title: Fallback tests for co-primary endpoints.
abstract: When efficacy of a treatment is measured by co-primary endpoints, efficacy is claimed only if for each endpoint an individual statistical test is significant at level α. While such a strategy controls the family-wise type I error rate (FWER), it is often strictly conservative and allows for no inference if not all null hypotheses can be rejected. In this paper, we investigate fallback tests, which are defined as uniform improvements of the classical test for co-primary endpoints. They reject whenever the classical test rejects but allow for inference also in settings where only a subset of endpoints show a significant effect. Similarly to the fallback tests for hierarchical testing procedures, these fallback tests for co-primary endpoints allow one to continue testing even if the primary objective of the trial was not met. We propose examples of fallback tests for two and three co-primary endpoints that control the FWER in the strong sense under the assumption of multivariate normal test statistics with arbitrary correlation matrix and investigate their power in a simulation study. The fallback procedures for co-primary endpoints are illustrated with a clinical trial in a rare disease and a diagnostic trial. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.
authors.affiliation: Center for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.
authors.forename: Robin
authors.initials: R
authors.lastname: Ristl
authors.affiliation: Center for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.
authors.forename: Florian
authors.initials: F
authors.lastname: Frommlet
authors.affiliation: Centre for Biometry, Medical Informatics and Medical Technology, Hannover Medical School, Carl-Neuberg-Str. 1, 30625 Hannover, Germany.
authors.forename: Armin
authors.initials: A
authors.lastname: Koch
authors.affiliation: Center for Medical Statistics, Informatics, and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.
authors.forename: Martin
authors.initials: M
authors.lastname: Posch
mesh_terms: D001699:Biometry; D002986:Clinical Trials as Topic; D003627:Data Interpretation, Statistical; D023381:Endpoint Determination; D006801:Humans
keywords: Rüger test; diagonally trimmed Simes test; multiple endpoints; multiple testing; small populations