On identifying effective and superior drug combinations via Holm's procedure based on the Min tests

In this paper I consider a problem of identifying all effective and superior drug combinations. I formulate this problem in terms of a family of hypotheses and propose a two-stage method to solve it. The first stage uses individual p-values obtained via the Min tests, whereas Holm's approach is employed in the second stage to draw simultaneous inferences. This procedure is shown to control the family-wise error rate in a strong sense. The performance of the procedure is studied by simulation for different parameter settings. The conclusions of the simulation study are stated in terms of the power, family-wise error rate and lack of power.