Prediction of Cumulative Incidence Function under the Proportional Hazards Model

In the presence of dependent competing risks in survival analysis, the Cox model can be utilized to examine the covariate effects on the cause-specific hazard function for the failure type of interest. For this situation, the cumulative incidence function provides an intuitively appealing summary curve for marginal probabilities of this particular event. In this paper, we show how to construct confidence intervals and bands for such a function under the Cox model for future patients with certain covariates. Our proposals are illustrated with data from a prostate cancer trial.