A Review of Methods to Estimate Cause-Specific Mortality in Presence of Competing Risks

Abstract

Estimating cause-specific mortality is often of central importance for understanding the dynamics of wildlife populations. Despite such importance, methodology for estimating and analyzing cause-specific mortality has received little attention in wildlife ecology during the past 20 years. The issue of analyzing cause-specific, mutually exclusive events in time is not unique to wildlife. In fact, this general problem has received substantial attention in human biomedical applications within the context of biostatistical survival analysis. Here, we consider cause-specific mortality from a modern biostatistical perspective. This requires carefully defining what we mean by cause-specific mortality and then providing an appropriate hazard-based representation as a competing risks problem. This leads to the general solution of cause-specific mortality as the cumulative incidence function (CIF). We describe the appropriate generalization of the fully nonparametric staggered-entry Kaplan–Meier survival estimator to cause-specific mortality via the nonparametric CIF estimator (NPCIFE), which in many situations offers an attractive alternative to the Heisey–Fuller estimator. An advantage of the NPCIFE is that it lends itself readily to risk factors analysis with standard software for Cox proportional hazards model. The competing risks–based approach also clarifies issues regarding another intuitive but erroneous “cause-specific mortality” estimator based on the Kaplan–Meier survival estimator and commonly seen in the life sciences literature.