All-Comer Trials With Prespecified Subgroup Claims

Why Prespecify a Subgroup Claim in an All-Comer Trial?

An all-comer trial enrolls eligible participants without restricting entry to one biomarker group. If a treatment may work differently according to a biomarker, the trial can still make a planned claim about that subgroup—but the subgroup, outcome, effect scale, and testing rule must be set before outcome data are examined. The trial must enroll enough participants in the subgroup to estimate its treatment effect with useful precision.

This design differs from fixed enrichment in biomarker-positive populations, where enrollment is restricted to that population. In an all-comer trial, the study can estimate both the treatment effect in the full target population and effects within prespecified biomarker groups. Those are distinct estimands: a positive result in one does not automatically establish a result in the others.

The target population and its biomarker prevalence matter: an all-comer effect for a population with \(\pi=0.2\) need not equal the effect for one with \(\pi=0.6\). For a trial-based estimate, the weighting should reflect the prespecified target population; using the observed trial prevalence is appropriate when the trial’s enrolled population represents that target. Earlier material on population-specific estimands for enrichment designs distinguishes these target-population choices.

Specify Enrollment, Estimands, and Claims

Before recruitment, specify the eligibility criteria, assay and cutoff, timing of biomarker measurement, clinical outcome and assessment time, treatment contrast, and target population. Enroll eligible participants regardless of biomarker status, and plan enough overall accrual to obtain the required number of evaluable participants in each group. A subgroup claim is not well supported if biomarker status is unavailable for many participants or if one subgroup contributes too little information.

State the claims as hypotheses. For example, a two-sided test of no treatment effect in the positive group is \(H_0:\Delta_+=0\) against \(H_a:\Delta_+\ne 0\). A test of no effect modification on the additive scale is \(H_0:\Delta_+-\Delta_-=0\). The all-comer claim tests \(H_0:\Delta_{\mathrm{all}}=0\). These hypotheses answer different questions: the interaction test asks whether effects differ between groups, not whether the treatment works in either group.

A confirmatory plan must also state how type I error is controlled across the claims. If both the all-comer and positive-subgroup effects may independently support a claim, testing both at the full nominal \(\alpha\) can inflate the chance of at least one false positive. A simple prespecified option is Bonferroni allocation: for \(m\) claims, test each at \(\alpha/m\). Other prespecified multiplicity procedures can be suitable, but the chosen rule must match the intended claims. An interaction test may be included as a separate confirmatory claim only if it is included in that error-control plan.

Model and Assess the Treatment-by-Biomarker Interaction

For a continuous outcome, a standard starting model is a linear model with treatment \(A=1\) for the experimental treatment and \(A=0\) for control, biomarker \(B\), and their product:

Here \(Y\) is the outcome for a participant and \(\varepsilon\) is an individual residual. In this parameterization, the control mean is \(\beta_0\) for \(B=0\) and \(\beta_0+\beta_B\) for \(B=1\). The treatment effect is \(\Delta_-=\beta_A\) for the negative group and \(\Delta_+=\beta_A+\beta_{AB}\) for the positive group. Therefore, \(\beta_{AB}=\Delta_+-\Delta_-\): it is the interaction, or difference between subgroup treatment effects, on the mean-difference scale.

This model presumes independent participants, correct classification of biomarker status, and a suitable mean model. The familiar pooled-variance standard error also presumes a common residual variance across the four treatment-by-biomarker cells and uses a normal-reference approximation when sample sizes are adequate. If variances differ, observations are clustered, or the outcome model is unsuitable, the standard error and analysis must be adapted. The outcome scale matters: interaction on a difference scale is not the same as interaction on a ratio scale.

The arithmetic in this example is sensitive to the four variance contributions: the displayed sum is about 3.1746, not 6.349. Its square root is about 1.782 points, and the corresponding statistic is about 2.806. Checking the sum before taking its square root is an essential safeguard in interaction calculations.

Make Population-Level Claims With Error Control

A treatment-effect estimate in the positive subgroup and an all-comer effect can both be clinically relevant, but the two claims must be distinguished. A statistically significant effect in one subgroup and a nonsignificant effect in another does not prove that the effects differ. The interaction contrast directly evaluates that difference. Conversely, a subgroup effect can be estimated precisely enough to support a prespecified subgroup claim even when the interaction test is not significant; the evidence for that claim and the evidence of heterogeneity answer separate questions.

Diagnostics, Alternatives, and Limitations

Before interpreting results, check that biomarker status was measured consistently with the prespecified assay and cutoff, subgroup counts are adequate, and outcome availability is reported by treatment and biomarker group. Examine cell-specific outcome distributions and residual behavior for influential observations, skewness, or variance differences that could undermine the chosen model and standard error. Review whether the observed prevalence represents the target population used for the all-comer estimand. If the outcome is missing differentially across treatment or biomarker groups, a complete-case comparison may not estimate the intended treatment effects without additional assumptions and methods.

The main alternatives answer different design questions. A fixed-enrichment trial concentrates recruitment on the biomarker-positive group and can be more efficient for a claim confined to that group, but it does not directly estimate effects for all-comers. An all-comer trial with a prespecified subgroup claim retains the broader target population and can support explicitly planned claims for both the subgroup and overall population, at the cost of needing adequate accrual in each relevant group and a multiplicity plan. An unplanned subgroup search is not a valid substitute: choosing a marker cutoff or subgroup after viewing outcomes makes nominal p-values and intervals misleading unless selection is accounted for.

Interaction tests can have limited power because they compare treatment effects and depend on information from all four cells. A non-significant interaction is not proof of equal effects. A significant interaction is also scale-specific and does not alone establish clinically meaningful benefit in a subgroup. In addition, prevalence-based weighting and subgroup estimates can be unstable when the marker is rare, classification is imperfect, or data are missing. These limitations should be considered in the design and reflected in the wording of any claim.

Common Mistake

Wrong reasoning: “The treatment effect is significant in biomarker-positive participants but not significant in biomarker-negative participants, so the treatment works differently by biomarker status.” This compares two significance decisions rather than comparing the effects. Correction: estimate \(\Delta_+-\Delta_-\) and assess the prespecified interaction test if the scientific claim is that treatment effects differ. Separately test the treatment effect for any subgroup or population claim using the planned multiplicity procedure.