Biomarker-stratified clinical trials assess the biomarker signature of subjects and split them into subgroups so that treatment is of benefit to those who are likely to respond. Since multiple hypotheses are tested, it becomes important to control the type I error. Current methods control the false positive rate where one rejects the null hypothesis while in reality that was true. For two subgroups, the false positive rate is controlled across the two hypotheses as a Family Wise Error Rate (FWER) to an overall predetermined significance level.
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Parashar et al. (2015) studied this question.