figure the settings tab is displaying variuos aspects of minimization protocol such as probability method and distance measure

CONCLUSIONS

With the advent of computer program and online services for randomization and minimization in clinical trials, an increasing number of randomized clinical trials are going to make efficient use of them. However, there are few aspects of these program and services that need more attention to make them more acceptable for various needs of clinical researches. Also it can be concluded that there is an increasing need to move toward open-source development, to enhance the quality of the produced software and make them available to the critiques of different clinical and software specialists.

Appendix A: Running MS-DOS Programs

MS-DOS programs usually do not need installation. To run the program you need an MS-DOS operating system. Alternatively, you can run the program in a DOS console under Windows. For the latter, click the start menu and select Run. A dialog window appears. Type ‘cmd’ (without quotes) in this dialog window, to open a DOS terminal, with the blinking cursor in front of a greater than sign (>). Command and programs are run by typing their names in front of this command prompt. First change the current directory to the one where your program is situated. Here we suppose your program name is prog.exe and it is in the C: \myprog folder:

> cd\

> cd myprog

> prog.exe

Below is a typical minim program session that displays questions the program asks (in italic) and sample answers to the questions (bold). Texts between braces ({.}) are comments provided here to further elaborate the answers to questions:

What is the title for this trial? Test Trial

Type variable name No. 1 (‘*’ to end) ? Gender

How many categories has Gender ? 2

What name for category 1? Male

What name for category 2? Female

What weighting should Gender have? 1

{The weight of this variable showing its relative importance. A value of 1 means no special importance}

Type variable name no. 2 (‘*’ to end) ? Age

How many categories has Age? 3

What name for category 1? < 20 YO

What name for category 2? 20 – 50 YO

What name for category 3? > 50 YO

What weighting should Age have? 1

Type variable name no. 2 (‘*’ to end) ? *

Give the name of treatment group 1? Acetaminophen

Give a symbol to represent Acetaminophen ? A

Give a value for proportional allocation ? 1

{The ratio of allocation for this group. It is the partial contribution of this group in total sample size. Default is 1}

Give the name of treatment group 2? Placebo

Give a symbol to represent Placebo ? P

Give the name of treatment group 3 (‘*’ to end) ? *

Is that all correct ? Y

Type ‘A’ for Allocating new patients by minimization, or ‘U’ for Updating data with manually entered patients, or ‘S’ to StoP >> A

Do you have details of a patient ? Y

What is the value of Gender for this patient?

Value, or code in range 1 to 2 ? 1

What is the value of Age for this patient?

<20 YO. 1

20 – 50 YO. 2

>50 YO. 3

Value, or code in range 1 to 3 ? 2

Current patient details are:

Do you want to alter any of these details? N

Patient allocated to treatment Placebo.

Do you have details on a patient?

Mahmoud Saghaei is a professor in the Department of Anesthesia at the Faculty of Medicine, Isfahan University of Medical Sciences, Isfahan, Iran. He is also a part time member of Medical Image and Signal Processing Research Center ( http://misp.mui.ac.ir/en/ ), which works on different aspects of biomedical engineering solutions to link the medical society with engineers.

Source of Support: Nil

Conflict of Interest: None declared