It is often of interest to determine treatment effects in the overall study population, as well as in certain subpopulations. These subpopulations could be defined by a risk factor, such as a biomarker, measured at baseline. We consider situations where the overall population is
partitioned into two subpopulations of interest.
If the null hypothesis of no treatment effect in the overall population is rejected, a natural question is what can be said about these subpopulations.
Whenever there is a treatment effect in the overall population, it follows logically that there must be a treatment effect in at least one of these
subpopulations. Therefore, it would be desirable to reject at least one subpopulation null hypothesis whenever the null hypothesis for the overall
population is rejected. Furthermore, it would be desirable to do so without sacrificing any power for detecting a treatment effect in the overall population. We give the first multiple testing procedure that has both these properties and that strongly controls the familywise Type I error rate at
level 0.05. Our procedure is simple to implement and can be used with binary, continuous, or time-to-event outcomes. In addition, this procedure is the first to satisfy a certain maximin optimality property in this setting. The proofs of these properties rely on a general method for transforming analytically difficult expressions arising in some multiple testing problems
into more tractable nonlinear optimization problems, which are then solved using intensive computation.
Statistical Methodology | Statistical Theory
Rosenblum, Michael, "TESTS THAT REJECT AT LEAST ONE SUBPOPULATION NULL HYPOTHESIS AFTER REJECTING FOR OVERALL POPULATION" (July 2012). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 236.