Combining global and marginal tests to compare two treatments on multiple endpoints

We consider the problem of comparing two treatments on multiple endpoints where the goal is to identify the endpoints that have treatment effects, while controlling the familywise error rate. Two current approaches for this are (i) applying a global test within a closed testing procedure, and (ii) adjusting individual endpoint p-values for multiplicity. We propose combining the two current methods. We compare the combined method with several competing methods in a simulation study. It is concluded that the combined approach maintains higher power under a variety of treatment effect configurations than the other methods and is thus more power-robust.