Understanding Mis-Stratification in Randomized Controlled Clinical Trials

Stratified randomization is a common practice in randomized, controlled clinical trials. It ensures that key characteristics are evenly distributed across treatment groups and the treatment assignments are balanced within each randomization stratum, enhancing the validity of study results. However, during the course of a trial, mis-stratification can occur—this happens when an incorrect stratification stratum is used during randomization. Let's explore what this means, why it happens, and how it impacts clinical trials.

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What is Mis-Stratification?

In clinical trials, stratification factors (e.g., age, disease severity, disease subgroup, or background medication use) are used to group participants before randomization. Stratified randomization is used to ensure that equal numbers of subjects with one or more characteristic(s) thought to affect the treatment outcome in efficacy measure will be allocated to each comparison group. Mis-stratification - a type of randomization errors, occurs when:

• An incorrect stratification factor is used for randomization, or
• A participant is placed in the wrong stratum due to an error.

Despite this, the treatment assignment and drug dispensation remain accurate, making it a minor deviation rather than a critical error. When mis-stratification occurs, the random code and the treatment assignment is pulled from an incorrect stratum. 

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Historical Approach: Intention-to-Treat Principle

Traditionally, clinical trials have adhered to the Intention-to-Treat (ITT) principle, where participants are analyzed according to the group they were originally randomized to, regardless of any errors. This approach maintains the integrity of the randomization process.

In practice, this means using the original stratification data—even if incorrect—in the statistical analysis. A typical Statistical Analysis Plan (SAP) might state:

“All original stratification information used in the randomization procedure will be used for analyses, regardless of whether it was later found to be incorrect. All efficacy analyses will be performed primarily on the ITT Population.”

This approach minimizes bias and reflects the 'real-world' impact of treatment. However, in the mis-stratification situation, using the incorrect stratum information in analyses may be too harsh and too strict unnecessarily.

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Why Does Mis-Stratification Occur?

Mis-stratification can result from several factors, including:

• Too Many Stratification Factors: More factors increase the complexity and likelihood of error.
• Local vs. Central Lab Results: Differences between local and central lab measurements can lead to misclassification.
• Timing of Measurement: Stratification factors measured at different times (baseline vs. screening) may not align.
• Medication Use: Stratifying by prior or concomitant medication use can be complicated by variations in patient reporting or prescription practices.

These issues highlight potential flaws in protocol design and study quality, emphasizing the need for clear definitions and consistent procedures.

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Regulatory Perspective: FDA Guidance

The FDA's guidance document, “Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products,” provides clarity on handling mis-stratification:

“Randomization is often stratified by baseline covariates. A covariate adjustment model should generally include strata variables and can also include covariates not used for stratifying randomization. In some cases, incorrect stratification may occur and result in actual and as-randomized baseline strata variables. A covariate adjustment model can use either strata variable definition as long as this is prespecified.  “

This guidance supports the use of either the originally assigned stratification or the actual baseline data in the analysis, provided it is specified before data unblinding. This flexibility helps maintain the study's validity while addressing stratification errors transparently.

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Impact on Study Results

Mis-stratification is generally considered a minor deviation because its impact on efficacy and safety analyses is minimal. It does not affect treatment assignment or drug dispensation but only the stratum from which the assignment was drawn.

When incorrect stratification occurs, the actual stratification information is collected in the Electronic Data Capture (EDC) system and can be used in sensitivity analyses to evaluate the robustness of the study results.

There is an article "Handling misclassified stratification variables in the analysis of randomised trials with continuous outcomes" where the authors did the simulation study to investigate the impact of the mis-stratification on the statistical analyses. 

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Minimizing Mis-Stratification in Randomization

Too many mis-stratification errors indicate the poor quality of the clinical trial. To reduce the risk of mis-stratification, consider the following best practices:

• Limit Stratification Factors: Use the minimum necessary factors to reduce complexity.
• Consistent Measurement Timing: Align the timing of stratification factor measurements (e.g., always at baseline).
• Clear Definitions: Ensure stratification criteria are clearly defined, identified or measured, and uniformly applied.
• Training and Quality Checks: Provide thorough training for study personnel and implement rigorous quality checks.

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Conclusion

While mis-stratification is not ideal, its impact on clinical trial results is usually minimal. By adhering to the Intention-to-Treat principle and following regulatory guidance, researchers can maintain the integrity of their analyses. As clinical trial designs become more complex, understanding and managing mis-stratification will continue to be crucial for maintaining study quality and reliability.

Known knowns and Unknown Unknowns

On several occasions during scientific presentations, I have come across citations of Donald Rumsfeld's statement. Donald Rumsfeld was one of the most famous US Secretary of Defense.

"There are known knowns; there are things we know that we know. 

There are known unknowns; that is to say, there are things we now know we don't know.

But there are also unknown unknowns - there are things we do not know we don't know."

Wikipedia includes an entry on the phrase 'there are unknown unknowns,' a term popularized by Donald Rumsfeld. He famously used it in response to a question about the absence of evidence linking the Iraqi government to the supply of weapons of mass destruction to terrorist groups.

