The choice to define competing risk events as censoring events and implications for causal inference

Abstract

In failure-time settings, a competing risk event is any event that makes it impossible for the event of interest to occur. Different analytical methods are available for estimating the effect of a treatment on a failure event of interest that is subject to competing events. The choice of method depends on whether or not competing events are defined as censoring events. Though such definition has key implications for the causal interpretation of a given estimate, explicit consideration of those implications has been rare in the statistical literature. As a result, confusion exists as to how to choose amongst available methods for analyzing data with competing events and how to interpret effect estimates. This confusion can be alleviated by understanding that the choice to define a competing event as a censoring event or not corresponds to a choice between different causal estimands. In this paper, we describe the assumptions required to identify those causal estimands and provide a mapping between such estimands and standard terminology from the statistical literature---in particular, the terms "subdistribution function", "subdistribution hazard" and "cause-specific hazard". We show that when the censoring process depends on measured time-varying risk factors, conventional statistical methods for competing events are not valid and alternative methods derived from Robins's g-formula may recover the causal estimand of interest.