Convexity issues in multivariate multiple testing of treatments vs. control

Arthur Cohen and Harold Sackrowitz

Journal of Multivariate Analysis, 2016, vol. 143, issue C, 1-11

Abstract: The problem of multiple testing of each of several treatment mean vectors versus a control mean vector is considered. Both one-sided and two-sided alternatives are treated. It is shown that typical choices for marginal test procedures will lead to step-down procedures that do not have convex acceptance regions. This lack of convexity has both intuitive and theoretical disadvantages. The only exception being linear tests in the one-sided problem. Although such a procedure is atypical, it not only has convex acceptance regions but is such that critical values are obtainable so that the overall procedure can control FDR or FWER.

Keywords: Convex acceptance region; Co-primary endpoints; Positive regression dependence; False discovery rate; Familywise error rate; Step-down procedure (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.jmva.2015.08.010

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