With respect to awareness and understanding, unknown unknowns can be compared to other types of problems in the following matrix:

In clinical trials, comparing an experimental therapy to a control group is often complicated by confounding factors—both known and unknown. Randomization is a key method for addressing these challenges, as it helps balance these factors across treatment groups. By randomly assigning participants to different groups, randomization ensures that potential confounders are evenly distributed, enabling a more accurate comparison of treatment effects.

For known confounding factors, stratified randomization can be employed. This approach involves dividing participants into strata based on specific factors and then randomizing them within each stratum, ensuring an equal probability of assignment to either treatment group within each category. For unknown known or unknown unknown confounding factors, the only way to minimize the impact is to utilize the randomization. 

Randomization is regarded as the cornerstone of causal inference in randomized controlled trials (RCTs). It enables researchers to attribute differences in outcomes between groups to the treatment under investigation, rather than to pre-existing differences among participants, thereby strengthening the validity of the findings.

The awareness-understanding matrix, which includes concepts like 'known unknowns' and 'unknown unknowns,' can be applied to scenarios such as xenotransplantation—for instance, the transplantation of porcine organs into humans. In the context of xenotransplantation, there is always a potential risk of zoonotic infections, where pathogens may be transmitted from animals to humans. There are known pathogens (viruses) and there are unknown pathogens. As Dr Jay Fisherman discussed the issue in his paper "Xenotransplantation-associated infectious risk: a WHO consultation":

"In xenotransplantation, there is the unique potential risk for the transmission of both known and unknown zoonotic infectious agents of animal origin into human recipients and into the wider human population."

"Xenotransplantation will necessitate the development of surveillance programs to detect known infectious agents as well as previously unknown or unexpected pathogens in the absence of recognizable clinical syndromes. This may include assays for known infectious agents, probes for classes of infectious agents (e.g., common genes or antigens of herpesviruses), and assays for unknown pathogens in a variety of tissues."

 "Unknown pathogens: Organisms not known to be human pathogens, not known to be present in the source animals, or for which clinical syndromes and microbiologic assays are poorly described or unknown"

The awareness-understanding matrix is dynamic. With advancements in science, today's unknown unknowns may eventually evolve into known unknowns or even known knowns.

Clinical trials with external control, historical control, concurrent control, contemporaneous control, and synthetic control

Three critical features for modern clinical trials are control, randomization, blinding. For the golden standard of RCTs (randomized controlled clinical trials), a concurrent control group is critical. With recent advances in clinical trial designs, non RCTs such as real-world data (RWD)/real-world evidence (RWE), single arm trial, registry studies have been much discussed. The control group is now expanded to include concurrent control, external control, historical control, contemporaneous control. 

Concurrent Control: ICH E10 "Choice of Control Group in Clinical Trials" defined the concurrent control as the following: 

A concurrent control group is one chosen from the same population as the test group and treated in a defined way as part of the same trial that studies the test treatment, and over the same period of time. The test and control groups should be similar with regard to all baseline and on-treatment variables that could influence outcome, except for the study treatment. Failure to achieve this similarity can introduce a bias into the study. Bias here (and as used in ICH E9) means the systematic tendency of any aspects of the design, conduct, analysis, and interpretation of the results of clinical trials to make the estimate of a treatment effect deviate from its true value. Randomization and blinding are the two techniques usually used to minimize the chance of such bias and to ensure that the test treatment and control groups are similar at the start of the study and are treated similarly in the course of the study (see ICH E9). Whether a trial design includes these features is a critical determinant of its quality and persuasiveness.

Concurrent control is the feature of the RCTs and involves the randomization. The subjects are randomized into the test group or control group over the same period of time. 

External Control and Historical Control: ICH E10 "Choice of Control Group in Clinical Trials" defined the external control (including historical control) as the following:

External Control (Including Historical Control)

An externally controlled trial compares a group of subjects receiving the test treatment with a group of patients external to the study, rather than to an internal control group consisting of patients from the same population assigned to a different treatment. The external control can be a group of patients treated at an earlier time (historical control) or a group treated during the same time period but in another setting. The external control may be defined (a specific group of patients) or non defined (a comparator group based on general medical knowledge of outcome). Use of this latter comparator is particularly treacherous (such trials are usually considered uncontrolled) because general impressions are so often inaccurate. So-called baseline controlled studies, in which subjects' status on therapy is compared with status before therapy (e.g., blood pressure, tumor size), have no internal control and are thus uncontrolled or externally controlled (see section 2.5).

 Historical control is also external control. External control may or may not be historical control 

Contemporaneous Control may also be called contemporaneous cohort. In clinical trials with contemporaneous control group, subjects are recruited (not randomized) into the test group and the control group over the same period of time. The key idea is to compare subjects in the same time frame. For example, in a comparison of surgery versus chemotherapy for breast cancer, you wouldn't want to use surgery patients from 20 years ago as a control group to compare against a current chemo group. 

An great example of a clinical trial with a contemporaneous control group is a study assess the EVLP (ex-vivo lung perfusion) lung versus traditional (normal) lung in lung transplantations. In a non-randomized study "Extending Preservation and Assessment Time of Donor Lungs Using the Toronto EVLP System™ at a Dedicated EVLP Facility", according to the the study protocol, a contemporaneous control group was included to provide context for EVLP results and to inform control measures for future research. For every EVLP lung transplantation, a contemporaneous control lung transplantation with matched study center, single and double lung transplantation, lung allocation score. It is possible that for some EVLP lung transplants, the contemporaneous controls may not be identified which results in the large sample size in EVLP group than the contemporaneous control group. 

