Weighted analysis of composite endpoints with simultaneous inference for flexible weight constraints

Composite endpoints are widely used as primary endpoints of randomized controlled trials across clinical disciplines. A common critique of the conventional analysis of composite endpoints is that all disease events are weighted equally, whereas their clinical relevance may differ substantially. We address this by introducing a framework for the weighted analysis of composite endpoints and interpretable test statistics, which are applicable to both binary and time‐to‐event data. To cope with the difficulty of selecting an exact set of weights, we propose a method for constructing simultaneous confidence intervals and tests that asymptotically preserve the family‐wise type I error in the strong sense across families of weights satisfying flexible inequality or order constraints based on the theory of [Formula: see text] ‐distributions. We show that the method achieves the nominal simultaneous coverage rate with substantial efficiency gains over Scheffé's procedure in a simulation study and apply it to trials in cardiovascular disease and enteric fever. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.