Dealing with competing risks in clinical trials: How to choose the primary efficacy analysis?

We investigate different primary efficacy analysis approaches for a 2-armed randomized clinical trial when interest is focused on a time to event primary outcome that is subject to a competing risk. We extend the work of Friedlin and Korn (2005) by considering estimation as well as testing and by simulating the primary and competing events' times from both a cause-specific hazards model as well as a joint subdistribution-cause-specific hazards model. We show that the cumulative incidence function can provide useful prognostic information for a particular patient but is not advisable for the primary efficacy analysis. Instead, it is preferable to fit a Cox model for the primary event which treats the competing event as an independent censoring. This is reasonably robust for controlling type I error and treatment effect bias with respect to the true primary and competing events' cause-specific hazards model, even when there is a shared, moderately prognostic, unobserved baseline frailty for the primary and competing events in that model. However, when it is plausible that a strongly prognostic frailty exists, combining the primary and competing events into a composite event should be considered. Finally, when there is an a priori interest in having both the primary and competing events in the primary analysis, we compare a bivariate approach for establishing overall treatment efficacy to the composite event approach. The ideas are illustrated by analyzing the Women's Health Initiative clinical trials sponsored by the National Heart, Lung, and Blood Institute.