Once the donor lung is accepted following EVLP, the eligible recipient, who has provided written informed consent, and receives the lung transplant, is enrolled into the study. Patients who consent for the current EVLP , but receive a conventional (i.e., non-EVLP) lung transplant will be considered for a contemporaneous control group matched to the EVLP treatment group (66 subjects each). This matching will take place on a patient-by-patient basis and only after an EVLP subject has been enrolled at that Study Center. Investigators and their team will be notified by the Sponsor on a real-time basis of the specific matching criteria required for a control subject as EVLP subjects are enrolled. In order to be considered for eligibility, the control patient must “match” a priori to at least one EVLP subject who has already been enrolled at that Study Center based on the following criteria: SLT versus DLT and Lung Allocation Score Disease Diagnosis Group (LASDDG).

Contemporaneous control group is external, but concurrent control. Contemporaneous control group is similar to the matched control group in epidemiological case-control and cohort studies - similar statistical analysis approaches (such as conditional logistic regression) may be used for analyses.

Synthetic Control: synthetic control was discussed in a previous post "Synthetic Control Arm (SCA), External Control, Historical Control". Synthetic control includes subjects who are selected from historical clinical trials and who are on standard of case, and whose baseline characteristics match the current-day experiment group. Synthetic control is historical control, not concurrent control, but with matched baseline characteristics with the concurrent experiment treatment group. 

One Extra Point: 

One interesting discussion is about the control group in platform trial where multiple treatment arms are compared to the common control group. Since the different treatment arms may be added to or removed from the platform at different times, for a specific treatment - control group comparison, the control group may be not recruited over the same period of time. This issue was discussed in a NEJM paper "
Platform Trials — Beware the Noncomparable Control Group" and a JAMA paper "How to Use and Interpret the Results of a Platform Trial".

In platform trial, control group from a randomized trial may not be concurrent control.  

Randomization and elements of randomization specifications

Randomization is the process of assigning trial subjects to treatment or control groups using an element of chance to determine the assignments to reduce bias. Randomization is the most critical feature of the RCT (randomized, controlled trials). In FDA's Good Review Practice: Clinical Review of Investigational New Drug Applications, the randomization is defined as the following: 

In the context of clinical trial design, randomization is defined as the allocation of patients to the investigational drug and control arms by chance. Randomization is intended to prevent any systematic difference between patients assigned to the treatments being compared and is a critical assumption for valid statistical comparisons. It is also intended to produce groups that are comparable (statistically balanced) with respect to both known and unknown factors. 

Randomization Schedule (also called a randomization scheme) is a list of randomization numbers and the corresponding treatment assignments in a data set (or in a printout in the early days). Randomization Schedule can be generated using SAS Proc Plan. A SUGI paper"Generating Randomization Schedules Using SAS Programming" I wrote 20 years ago is still applicable. 

Three steps for generating the randomization schedule for use in clinical trials: 

• Create randomization specifications according to the study protocol requirements
• Create and validate dummy randomization schedule for review and approval
• Create and validate the final randomization schedule - the final randomization schedule for implementation

The dummy randomization schedule and the final randomization schedule have the same display but are generated with different random seeds (therefore different treatment assignments). The dummy randomization schedule can be reviewed by the study team and the final randomization schedule can only be distributed to the designated recipients who are unblinded to the treatment assignments. 

Here is an example randomization specification: 

Here are the elements for the randomization specifications: 

Study Design: clinical trial design dictates how the subjects are assigned to receive different study treatments. In clinical trials with parallel design, subjects are randomized to receive the treatments; in clinical trials with cross-over design, subjects are randomized to different treatment sequences. 

The study design will also include a randomization strategy: 

Fixed randomization: 

• fixed-randomization scheme (rarely used)
• block randomization
• stratified randomization, 

Dynamic randomization: 

       Adaptive randomization. 

See FDA's Good Review Practice: Clinical Review of Investigational New Drug Applications for definitions of these different types of randomizations. 

Blind and blindness: concealing treatment assignments and treatment allocations. 

Block: Block randomization works by randomizing subjects within blocks such that within each block, the # of subjects is balanced between treatment groups or according to the randomization ratio. 

Block Size: The size of each block. Block sizes must be multiples of the number of treatments and take the allocation ratio into account. For 1:1 randomization of 2 groups, blocks can be sizes 2, 4, 6 etc. For 1:1:1 randomization of 3 groups or 2:1 randomization of 2 groups, blocks can be sizes 3, 6, 9 etc. 

If the randomization is by site, to prevent the potential unblinding/guessing, the block size can be set up as variable for different blocks or is not revealed to the investigators and study team. With central randomization, potential unblinding is less of a concern and the block size can be the smallest multiples (for 1:1 randomization of 2 groups, the block size can be 2). 

