Inference for cumulative incidence on discrete failure times with competing risks

In the competing risks analysis, most inferences have been developed based on continuous failure time data. However, failure times are sometimes observed as being discrete. We propose nonparametric inferences for the cumulative incidence function for pure discrete data with competing risks. When covariate information is available, we propose semiparametric inferences for direct regression modelling of the cumulative incidence function for grouped discrete failure time data with competing risks. Simulation studies show that the procedures perform well. The proposed methods are illustrated with a study of contraceptive use in Indonesia.