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Abstract:
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A variety of sequentially rejective, weighted Bonferroni-based multiple testing procedures(MTPs) are applied in clinical trials for addressing multiple research questions. However, such MTPs may become increasingly complex with the increasing sources of multiplicity. In order to make testing strategies more explicit and intuitive to communicate with non-statisticians, several flexible and powerful graphical approaches have recently been introduced. However, a main drawback of existing graphical approaches is that they only allow one rejection at each step. In this talk, we will introduce a novel generalized graphical approach, which allows one to reject more than one hypothesis at each step. Some clinical examples are used to illustrate the flexibility and computational efficiency of the proposed approach. Theoretically, we prove that the generalized graphical approach strongly controls the FWER under arbitrary dependence. In order to show the control of the FWER, as a byproduct, we introduce a new concept of a multivariate critical value function and based on this concept, we extend Goeman and Solari's sequential rejection principle from the case of univariate to multivariate.
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