Number of Blocks

Total Number of Randomizations: Total number of randomization numbers to be generated. Total number of randomizations = Number of blocks x Block size. Usually, randomization numbers more than the protocol-specified sample size are generated to make sure that there is a sufficient number of randomizations in the situation that the sample size may be increased or randomization errors that results in some randomization numbers not being used. If the study protocol specifies 300 subjects to be randomized, it may be good to generate 600 randomizations. 

Strata and Stratification Factors: Stratification factors are those known factors that may have an impact on treatment responses. Stratification factors are the known confounders. The most common stratification factor is the baseline disease severity which usually has an impact on the treatment responses. When stratification factors are specified, stratified randomization is employed to prevent imbalance between treatment groups for known factors that influence prognosis or treatment responsiveness. The randomization schedule is essentially generated for each stratum. 

See previous posts "Restricted randomization, stratified randomization, and forced randomization"; "Minimization Algorithm to Achieve Treatment Balance across Strata in Stratified Randomization", and "Handling Randomization Errors in Clinical Trials with Stratified Randomization"

Randomization Ratio (or allocation ratio): The ratio for treatment groups. The typical randomization ratio is balanced: 1:1 ratio for two treatment groups (if the block size is 2, for every 2 subjects randomized, there will be one assigned to group A and one assigned to group B); 1;1:1 ratio for three treatment groups, ... The randomization ratio can also be unbalanced such as 2:1 (if the block size is 3 (minimal), for every three subjects randomized, there will be two assigned to group A and one assigned to group B) and 3:1,...  FDA's Good Review Practice: Clinical Review of Investigational New Drug Applications described the randomization ratio (allocation ratio) as the following: 

Allocation of patients to treatment and control arms can be uniform or nonuniform. Uniform allocation (i.e., equal numbers allocated to each arm) is the usual practice and provides the most statistical power for a given total sample size. Nonuniform allocation  may lower costs (if one arm is substantially more expensive) and improve recruitment (if one arm is generally preferred) and may increase the size of the exposed patient safety database. In general, the loss of statistical power in seeking to detect a difference between treatments going from uniform allocation to 2:1, or even 3:1, is fairly small; however, as more imbalanced allocation occurs, power drops off more rapidly. A special case is where a trial seeks both to show effectiveness versus placebo and to compare the test drug with an active control. In that case, it usually is necessary for the active treatment groups to be substantially larger to examine the smaller differences between the active treatments. 

Randomization Number: a series of sequential numbers corresponding to treatment assignments. 'randomization number' is not random, the associated treatment assignments are random. 

Randomization can be recorded in the database and serve as the subject identifier (same as the subject number). Seeing the randomization number will not unblind the subject's treatment assignment.  

Treatment Code: short description or abbreviation for long treatment descriptions. Treatment code can be just the letters (such as A = Active; P = Placebo). 

Treatment Description: the detailed description of the treatment groups. It can be just 'Active', 'Placebo' or more descriptive as "Inhaled drug X BID', 'Inhaled Placebo BID'.

Dummy Randomization Schedule: also called surrogate randomization schedule - the randomization schedule for review and approval purposes. The dummy randomization schedule should have exactly the same features as the final randomization schedule except that a different random seed is used (therefore, the treatment assignments are different). 

Random Seed: A number (integer) used to initiate a pseudorandom number generator. Random Seed is a number used in SAS Proc Plan to generate the randomization schedule. Random Seed needs to be specified in the program in order to reproduce the same randomization schedule. 

After dummy randomization schedule is reviewed and approved, a final randomization schedule can be generated for implementation by changing the random seed. 

Randomization Envelopes: Envelopes that contain the treatment assignment information. The outside of the envelope contains the randomization number, and the inside of the envelope contains the randomization number and the corresponding treatment assignments and treatment descriptions. Randomization envelopes were used in the randomization process in the early days. The randomization process using randomization envelopes is now replaced with the Interactive Response Technology (IRT) including the Interactive Web Response System (IWRS) or Interactive Voice Response System (IVRS). 

Central Randomization is the opposite of randomization by the site. When a subject is eligible to be randomized, the site will contact a centralized contact (usually the computer system, IRT) to obtain the next available randomization number in the corresponding stratum regardless of the individual sites.

References: SAS/STAT User's Guide The PLAN Procedure

Common Issues in Implementing Randomization and Blinding

Randomization and blinding are two techniques to help prevent (conscious or unconscious) bias in clinical trials and they are the cornerstone of the randomized, controlled clinical trials (RCTs) and in FDA's terms, the cornerstone of the adequate & well-controlled clinical trials (A&WCs). As stated in FDA's Good Review Practice: Clinical Review of Investigational New Drug Applications:

Randomization and blinding are the two principal means of reducing bias and ensuring validity of trial conclusions. Randomization helps protect against the possibility that differences between groups at baseline will lead to outcome differences that might mistakenly be attributed to drug effect. Blinding protects against the possibility that differences in the on-trial treatment or assessment of subjects will lead to spurious outcome differences that are mistakenly attributed to a drug effect. 

In the context of clinical trial design, randomization is defined as the allocation of patients to the investigational drug and control arms by chance. Randomization is intended to prevent any systematic difference between patients assigned to the treatments being compared and is a critical assumption for valid statistical comparisons. It is also intended to produce groups that are comparable (statistically balanced) with respect to both known and unknown factors. 

