One consideration every sponsor of a biomarker-stratified confirmatory trial must take into account, is whether to evaluate the biomarker subpopulation (S) against the rest of the population (S') or against the full population (F).
Mathematically, one would think this makes very little difference as F is partitioned into S and S'. If the null hypothesis is rejected for both S and S' then clearly it is rejected for F too. Similarly, if it is rejected for S and not for S' then the therapy is effective for the biomarker subpopulation, and ineffective for the rest of the population.
As it turns out, whether or not a given biomarker is indeed a predictive biomarker should affect the choice of statistical methodology in time-to-event trials.