Should You Rerandomize if Treatment Groups Are Imbalanced at Baseline?

What Should You Do When the First Random Allocation Looks Unbalanced?

You have randomized participants into two treatment groups. Before the intervention begins, you examine their baseline characteristics and discover that one group has substantially higher prior achievement, greater disease severity, or a different distribution of another important characteristic.

Would it be reasonable to generate a new randomization sequence until the groups look more comparable?

Repeating randomization may seem like an obvious solution. After all, the goal is to create comparable treatment groups. But the methodological consequences depend on whether rerandomization was specified as part of the original allocation design or introduced informally after an unfavorable assignment appeared.

The distinction matters because a planned restriction on random allocation can be statistically defensible, while selectively accepting assignments after inspecting them can change the experiment in ways that conventional analyses fail to recognize.

Do Not Rerandomize Informally, but Prespecified Rerandomization Can Be Valid

When Rerandomization Is Methodologically Defensible

What Is Rerandomization?

Rerandomization is a restricted random allocation procedure in which candidate treatment assignments are generated and evaluated against a defined balance criterion. Assignments that do not satisfy the criterion are rejected, and the process continues until an acceptable allocation is obtained.

Unlike unrestricted randomization, which accepts the first valid allocation regardless of its baseline characteristics, rerandomization restricts the set of assignments that can ultimately be used.

Morgan and Rubin's methodological framework formalized rerandomization as a design strategy for improving covariate balance in randomized experiments.

The essential requirement is that the balance criterion be specified before examining candidate allocations and before treatment assignment is implemented.

When properly designed, rerandomization remains a chance-based allocation procedure. It does not require researchers to assign participants according to personal judgment or to choose whichever arrangement appears most favorable to the experimental intervention.

Why Is Informal Rerandomization Problematic?

Suppose researchers generate a valid allocation, examine the baseline table, and decide that the groups do not look sufficiently similar. They generate another allocation, inspect it, and continue until the differences appear acceptable.

If the decision criteria were not established beforehand, the final allocation may depend on subjective judgments or preferences about which participants should receive each treatment.

The actual allocation process is no longer the unrestricted randomization procedure originally described in the protocol.

This creates two related concerns. First, investigator discretion may compromise the protection against selection bias. Second, statistical analyses based on the originally assumed randomization distribution may not reflect how the final assignment was selected.

Even when investigators have no intention of favoring a particular intervention, undocumented selection among candidate allocations can undermine reproducibility and transparency.

The problem is therefore not that every repeated draw is inherently invalid. It is that the rules governing which allocation is accepted must be defined and incorporated into the design.

How Is Planned Rerandomization Different?

In a planned rerandomization design, investigators specify the relevant baseline variables and an objective balance criterion before generating candidate treatment assignments.

For example, researchers might require the difference in baseline achievement between two groups to remain within a prespecified tolerance.

The allocation system generates a candidate assignment, evaluates it against the criterion, and either accepts it or generates another candidate.

Crucially, the decision does not depend on the observed intervention outcomes or on researchers' preferences about which participants should receive the experimental condition.

The final assignment is drawn from the set of allocations satisfying the predetermined criterion, subject to the properties of the sampling algorithm.

Only the first two represent clearly defined randomization designs when properly implemented. The third creates avoidable uncertainty about the actual allocation mechanism.

What Makes a Balance Criterion Acceptable?

A balance criterion should be objective, reproducible, and based on baseline characteristics that are scientifically relevant to the primary outcome or the intended comparison.

It should be specified before candidate allocations are examined.

Researchers might use absolute standardized differences, a multivariate balance measure, or predefined restrictions on treatment-group composition.

The criterion should also be feasible. Requiring nearly identical groups on many characteristics may leave very few acceptable assignments and make the allocation procedure excessively restrictive.

Importantly, the criterion should not depend on the direction of treatment assignment in a way that deliberately favors one intervention. A symmetric balance criterion is generally desirable because it treats exchanges of treatment labels consistently.

Researchers should justify why the selected characteristics matter rather than attempting to balance every measured variable.

How Can Mahalanobis Distance Be Used?

Mahalanobis distance provides a multivariate measure of separation between treatment-group covariate means while accounting for the covariance structure among those characteristics.

In rerandomization designs, it can be used to assess whether the overall baseline difference across selected covariates falls within a prespecified acceptable range.

For a two-group experiment with a fixed set of units and an invertible covariate covariance matrix, a commonly used form is:

The threshold of 2 in this example is hypothetical and not a recommended universal cutoff.

For multiple covariates, the calculation incorporates their correlations. A covariance matrix that is singular or poorly estimated can create difficulties, particularly when the number of covariates is large relative to the number of randomized units.

Mahalanobis distance is one possible balance criterion, not a requirement for every rerandomization design.

Why Must the Statistical Analysis Account for Rerandomization?

Rerandomization changes the distribution of possible treatment assignments by excluding allocations that fail the balance criterion.

Consequently, the randomization distribution differs from that of an unrestricted experiment.

Statistical inference should reflect the actual assignment mechanism, especially when using randomization-based tests or confidence intervals.

For example, a randomization test can generate candidate assignments according to the original procedure and retain only those satisfying the same prespecified balance criterion.

Analytical methods that account for the restricted design and appropriate covariate adjustment may also be used under their stated assumptions.

It would be incorrect to assume that any conventional analysis automatically remains exact after rerandomization.

The consequences depend on the estimand, outcome model, number of randomized units, acceptance criterion, and inferential method.

Statistical planning should therefore occur before implementing rerandomization rather than after the final allocation has been selected.

Does Rerandomization Guarantee Identical Treatment Groups?

No. Rerandomization improves balance according to the selected criterion, but it does not make participants identical.

