A general multistage procedure for k‐out‐of‐n gatekeeping. (18th October 2013) - Xi, Dong; Tamhane, Ajit C.
<x xml:space="preserve">Abstract</x> We generalize a multistage procedure for parallel gatekeeping to what we refer to as k‐out‐of‐n gatekeeping in which at least k out of n hypotheses ( 1 ⩽ k ⩽ n) in a gatekeeper family must be rejected in order to test the hypotheses in the following family. This gatekeeping restriction arises in certain types of clinical trials; for example, in rheumatoid arthritis trials, it is required that efficacy be shown on at least three of the four primary endpoints. We provide a unified theory of multistage procedures for arbitrary k, with k = 1 corresponding to parallel gatekeeping and k = n to serial gatekeeping. The theory provides an insight into the construction of truncated separable multistage procedures using the closure method. Explicit formulae for calculating the adjusted p‐values are given. The proposed procedure is simpler to apply for this particular problem using a stepwise algorithm than the mixture procedure and the graphical procedure with memory using entangled graphs. Copyright © 2013 John Wiley & Sons, Ltd.