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Abstract:
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A closed testing procedure that Generalizes Hochberg's step-up procedure is proposed. This is an extension of Rom, Chen, and McTague (2015) who generalized Hochberg's procedure for the case of two hypotheses. In this presentation, we extend the procedure to three or more hypotheses. The 'Closure Principle' is used in a way that allows to reject an individual hypothesis when the generalized Hochberg procedure rejects the global null hypothesis. Thus this procedure is consonant, and can be powerful under various configurations commonly encountered in clinical trials. We show that under independence or positive dependence, the proposed procedure strongly controls the Familywise Error Rate (FWER). Simulations show that the proposed procedure has a power advantage in various settings compared to other procedures commonly used in practice.
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