While every effort is made to prevent the mistakes in implementing the randomization, it is inevitable to have the randomization errors and mistakes here and there. Here are some of the randomization errors that may be seen in clinical trials. 

Ineligible subjects are randomized: Clinical trials contain a screening period for verifying the eligibility of the study participants. All inclusion and exclusion criteria are checked during the screening period. If a subject meets all inclusion and exclusion criteria, the subject is eligible to be randomized. Sometimes, subjects are thought to be eligible for randomization, but only, later on, are found to be ineligible for one or more entry criteria. When ineligible subjects are randomized into the study and receive the assigned study treatments, the subjects are considered to be in the study. According to the intention-to-treat principle, the subjects will be included in the analyses regardless of the violation of the inclusion or exclusion criteria. If the critical criteria that are violated have an impact on the efficacy evaluation, the subjects may be excluded from the per-protocol population and sensitivity analyses are conducted with the per-protocol population to assess the robustness of the results from the primary analysis. 

Choosing the wrong stratum for randomization: For clinical trials with stratified randomization, the randomization is executed within each stratum. When a new subject is eligible to be randomized, the next available randomization number in the corresponding stratum (for example, based on the subject's gender, baseline disease severity category,...) is allocated to the subject. 

It is not uncommon that the investigational sites to select an incorrect stratum for the randomization especially when the strata information requires additional derivation and calculation, for example, if a  subject with or without using one class of background medications is a stratification factor, the information about the use one class of background medication may need to be derived. 

If a randomization stratification factor is measured more than one time, which measure will be used for randomization needs to be clearly stated in the protocol. If a spirometry parameter (for example, % predicted FEV1 >= 50% versus <50%) is used as a randomization stratification factor and spirometry tests are performed at both screening and baseline visits, the protocol needs to be specific regarding whether the results from screening visit or the baseline visit will be used for randomization - typically, the measures at the baseline visit should be used for randomization. If a laboratory parameter is used for randomization and there are both local lab and central lab, the protocol needs to be specific regarding which lab results will be used for randomization - typically the central lab results at the baseline will be used for randomization unless the central lab results can not be obtained in time for the randomization. 

See previous post "Handling Randomization Errors in Clinical Trials with Stratified Randomization"

Randomize the patients too early before all eligibility criteria are met: The investigator rushed to go to the randomization system (IRT) and randomized the subject to trigger the downstream activities, then realized that one or more screening results were still pending. 

Once the subject is randomized, it can’t be undone in the randomization system (IRT system). However, the site can hold on to the randomization information obtained and wait for the last pieces of the screening results to confirm the eligibility. If the last piece of the screening results confirms that the subject is eligible to be randomized, the previously obtained randomization information will then be used. The subject can move on to initiate the assigned study treatment. If the last piece of the screening results indicates that the subject is ineligible to be randomized, we will then need to decide if the subject is allowed to be in the study. If so, it will become the situation mentioned in the previous section "Ineligible subjects are randomized". 

In either situation, a protocol deviation needs to be recorded to document this incident. 

The PI was practicing the randomization system to see how the randomization works but accidentally randomized the subject in a live system. In this situation, there was no actual and real subject to be randomized. The subject information entered into the randomization system was not real, but one of the randomization numbers was assigned and treatment assignment was used. 

While this subject may remain in the randomization system (IRT), the subject is fake and should be removed from the downstream clinical database. This is usually a rare event, therefore, has no big impact on the integrity of the original randomization. 

Randomization system (IRT system) is down at the time of randomization or the internet is down: sometimes, the randomization needs to be performed immediately after the last eligibility criterion is confirmed. It is critical to have immediate access to the randomization information in order to randomize the subject in time for initiating the randomized treatment. However, it could happen that the IRT system is down or the internet is down when the randomization number and treatment assignments are needed. 

If this is a situation, the advice is to have a backup manual randomization system (for example, calling an unblinded person or group). 

Dispense the incorrect drug kit: nowadays, the randomization system is embedded in the system for clinical trial supplies (IRT system). In addition to the treatment assignments, a separate drug kit list will be generated. When a subject is randomized and a treatment group is assigned, the drug kits that are corresponding to the assigned treatment will be allocated and dispensed to the subject. 

See a previous post "Monitoring the double-blind study: unblinded pharmacist, unblinded monitor, and drug kit"

Due to human error, it is possible to have the correct randomization information but dispense the incorrect kit numbers. When this happens, it is adverse to verify with the clinical trial supply manager (who are unblinded) if the incorrect drug kit is for the same treatment group as the drug kit that is supposed to be dispensed (Don't communicate about the actual treatment group). It is less an issue if the incorrect kit numbers are in the assigned treatment group.

If the incorrectly dispensed drug kits are not in the assigned treatment group, the subjects received the incorrect treatment. For the statistical analysis, the subject will be included in the intention-to-treatment analysis and will be included in the randomized treatment group  (so-called 'as randomized). The subject can be excluded from the per-protocol population for sensitivity analysis. 

Recording the randomization date/time (local time versus backend system time): When a subject is randomized in the IRT system, a randomization message or printout, or randomization report will indicate the subject number, randomization number, the stratification factors used for randomization, randomization date/time. The investigator can record the randomization information in the case report form. Only blinded information can be included in the randomization report. 

