An Extension of the Holm Procedure Based on Partitioning Principle for Adaptive Treatment Selection Designs with Structured Hypotheses

Multiple comparisons are attracting increasing attention in the evaluation of statistical evidence in clinical trials including at least one or any combination of (i) multiple hypotheses, (ii) repeated hypotheses testing at interim analyses, and (iii) mid-course design adaptations. In this paper, we discuss an efficient and sensible multiple testing procedure for two-stage adaptive treatment selection designs including structured hypotheses. Specifically, we extend the Holm procedure for serial gatekeeping structured hypotheses in adaptive clinical trials. The proposed approach is based on the idea of combining partition testing with the inverse normal combination test. A clinical trial example is used to illustrate the implementation of the proposed procedure.