The Closure Principle Revisited

TitleThe Closure Principle Revisited
Publication TypePresentation
Year of Publication2014
AuthorsRom, D
KeywordsSymposium III

Marcus, Peritz, and Gabriel (1976) have laid out the foundation for the Closure Principle. Procedures following this principle have been termed: Closed Testing Procedures, and have emerged as the most commonly used procedures in multiple hypothesis testing. These procedures can be shown to control the Familywise Error Rate (FWER) in the strong sense. Examination of the Closure Principle reveals that while the conditions set in Marcus et al. (1976) indeed give rise to the strong control of FWER, the principle can be applied in a manner that deviates from the structure of commonly used procedures, such as Hochberg's, which use the ordered p-values for testing the various hypotheses in the closed family. The concept is illustrated by a few examples with application to multiple endpoints in clinical trials.