Reverse graphical approaches for multiple test procedures

The graphical approach has been proposed as a general framework for clinical trial designs involving multiple hypotheses, where decisions are made only based on the observed marginal $$-values. The graphical approach starts from a graph that includes all hypotheses as vertices and gradually removes some vertices when their corresponding hypotheses are rejected. In this paper, we propose a reverse graphical approach, which starts from a set of singleton graphs and gradually adds vertices into graphs until rejection of a set of hypotheses is made. Proofs of familywise error rate control are provided. A simulation study is conducted for statistical power analysis, and a case study is included to illustrate how the proposed approach can be applied to clinical studies.