Simultaneous inference of a binary composite endpoint and its components

Binary composite endpoints offer some advantages as a way to succinctly combine evidence from a number of related binary endpoints recorded in the same clinical trial into a single outcome. However, as some concerns about the clinical relevance as well as the interpretation of such composite endpoints have been raised, it is recommended to evaluate the composite endpoint jointly with the involved components. We propose an approach for carrying out simultaneous inference based on separate model fits for each endpoint, yet controlling the familywise type I error rate asymptotically. The key idea is to stack parameter estimates from the different fits and derive their joint asymptotic distribution. Simulations show that the proposed approach comes closer to nominal levels and has comparable or higher power as compared to existing approaches, even for moderate sample sizes (around 100-200 observations). The method is compared to the gatekeeping approach and results are provided in the Supplementary Material. In two data examples we show how the procedure may be adapted to handle local significance levels specified through a priori given weights.