Consistency-ensured parametric tests for critical events of composite endpoints

Composite endpoints (CEs) are commonly used in clinical trials when clinically important events are rare or when the disease is multifaceted. However, components of a CE often differ markedly in their clinical importance. The overall treatment effect on the composite can be driven by less-important, yet more frequently occurring, components, with no effects on some clinically important components. These situations create difficulties in interpreting the results of the CE. The literature has proposed several approaches for handling these conditions, for example, by setting requirements on the results of the clinically important components. However, for a rare event, it can be difficult to draw an appropriate conclusion about its contribution to the overall result of the composite. Here, we propose combining clinically important components to jointly increase their power and to require that their findings meet a prespecified level of evidence, called the consistency criterion. With the increase in power, the study can then be designed with the objectives of establishing efficacy for the composite and/or for the subset of clinically critical components. In this regard, we introduce multiple testing strategies, which account for the consistency requirement and for the correlation between these two endpoints. We illustrate the methodology using the PROactive trial.