One issue for this report is the randomization date/time - is it based on the IRT system date/time or the local date/time?  The local date/time should be used as the randomization date/time. If the IRT system is located in the UK and the subject is randomized in the US, the local and system time can differ in 5-8 hours. Local date/time, not the system date/time should always be used as the randomization date/time.  

The same subject is randomized twice (unless it is the micro-randomized trial)

The majority of these randomization errors that occurred in the study were not included in the publications and regulatory submissions - the randomization issues appear to be less than what actually occurred. Some of the examples of the randomization errors can still be found in the literature: 

• This article by Downs et al "Some practical problems in implementing randomization" documented some situations with randomization errors. 
• in a Takeda study SAP, a section was included to describe the handling of randomization errors. 

• in the recent FDA's advisory committee meeting to discuss Amylyx pharmaceuticals' ALS drug, the randomization issues in their randomized trial (CENTRAUR trial) were discussed. Here is what in the presentations: 

"To start, at the beginning of CENTAUR, a randomization implementation problem was identified and addressed by the unblinded statistician. Let’s walk through the details. In CENTAUR, kits were shipped one by one after successful screening visits. While preparing for the first Data Safety Monitoring Board meeting in November 2017, the unblinded statistician found that the initial 18 study kits shipped were all active. This was due to an error at the distribution center. They proceeded to instruct the distribution center to balance these 18 kits by shipping a block of 9 placebo kits to maintain randomization. After correction, the 2:1 active:placebo ratio was maintained. The unblinded statistician notified Amylyx of this issue in January 2020, two months after study unblinding in November 2019. Participants, investigators, and study staff were never unblinded due to this error. Upon notification, Amylyx initiated a thorough investigation of the root cause, in consultation with the unblinded statistician and the distribution center. Amylyx also consulted with external statisticians to determine the best approach to assess the impact. The statisticians recommended a sensitivity analysis to exclude the participants affected by the error."

•  in a paper by Douglas et al, "Fluid Response Evaluation in Sepsis Hypotension and Shock: A Randomized Clinical Trial", 4 subjects with randomization errors were excluded from the intention-to-treat analyses even though there was no mention what kind of randomization errors were.
• in a paper by Martinez et al "Treatment of Persistent Cough in Subjectswith Idiopathic Pulmonary Fibrosis (IPF)with Gefapixant, a P2X3 Antagonist, in a Randomized,Placebo-Controlled Clinical Trial", a programming error in IWRS caused the randomization errors.

Randomization, Re-Randomization, and Micro-Randomization

 I recently saw a Twitter post mentioning "Micro-Randomized Study Design Example - Maryland Alcohol-Dependent Moms Abstinence (MAMA) Study" and found the term 'micro-randomization' interesting and prompted me to compare the concept of randomization, re-randomization, and micro-randomization. Based on the number of times that a subject can be randomized in a study, we can differentiate the studies as randomized, re-randomized, and micro-randomized trials. 

Randomization is the process of assigning subjects (patients, clinical trial participants) by chance to groups that receive different treatments. In the simplest trial design (parallel-group design), the investigational group receives the new treatment and the control group receives standard therapy. At several points during and at the end of the clinical trial, researchers compare the groups to see which treatment is more effective or has fewer side effects. Randomization helps prevent bias. Bias occurs when a trial's results are affected by human choices or other factors not related to the treatment being tested.

ICH Topic E 9Statistical Principles for Clinical Trials has an entire section discussing randomization as the key design technique to avoid biases:

"2.3.2 Randomisation

Randomisation introduces a deliberate element of chance into the assignment of treatments to subjects in a clinical trial. During subsequent analysis of the trial data, it provides a sound statistical basis for the quantitative evaluation of the evidence relating to treatment effects. It also tends to produce treatment groups in which the distributions of prognostic factors, known and unknown, are similar. In combination with blinding, randomisation helps to avoid possible bias in the selection and allocation of subjects arising from the predictability of treatment assignments.

The randomisation schedule of a clinical trial documents the random allocation of treatments to subjects. In the simplest situation it is a sequential list of treatments (or treatment sequences in a crossover trial) or corresponding codes by subject number. The logistics of some trials, such as those with a screening phase, may make matters more complicated, but the unique pre-planned assignment of treatment, or treatment sequence, to subject should be clear. Different trial designs will require different procedures for generating randomisation schedules. The randomisation schedule should be reproducible (if the need arises).  

......"

In typical clinical trials, the study participants will be randomized only one time whether to different treatments or different treatment sequences. For clinical trials with parallel-group design, subjects are randomized to receive one of two or more treatments. For clinical trials with cross-over design, subjects are randomized to follow one of two or more treatment sequences. Once the treatment sequence is determined, subjects will follow the sequence to receive multiple treatments (for example, treatment A then treatment B or treatment B than treatment A,...)

