Preserving the Target During Biomarker Enrichment

Why the Target Can Change When Eligibility Narrows

Biomarker enrichment can make a trial more focused: after an interim decision, eligibility may narrow to patients who test positive for a baseline biomarker. But narrowing eligibility also changes the population represented by new enrollees. A treatment effect estimated from the positive-only stage is not automatically an effect for all eligible patients. The central question is therefore not only who is randomized after adaptation, but which population the treatment-effect estimand is intended to describe.

The distinction matters even when the treatment conditions, outcome, and analysis method remain unchanged. If treatment effects differ between biomarker-positive and biomarker-negative patients, a change in the proportion enrolled from each group can change the overall effect. The target population and its weights must therefore be specified separately from the trial’s evolving eligibility rules.

The word “target” is essential in these definitions. The value of \(w\) is not necessarily the proportion positive among patients enrolled after the adaptation, nor the proportion positive in the final trial sample. For an all-comer target population, \(w\) should represent the positive proportion in that target population. If the intended target is a different population, its stratum proportions may define different weights. Earlier material on fixed baseline subgroup estimands and weighted population estimands establishes why these choices should be tied to the population of interest rather than selected after seeing the results.

How the Three Targets Relate

For a mean-difference estimand, the all-comer effect has an exact decomposition into the two biomarker-stratum effects. Write \(q=P(B=1)\) for the positive proportion in the all-comer target population. By the law of total expectation, the mean outcome under each treatment strategy is the weighted average of its stratum-specific means. Subtracting those two averages gives:

Thus, the all-comer target is retained by a weighted estimand with \(w=q\), provided the stratum effects refer to the same target population and treatment strategies. The biomarker-positive estimand is a different target unless the all-comer target itself consists entirely of positive patients or the stratum effects happen to coincide. Equality of effects would make the numerical estimates equal, but it would not make their target populations identical.

This decomposition is specific to a mean difference, because differences of weighted means decompose linearly. For another outcome summary, such as a ratio of odds, one should define the desired population-level summary first and standardize the relevant outcome distributions or means accordingly; simply averaging subgroup-specific ratios need not produce the marginal ratio for the target population.

What a Narrowed Eligibility Rule Directly Targets

Once eligibility is restricted to \(B=1\), newly enrolled participants directly represent the biomarker-positive population, subject to the trial’s recruitment and sampling limitations. A treatment contrast estimated solely from this stage is therefore naturally interpreted as evidence about \(\Delta_+\), not \(\Delta_{\mathrm{all}}\). Randomization within the positive subgroup supports a treatment comparison for that subgroup; it does not by itself supply the missing negative-subgroup effect or determine the all-comer weights.

An all-comer target can still be estimated after enrichment if the trial has sufficient relevant information for both strata. For example, the initial stage may have randomized positive and negative participants, with biomarker status recorded before treatment, while the later stage enrolls only positive participants. The negative-stratum data then come from the initial stage. Using them for an all-comer estimate requires that the treatment conditions and outcome definition remain compatible across stages and that the available data identify the required stratum-specific contrast. If treatment effects or outcome distributions vary by stage, a simple pooled stratum contrast may not represent the intended target without an appropriate stage-specific model and standardization.

The enrollment proportions themselves can be especially misleading. After enrichment, the final sample may contain many more positive patients than the all-comer target does. A raw average over all trial participants gives more influence to whichever stratum contributed more participants; it is not automatically a standardized estimate for the original population.

Conditions for Preserving the Original Target

The target is preserved by defining and estimating the relevant population contrast, not simply by retaining the label “all-comer.” For the mean-difference decomposition to support an all-comer interpretation, the following conditions must be addressed:

• Baseline classification: Biomarker status is defined before randomization or treatment, and is available for the patients needed to estimate the target-stratum effects. A post-treatment marker can introduce selection problems and does not serve as the same baseline subgroup definition.
• Target weights are specified: The all-comer target’s positive proportion \(q\), or the external information used to determine it, is defined independently of the post-adaptation enrollment mix.
• Both stratum effects are identified: There are randomized treatment and control observations in each target stratum, or justified information from another source. If the negative subgroup has no treatment comparison, its effect cannot be recovered from the positive-only stage by changing weights.
• Strategies and outcome summary are compatible: The treatment and control strategies and outcome are defined consistently across stages, as required by the estimand. Differences in treatment versions, follow-up, or outcome measurement can make stage-specific contrasts refer to different quantities.
• Transport and sampling are appropriate: The observed participants’ stratum-specific effects apply to the target strata, or any relevant differences are handled by suitable standardization. Randomization identifies comparisons within the randomized trial population; it does not alone establish representativeness of a broader target population.

These are identification and interpretation conditions, not a guarantee that an estimator will be precise. In particular, if the initial stage includes few negative patients, the all-comer estimate may be noisy because much of the target weight is attached to a poorly estimated \(\Delta_-\). The estimand can remain well-defined while the available data provide weak information about it.

Diagnostics, Alternatives, and Limitations

A practical diagnostic is to place three items side by side: the target population and its stratum weights, the enrolled population in each stage, and the source of each estimated stratum effect. If the target has positive weight for a stratum with no randomized comparison, the data do not directly identify the all-comer effect. If the final sample’s stratum proportions differ from the target weights, a raw pooled contrast generally targets the sample mixture rather than the intended population mixture.

Compare the principal choices as follows:

The weighted approach is not a device for manufacturing information. It combines stratum-specific information according to the target population; it cannot infer an unobserved stratum effect without additional assumptions or data. Nor does matching the weights alone ensure that earlier and later stages are comparable. Trial-stage differences, biomarker measurement error, missing biomarker values, or changes in the outcome process can compromise the applicability of the stratum effects. These issues should be investigated and described rather than hidden by a single pooled number.

A further limitation is that “all-comer” must be operationally precise. It should identify which patients the target includes and the population distribution to which results are standardized. If the intended population changes, the weights may change as well, and so may the weighted estimand. Conversely, an all-comer target can be retained even when later enrollment is restricted, but only if the target definition remains fixed and the evidence still supports its component effects.

Common Mistake

Wrong reasoning: “The trial began with all-comer enrollment, so the final treatment-effect estimate is automatically an all-comer effect.” This is not necessarily true. Later positive-only enrollment can substantially change the final trial mix, and an unweighted pooled contrast can reflect that changed mix. Earlier all-comer enrollment does not by itself establish that the final analysis uses the original target weights.

Correction: State the target population and its weights explicitly, then determine whether the available randomized data support the required effects in each stratum. A positive-only contrast targets the positive subgroup. An all-comer contrast requires the all-comer weights and information about every stratum receiving positive target weight, or clearly stated and defensible assumptions that supply the missing information.