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Optimal weighted Bonferroni tests and their graphical extensions

Chen, Yao and Xi, Dong (2023) Optimal weighted Bonferroni tests and their graphical extensions. Statistics in Medicine. ISSN 0277-67151097-0258


Regulatory guidelines mandate the strong control of the familywise error rate in confirmatory clinical trials with primary and secondary objectives. Bonferroni tests are one of the popular choices for multiple comparison procedures and are building blocks of more advanced procedures. It is usually of interest to find the optimal weighted Bonferroni split for multiple hypotheses. We consider two popular quantities as the optimization objectives, which are the disjunctive power and the conjunctive power. The former is the probability to reject at least one hypothesis and the latter is the probability to reject all hypotheses. We investigate the behavior of each of them as a function of different Bonferroni splits, given assumptions about the alternative hypotheses and the correlations between test statistics. Under independent tests, unique optimal Bonferroni weights exist; under dependence, optimal Bonferroni weights may not be unique based on a fine grid search. In general, we propose an optimization algorithm based on constrained non-linear optimization and multiple starting points. The proposed algorithm efficiently identifies optimal Bonferroni weights to maximize the disjunctive or conjunctive power. In addition, we apply the proposed algorithm to graphical approaches, which include many Bonferroni-based multiple comparison procedures. Utilizing the closed testing principle, we adopt a two-step approach to find optimal graphs using the disjunctive power. We also identify a class of closed test procedures that optimize the conjunctive power. We apply the proposed algorithm to a case study to illustrate the utility of optimal graphical approaches that reflect study objectives.

Item Type: Article
Date Deposited: 27 Dec 2023 00:45
Last Modified: 27 Dec 2023 00:45