Multiple and Repeated Testing of Primary, Coprimary, and Secondary Hypotheses

Abstract

In confirmatory clinical trials the Type I error rate must be controlled for claims forming the basis for approval and labeling of a new drug. Strong control of the familywise error rate is usually needed for hypotheses related to the primary endpoint(s). For hypotheses related to secondary endpoint(s) which are only of interest if the corresponding “parent” primary null hypotheses have been rejected, less strict error rate control might be sufficient. We review and extend procedures for families of primary and secondary hypotheses when either at least one of the primary hypotheses or all coprimary hypotheses must be rejected to claim success for the trial. Such families of hypotheses arise naturally from comparing several treatments with a control, combined noninferiority and superiority testing for primary and secondary variables, the presence of multiple primary or secondary endpoints or any combination thereof. We show that many of the procedures proposed in the literature follow a common underlying principle and in some cases can be improved. In addition we present some general results on Type I error rates for the different families and subfamilies of hypotheses and their relation to group-sequential testing of multiple hypotheses.

Keywords: :

• Closed testing
• Confirmatory trial
• Familywise error rate
• Gatekeeping procedure
• Graphical approach
• Simes’ test