A Generalized Multistage Gatekeeping Procedure

• Activity Number: 661
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Dong Xi*+ and Ajit C. Tamhane
• Companies: Northwestern University and Northwestern University
• Keywords: Serial gatekeeping ; Parallel gatekeeping ; Closed procedures ; Truncated procedures ; Graphical procedures ; Mixture procedures

Abstract

A generalized multistage gatekeeping procedure is proposed to provide a general framework to arbitrary gatekeeping problems including serial and parallel gatekeeping. We consider the problem in which the successive family can be tested if and only if at least r out of n hypotheses in the current family are rejected, where r can be any integer number ranging from 1 to n. Thus serial and parallel gatekeeping are two special cases of this framework. We use the same idea of carrying forward the Type I error rate for any newly rejected hypotheses after r-1 rejections to test hypotheses in the next ordered family by using general separable multiple testing procedures (MTPs). Truncated versions of many standard MTPs such as Holm, Hochberg, Hommel, fallback and Dunnett are introduced by first defining truncated closed procedures. Connections among the proposed procedure, mixture procedures and graphical approaches are also discussed.