On the analysis of discrete time competing risks data

Regression methodology has been well developed for competing risks data with continuous event times, both for the cause-specific hazard and cumulative incidence functions. However, in many applications, including those from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute, the event times may be observed discretely. Naive application of continuous time regression methods to such data is not appropriate. We propose maximum likelihood inferences for estimation of model parameters for the discrete time cause-specific hazard functions, develop predictions for the associated cumulative incidence functions, and derive consistent variance estimators for the predicted cumulative incidence functions. The methods are readily implemented using standard software for generalized estimating equations, where models for different causes may be fitted separately. For the SEER data, it may be desirable to model different event types on different time scales and the methods are generalized to accommodate such scenarios, extending earlier work on continuous time data. Simulation studies demonstrate that the methods perform well in realistic set-ups. The methodology is illustrated with stage III colon cancer data from SEER.