The vast majority of randomized clinical trials are falling into this category and this includes:

• randomized double-blind trials: randomization + blinding 
• randomized open-label trials: randomization without blinding
• randomized cross-over trials: randomization to the sequence of treatments
• adaptive randomized trials: adjust the randomization ratio
• "N of 1" clinical trials: can be considered as a high order crossover, once the sequence is decided, the treatments at various stages are decided

Re-randomization is the process describing a situation where each patient can be randomized more than one time in the same study.  There are two types of re-randomization:

re-randomization in SMART trial design framework - SMART stands for Sequential Multiple Assignment Randomized Trial. In a trial with SMART designs, the same subject may be randomized more than once depending on the response to the initial assigned treatment after the initial randomization. According to the paper by Kidwell et al "Sequential, Multiple Assignment, Randomized Trial Designs in Immuno-oncology Research", A SMART is a multistage, randomized trial in which each stage corresponds to an important treatment decision point. Participants are enrolled in a SMART and followed throughout the trial, but each participant may be randomized more than once. Subsequent randomizations allow for unbiased comparisons of post-initial randomization treatments and comparisons of treatment pathways. The goal of a SMART is to develop and find evidence of effective treatment pathways that mimic clinical practice.

In a review paper by Wallace at el "SMART Thinking: a Review of Recent Developments in Sequential Multiple Assignment Randomized Trials", the following general diagram was given for SMART design:

We saw that SMART design with re-randomization was used in clinical trials in different therapeutic areas:

In a paper by Almirall et al "Introduction to SMART designs for the development of adaptive interventions: with application to weight loss research", the following diagram was used to illustrate a SMART design for weight loss research. After the initial randomized treatment period, the responders and non-responders are identified. The non-responders were re-randomized to different treatments. 

Ruppert et al described a study with SMART design in CLL "Application of a sequential multiple assignment randomized trial (SMART) design in older patients with chronic lymphocytic leukemia" where patients with complete response after stage 1 were re-randomized to receive two different treatments at stage 2. 

We conducted an ICE study - a registration study with IGIV-C in CIDP (a rare neurology disease) "Intravenous immune globulin (10% caprylate chromatography purified) for the treatment of chronic inflammatory demyelinating polyradiculoneuropathy(ICE study): a randomised placebo-controlled trial". We did not explicitly state the SMART design but did employ the re-randomization in the study. The subjects who were responders (to the blinded treatment) were re-randomized to receive either IGIV-C or Placebo in additional six months follow-up period. The re-randomized portion of the study was to compare the relapse rate between two treatment groups - a key secondary efficacy endpoint. 

With the re-randomized portion of the study, we built in two randomizations in the same study and demonstrated the treatment effect of IGIV-C in the primary efficacy endpoint of improving the responder rate and also the treatment effect of IGIV-C in preventing the relapse in the additional follow-up period - essentially two studies in one. This was used as a rationale for a single pivotal trial (two studies in one) to provide substantial efficacy for effectiveness. 

Re-randomization is also discussed for use in different settings where the subjects who complete the initial randomized period are put back to the randomization pool. Subjects were re-randomized to the study as if they are new to the study. In other words, the same subject was re-used and re-randomized into the study. Kahan et al described this type of re-randomized trial as the following: 

This type of re-randomized design is very rarely used and may be used in clinical trials with ultra-rare diseases that patient recruitment is extremely challenging. 

A Micro-randomized trial (MRTs) can be considered as an extension of the SMART design. The same subject can be randomized and re-randomized many times to different interventions. The time scale is much more frequent and short (for example several times in a day). The term 'micro-' can be confusing, but it is used to differentiate this type of randomization from the classical setting where randomization can not be too frequently. The term 'micro-' is used to describe a setting where the randomization/re-randomization needs to be conducted more frequently on a much short time scale - almost continuous time points. A Micro-randomized trial is good for the interventions that are delivered through mobile devices (such as push notification) and is good for interventions that are intended for changing subjects' behaviors. 

Here is a website describing what the micro-randomized trial is:

In micro-randomized trials (MRTs), individuals are randomized hundreds or thousands of times over the course of the study. The goal of these trials is to optimize mobile health interventions by assessing the relative effect of different intervention options and assessing whether the intervention effects vary with time or the individual's current context. With MRTs we can gather data to construct optimized just-in-time adaptive interventions (JITAIs).

Intervention options can include either or both engagement strategies and therapeutic treatments. Consider the Heartsteps MRT (described below) that is designed to promote physical activity among sedentary people. Heartsteps includes phone notifications with tailored activity suggestions to encourage physical activity; these are therapeutic in focus. On the other hand the SARA MRT (also described below) is designed to promote engagement by young adults in substance abuse research. SARA includes rewards for participants who complete assessments; these are engagement strategies. The design of both of these projects can be seen in the “Projects Using MRTs” section, below.

In an MRT, each participant can be randomized many times. For example in the Heartsteps project, the researchers identified five times throughout the day when people are mostly likely to be available to take a brief walk. At each of the five time points, the application randomizes between delivering a phone notification containing a tailored activity suggesion or to not deliver anything; as a result over the course of the 42 days, each participant is randomized 210 times. This sequence of both within-participant and between-participant randomizations comprises the MRT.

