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.
Simulations performed by Mehta, et al., show that in cases where the biomarker in question turns out not to be a predictive biomarker, and the therapy is effective across the full population, the method most likely to achieve the correct result for a sponsor may be that developed by Jenkins, Stone and Jennison in a 2011 paper in Pharmaceutical Statistics . However, when the biomarker is a predictive biomarker then the method even more likely to achieve the correct result is that developed by Mehta, et al., in a 2014 paper published in Statistics in Medicine .
According to the findings of Mehta, et al., the JSJ method which evaluates the null hypotheses on S and F is superior in cases where the biomarker is not a predictive biomarker because it has a higher probability of rejecting the null hypothesis when evaluating the full population, but not subpopulation S. By contrast, the MDSI Method (as developed by Mehta and colleagues) which compares S and S' has the advantage that it does not reject the null hypothesis on the full population simply because the subgroup without the biomarker consists of half of the sampled patients.
Related Items of Interest
 Jenkins, Martin, Andrew Stone, and Christopher Jennison. "An adaptive seamless phase II/III design for oncology trials with subpopulation selection using correlated survival endpoints." Pharmaceutical statistics 10.4 (2011): 347-356.
 Mehta, Cyrus, et al. "Biomarker driven population enrichment for adaptive oncology trials with time to event endpoints." Statistics in medicine 33.26 (2014): 4515-4531.