Fallback tests for co-primary endpoints.

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.