Fundamental Theory of Multiplicity Control (Closed Testing Procedure)

Abstract

For many clinical trials, including the confirmatory ones, it is usually required that the FWER should be strongly controlled. The closed testing procedure, which is proposed by Marcus et al. (1976), is a procedure for strongly controlling the FWER. It is widely used for many methods of multiplicity control, for example, Holm method, step-down Dunnett method, fixed sequence method, and gatekeeping methods, etc. This article addresses the fundamental theory of the closed testing procedure, including the proof of strongly controlling the FWER, and several examples. For introduction, Fisher's protected LSD method is examined and improved.