Consistency-adjusted alpha allocation methods for a time-to-event analysis of composite endpoints

Composite endpoints are often used as primary efficacy endpoints, particularly in the field of oncology and cardiology. These endpoints combine several time-to-event variables of interest within a single time-to-first-event variable. Thereby, it is intended to enlarge the expected effect size and thus to increase the power of the clinical trial. However, the interpretation of composite endpoints can be difficult, as the observed effect for the composite does not necessarily reflect the effects of the single components. Therefore, it might not be adequate to judge the efficacy of the new intervention exclusively on the composite effect. Including the most relevant components in an efficacy claim assessed by a confirmatory test strategy could overcome this problem but imposes the problem of multiplicity. Moreover, to show non-inferiority or even superiority of the new intervention with respect to single components is usually not realistic in these settings as the expected individual effects are small. Recently, consistency-adjusted alpha allocation methods were proposed in the literature which can be used and extended to establish a new efficacy claim for a composite endpoint and one main component. The power properties of the new approach are compared to the alternative efficacy claim of proving superiority for the composite and non-inferiority for the main component. Moreover, the methods are illustrated with a clinical trial example. Thereby, the general problem of correlation-adjusted multiple testing procedures is addressed by applying a bootstrapping algorithm to estimate the special correlation structure between a composite endpoint and an individual component in the time-to-event setting.11The R code is available online as supplementary material (see Appendix C).