The MRT data can then be used to assess the effectiveness of the tailored activity suggestions and to build rules for when to deliver the suggestions in order to help individuals be more active. To do this the application records a variety of outcomes. In this case, the app collects the minute-by-minute step count from the participant’s activity-tracking wristband throughout the day, the participant’s overall level of physical activity, and the participant’s context at each of the 5 times per day (using GPS to determine the person’s location and the local weather). The resulting data is used by researchers to assess the effectiveness of the activity suggestions and to build rules for when and where to deliver the suggestions. In other MRTs, the randomization could apply to what type of intervention to provide, rather than whether or not to provide an intervention. The ultimate goal of Heartsteps is the development of a JITAI that will successfully encourage higher levels of physical activity. The study design of the MRT used in Heartsteps is shown below.

MRTs are an emergent innovation in behavioral science.

We are in the digital era and digital tools will become more used in interventions (especially the adaptive intervention) for lifestyle and behavior changes. However, we don't think that the 'micro-randomized trials' will be suitable for drug trials for registration purposes. 

• On this date, there are 16 registries in clinicaltrials.gov using micro-randomized trials. Not surprisely, all micro-randomized trials are in the behavioral science field.  
• Xu et al "Multi-Level Micro-Randomized Trial: Detecting the Proximal Effect of Messages on physical activity"
• “Micro-randomized Trials in Mobile Health” with Zhenke Wu, PhD
• Dr. Susan Murphy: Micro-randomized Trials for JITAI Development

Randomization Using Envelopes In Randomized, Controlled, and Blinded Clinical Trials

I read an article by Clark et al “Envelope use and reporting in randomized controlled trials: A guide for researchers”. The article reminds me of the old times when envelopes were the popular ways for randomization and blinding (treatment concealment). In the 1990s and 2000s, for randomized, blinded clinical trials, the concealed envelope is the only way for the investigator to do the emergency unblinding (or code breaking) and sometimes the way to administer the randomization for single-blinded studies.

In Berende et al (2016, NEJM) “Randomized Trial of Longer-Term Therapy for Symptoms Attributed to Lyme Disease”, the study protocol described the following procedure for "unblinding of randomization" where sealed envelopes were used.  

I used to be an unblinded statistician to prepare the randomization schedule (including the randomization envelopes) for clinical trials. The following procedures will need to be followed:

• Based on the study protocol, develop the randomization specifications describing randomization ratio, stratification factors, block size, the number of randomization codes, recipients of the randomization schedule, or code-break envelopes
• Generate the dummy randomization schedule for the study team to review and approval
• Replace the random seed to generate the final randomization schedule (a list of all randomized assignments)
• Prepare the randomization envelopes (randomization number, stratification factors outside the envelope, and treatment assignment inside the envelope)
• QC the randomization envelopes (to make sure that inside/outside information matches the randomization schedule
• Shipping and tracking

For double-blinded studies, both the investigator and the patient are blinded to the treatment assignment. The randomization schedule will usually be sent to a third party (for example, the pharmacist) who is unblinded to the treatment assignment and can prepare the study drug for dispensing or administration. The third-party (for example, the pharmacist) must not be involved in other aspects of the clinical trial conduct. The concealed envelopes can be sent to the investigators for emergency unblinding. If there is a medical emergency requiring the unblinding of an individual subject, the investigator can open the code break envelope to reveal the treatment assignment for the specific subject.

For single-blinded studies, the investigator is unblinded to the treatment assignment and the patient is blinded to the treatment assignment. The randomization schedule and/or the randomization envelopes can be sent to the investigators.

Nowadays, randomization through envelopes is obsolete. The randomization procedures are integrated into the overall CTM (clinical trial material)  management process through the IRT (interactive response technologies). In the last 20 years, the randomization process has shifted from randomization envelopes -> IVRS (interactive voice response system) -> IWRS (Interactive Web Response System) - > IRT.

With IRT, the randomization schedule will be sent to the IRT vendor and uploaded into the IRT system. The study team members can be assigned different levels of access to the IRT system depending on their roles in the study. The investigators and pharmacovigilance personnel can be granted the emergency access code for them to gain the access to the treatment assignment in IRT when necessary.  

However, in some situations, randomization envelopes may still the best way for implementing the randomization.

In a study by Chetter et al “A Prospective, Randomized, MulticenterClinical Trial on the Safety and Efficacy of a Ready-to-Use Fibrin Sealant as an Adjunct to Hemostasis during Vascular Surgery”, the randomization occurred in the operation room and only after the target bleeding site (TBS) was identified after the surgical procedure. There would not be ideal for the surgeon (the investigator) to log into the IRT system to obtain the treatment assignment information. The better approach would be for the surgeon or surgeon’s assistant to open the randomization envelope to obtain the treatment assignment information in the operation room. The randomization procedure was described as the following in the paper:

Randomization

In the Primary Study, patients were randomized 2:1to treatment with FS Grifols or MC after the identification of the TBS during the procedure. Treatment group assignments were generated by the randomization function of the statistics software and communicated using sealed opaque envelopes. Due to the obvious differences between the 2 treatments, blinding of investigators was not possible following randomization

Additional Reads:

• Kennedy et al (2017) Subversion of allocation concealment in a randomised controlled trial: a historical case study
• Deng and Graz (2002) Generating Randomization Schedules Using SAS Programming
• Park et al (2012) Rapid, easy, and cheap randomization: prospective evaluation in a study cohort