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Abstract:
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In many statistical applications, such as clinical studies, different hypotheses may be differentially weighted according to their importance. Many weighted multiple testing procedures have been developed for controlling the familywise error rate. Among these procedures, two weighted Holm procedures are commonly used in practice: one(WHP) is based on ordered weighted p-values, the alternative weighted Holm procedure(WAP) is based on ordered raw p-values. In this paper, our goal is to study these two weighted Holm procedures and make recommendation for their application. First, we study the corresponding closed testing procedures of both weighted procedures and theoretically show that the WHP is uniformly more powerful than the WAP. Then, in order to provide an intuitive and clear way to communicate with non-statisticians, we visualize two procedures with graphical approaches. Finally, we discuss optimality of two procedures and show that the WHP is an optimal procedure in the sense that it cannot be improved by increasing even one of its critical values without losing control over the FWER. Simulations were conducted to provide numerical evidence of superior performance of the WHP.
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