A new approach to address multiplicity in hypothesis testing with constraints

We propose a novel approach named the covering principle to construct multiple testing procedures from the perspective of rejection regions in the sample space, which is different from the closed testing and the partitioning principles working in the parameter space. We prove that multiple testing procedures based on the covering principle strongly control the familywise error rate if the type I error is strongly controlled in each decomposed subfamily. Computer simulation shows that the new method rejects more hypotheses on the primary endpoints in most scenarios compared to both the graphical and the gate-keeping approaches.