Abstract
With the advent of personalized medicine, clinical trials studying treatment effects in subpopulations are receiving increasing attention. The objectives of such studies are, besides demonstrating a treatment effect in the overall population, to identify subpopulations, based on biomarkers, where the treatment has a beneficial effect. Continuous biomarkers are often dichotomized using a threshold to define two subpopulations with low and high biomarker levels. If there is insufficient information on the dependence structure of the outcome on the biomarker, several thresholds may be investigated. The nested structure of such subpopulations is similar to the structure in group sequential trials. Therefore, it has been proposed to use the corresponding critical boundaries to test such nested subpopulations. We show that for biomarkers with a prognostic effect that is not adjusted for in the statistical model, the variability of the outcome may vary across subpopulations which may lead to an inflation of the family-wise type 1 error rate. Using simulations we quantify the potential inflation of testing procedures based on group sequential designs. Furthermore, alternative hypotheses tests that control the family-wise type 1 error rate under minimal assumptions are proposed. The methodological approaches are illustrated by a trial in depression.