Characteristics excluded from the criterion may remain imbalanced. Even selected covariates may show differences within the accepted tolerance.

Nor does balancing measured baseline characteristics establish equality in unmeasured characteristics.

Randomization continues to provide protection against systematic allocation based on unmeasured prognostic factors, subject to the design and implementation.

The appropriate objective is to improve balance on scientifically important measured characteristics without undermining the random allocation process.

When Is Rerandomization Particularly Useful?

Rerandomization may be useful when the number of independently randomized units is relatively small and chance imbalance on important baseline characteristics could substantially reduce precision.

Cluster randomized trials are a common context for considering restricted allocation because the number of schools, clinics, communities, or institutions may be limited.

For example, a trial randomizing 12 schools may have substantial differences in baseline achievement, school size, or socioeconomic composition across candidate allocations.

A prespecified restricted randomization design could improve balance on selected school-level characteristics.

However, the number of acceptable allocations must remain sufficient to preserve a meaningful randomization mechanism and support the intended analysis.

Overly restrictive criteria can produce a very small set of possible assignments, creating inferential and operational problems.

How Does Rerandomization Compare With Stratification and Minimization?

Rerandomization, stratification, and minimization are different approaches to improving allocation balance.

These methods are not interchangeable. Their feasibility depends partly on whether participants are recruited sequentially or whether the complete set of randomization units is known before allocation.

When participants enter one at a time, conventional stratified blocking or covariate-adaptive methods may be more practical than repeatedly reallocating a fixed set of participants.

The decision about when to use stratified randomization should therefore consider the recruitment structure as well as the scientific importance of the selected covariates.

Can Rerandomization Be Used After Participants Have Received Treatment?

Generally, no. Once participants have received interventions, changing their treatment assignments is not simply another draw from the original randomization procedure.

Treatment exposure may already have influenced outcomes, behavior, or subsequent eligibility. Reassignment could introduce treatment-history effects, ethical concerns, and violations of the intended experimental comparison.

A planned rerandomization design is implemented before the treatment assignments become operational and before intervention exposure begins.

Researchers should distinguish rerandomization from legitimate designs involving multiple stages of random assignment, such as sequential multiple-assignment randomized trials. Those designs address different scientific questions and have their own prespecified procedures.

What If Randomization Was Implemented Incorrectly?

A documented randomization error requires a different response from ordinary chance imbalance.

For example, the allocation system may have assigned the wrong treatment, a recruiter may have accessed future assignments, or an incorrect stratification category may have been entered.

Such incidents should be documented and evaluated according to the protocol, trial governance procedures, and relevant ethical requirements.

Investigators should determine whether the problem affects participant safety, allocation integrity, or the validity of the intended comparison.

Repeating randomization is not automatically the appropriate remedy. Depending on the circumstances, the trial may require a documented correction, protocol amendment, sensitivity analysis, or other governance decision.

The key is to distinguish an actual implementation error from an unfavorable but valid chance allocation.

Why Is Allocation Concealment Still Important?

Even a prespecified rerandomization design can be compromised if recruiters or intervention providers gain access to candidate or final allocations before enrollment is appropriately finalized.

Researchers should ensure that allocation generation and acceptance are conducted through secure procedures.

Where possible, individuals who can influence participant enrollment should not be able to choose among acceptable assignments or anticipate the final treatment allocation.

The distinction between allocation concealment and blinding remains relevant because rerandomization does not remove the need to protect the assignment process.

What Should Be Reported About Rerandomization?

A trial using rerandomization should describe the selected baseline variables, balance criterion, acceptance threshold, allocation-generation procedure, and method used to select the final acceptable assignment.

Researchers should also report how allocation concealment was maintained and how the restricted randomization mechanism was reflected in the analysis.

Where relevant, the number or proportion of acceptable allocations and the extent of achieved balance may help readers evaluate the procedure.

CONSORT 2025 requires reporting the type of randomization and details of restrictions. A rerandomization design should be described sufficiently for readers to understand and, where possible, reproduce the allocation procedure.

Investigators should not describe the final allocation as unrestricted simple randomization if candidate assignments were screened using balance criteria.

Prespecified Rerandomization in a School-Level Trial

With 12 schools assigned equally to two conditions, there are 12!/(6! × 6!) = 924 possible labeled allocations before applying additional balance restrictions.

If a hypothetical criterion accepted 20% of these allocations, approximately 185 assignments would satisfy the criterion. The exact number would depend on the observed school characteristics and the specified rule.

The researchers should assess whether the resulting set of acceptable assignments supports the intended randomization and inferential procedures.

Now consider a different situation: the researchers generate one valid allocation, dislike its baseline table, and repeatedly regenerate assignments without having specified an acceptance rule. That is not the same transparent design. The final allocation would depend on an undocumented decision process.

The scientific justification for rerandomization lies in the planned restriction and its appropriate analysis, not simply in obtaining a more attractive baseline table.

Common Misconceptions About Rerandomization

How to Respond to Baseline Imbalance Without Compromising the Trial

If the trial has already been randomized properly, do not assume that an unfavorable baseline table requires new assignments.

Verify the allocation process, identify whether the imbalanced variables are prognostically important, and retain the prespecified analysis unless a documented methodological issue justifies further action.

The distinction between chance imbalance and a compromised allocation process should guide every decision.

For future trials, researchers can use prior evidence and simulation to determine whether restricted randomization would improve balance sufficiently to justify its complexity.

For an ongoing trial, preserving the integrity of the original allocation and transparently reporting limitations is generally preferable to changing assignments because the groups do not look sufficiently similar.

Before Deciding to Rerandomize

Questions About Rerandomization and Baseline Balance

Do Not Confuse Planned Restricted Randomization With Repeating an Unfavorable Draw

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