A general multistage procedure for k‐out‐of‐n gatekeeping. (18th October 2013)

• Record Type: Journal Article
• Authors: Xi, Dong; Tamhane, Ajit C.
• Is Part Of: Statistics in medicine. Volume 33:Number 8(2014)
• Page Start: 1321
• Page End: 1335
• Publication Date: 2013-10-18
• Subjects: Medical statistics -- Periodicals; Statistique médicale -- Périodiques; Statistiques médicales -- Périodiques; 610.727
• DOI: 10.1002/sim.6028
• Languages: English
• ISSNs: 0277-6715

Abstract

<abstract abstract-type="main" id="sim6028-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="sim6028-para-0001">We generalize a multistage procedure for parallel gatekeeping to what we refer to as <italic>k</italic>‐out‐of‐<italic>n</italic> gatekeeping in which at least <italic>k</italic> out of <italic>n</italic> hypotheses ( 1 <italic>⩽ k ⩽ n</italic>) 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 <italic>k</italic>, with <italic>k</italic> = 1 corresponding to parallel gatekeeping and <italic>k</italic> = <italic>n</italic> 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 <italic>p</italic>‐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 &amp; Sons, Ltd.</p> </abstract>