title: A general multistage procedure for k-out-of-n gatekeeping.
abstract: 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.
authors.affiliation: IIS Statistical Methodology, Novartis Pharmaceuticals Corporation, One Health Plaza, East Hanover, NJ 07936, U.S.A.
authors.forename: Dong
authors.initials: D
authors.lastname: Xi
authors.forename: Ajit C
authors.initials: AC
authors.lastname: Tamhane
mesh_terms: D000465:Algorithms; D000893:Anti-Inflammatory Agents / Q000494:pharmacology; D001172:Arthritis, Rheumatoid / Q000188:drug therapy; D002986:Clinical Trials as Topic / Q000379:methods*; D003627:Data Interpretation, Statistical; D007596:Joints / Q000187:drug effects
chemical_list: D000893:Anti-Inflammatory Agents
keywords: Hochberg procedure; Holm procedure; Hommel procedure; closed procedure; error rate function; familywise error rate; separable procedures; truncated procedures