Enrichment, Stratification, And Subgroup Selection

Why the Recruitment Strategy Changes the Question

A biomarker can be used to define who is eligible for a trial, to organize randomization while retaining a broad population, or to guide a change in eligibility during the trial. These choices are not interchangeable. They determine which patients contribute evidence, how treatment comparisons are protected against imbalances, and how broadly the results can be applied.

The key distinction is between who may enroll and how enrolled participants are assigned. Enrichment changes eligibility by restricting enrollment to a selected group. Stratified all-comer recruitment retains participants across biomarker groups and uses the groups to structure randomization. Adaptive subgroup selection begins with a broader population and uses an interim rule to decide whether recruitment or follow-up should continue in a narrower group. In all three cases, conclusions need to be interpreted in light of the population actually studied.

For this tutorial, assume the biomarker is measured before randomization, the group definitions are specified in advance, and the trial can classify participants consistently. Assume also that treatment assignment is randomized within each group where the design calls for stratification. These assumptions make the treatment comparisons interpretable within the enrolled groups; they do not by themselves ensure that a trial result applies to people who were excluded or poorly represented.

Three Designs, Three Recruitment and Randomization Patterns

In fixed biomarker enrichment, the biomarker criterion is an eligibility rule from the outset. A biomarker-negative person is not randomized, so the trial directly compares treatments in the eligible biomarker-positive population. This can concentrate enrollment where the treatment is expected to be useful or where the clinical question is focused. It cannot directly establish a treatment effect among the excluded group.

In stratified all-comer recruitment, both biomarker-positive and biomarker-negative participants are eligible, subject to the other trial criteria. Randomization is conducted separately within each group, often using the same treatment allocation ratio in both. Stratification helps ensure that treatment groups do not end up with very different biomarker-group compositions merely by chance. It does not mean that the trial is enriched: participants from both groups remain eligible.

In adaptive subgroup selection, the trial begins with a broader eligible population, often including more than one biomarker group. At an interim point, a prespecified rule can select one or more groups for continued recruitment or evaluation. Depending on the design, the selected group can become the only group eligible for the later stage. Participants assigned before the decision remain part of the trial data; selection does not erase their observations. Because the selected group is chosen using accumulating data, confirmatory interpretation must account for the selection and the trial’s testing plan.

How an All-Comer Average Relates to Subgroup Comparisons

When both biomarker groups are enrolled, a treatment comparison in the full trial population combines information from the groups. The relationship can be stated without assuming that treatment effects are equal. Let \(\Delta_+\) and \(\Delta_-\) denote the treatment-minus-control mean differences in a specified outcome for the positive and negative groups, respectively. Let \(\pi\) be the proportion biomarker-positive in the population whose overall effect is being described. If the groups partition that population and the outcome is measured on the same scale, the population-average contrast is the weighted average of the two subgroup contrasts.

The justification follows from linearity of expectation. Write \(Y(1)\) and \(Y(0)\) for the outcome under treatment and control, and let \(G\) identify the biomarker group. The overall mean outcome under treatment is the group-weighted mean \(E[Y(1)]=\pi E[Y(1)\mid G=+]+(1-\pi)E[Y(1)\mid G=-]\); the analogous expression holds under control. Subtracting the control expression from the treatment expression gives the displayed equation. This identity describes a population average; it does not say that the subgroup effects are equal or that the observed trial proportions necessarily match the population weights of interest.

Adaptive Subgroup Selection in Practice

An adaptive subgroup-selection design specifies, before the interim decision, which data will be reviewed, when they will be reviewed, what groups can be selected, and what follows from each possible decision. The rule might retain all groups, continue in one group, or stop for lack of a sufficiently promising group. This tutorial concerns the design distinction, not the construction of a particular testing rule.

A selection decision changes the evidence-generating process. The interim data help determine which population supplies later observations, so the selected group may have looked unusually favorable partly because of random variation. The selection rule should therefore be prespecified, implemented as written, and reflected in confirmatory analyses. An unplanned choice made after inspecting subgroup results is not equivalent to a prospectively designed adaptive rule.

Design Checks, Failure Modes, and Limitations

Before enrollment, verify that the protocol makes the eligibility and randomization rules operational: define the biomarker groups, state whether all groups are eligible, specify the randomization strata, and describe how any interim selection changes recruitment. During conduct, compare actual enrollment and randomization with the plan. In a stratified all-comer trial, check that each intended group is accruing and that treatment allocation remains balanced within groups. In an adaptive trial, verify that the interim data cut, decision, and post-decision eligibility match the prespecified rule.

Important failure modes include a biomarker group enrolling so slowly that it contributes little information, treatment allocation becoming imbalanced within a stratum, and an adaptive decision being implemented differently from the protocol. A further interpretive failure is to report a selected-group result as if it applied to the full population without evidence supporting that broader claim. The trial’s observed group mix may also differ from the mix in the population to which someone hopes to apply an overall result.

No one design is uniformly best. Fixed enrichment can focus resources and participants on a defined population, but gives no randomized evidence in excluded groups. Stratified all-comer recruitment preserves randomized comparisons in multiple groups and can support an overall result for the enrolled mix, but requires sufficient recruitment and information across those groups. Adaptive subgroup selection can allow the trial to narrow its later recruitment based on interim evidence, but introduces operational complexity and selection-related inferential challenges. The choice depends on the intended population, recruitment feasibility, and the claims the trial is designed to support.