Competing Risks Analyses: Overview of Regression Models
Joseph Gardiner, Director, Division of Biostatistics, Michigan State University, USA
In competing risks analyses, the time to a terminal event such as death is analyzed together with its cause. Death by one cause precludes occurrence of death by any other cause, because an individual can die only once. The cumulative incidence function CIF(j, t) is the probability of death by time t from cause j. Cause-specific hazard functions are the analogs of the hazard function when only a single cause is present. By incorporating explanatory variables in cause-specific hazard functions, provides an approach to accessing their impact on the CIF and on overall survival. We discuss methods for estimation of the CIF from event times and their associated causes, allowing for right censoring when the event and its cause are not observed. When covariates are present, a semi-parametric approach similar to Cox regression models the cause-specific hazards. The Fine-Gray model defines a sub-distribution hazard function that has an expanded risk set comprised of individuals at risk of the event by any cause at t, together with those who died before t from any cause other than the cause j of interest. Finally, with additional assumptions a full parametric analysis is also feasible. We illustrate the application of these methods with an empirical data set.