Nonparametric estimation of the cumulative intensities in an interval censored competing risks model

The nonparametric maximum likelihood estimation (NPMLE) of the distribution function from the interval censored (IC) data has been extensively studied in the extant literature. The NPMLE was also developed for the subdistribution functions in an IC competing risks model and in an illness-death model under various interval-censoring scenarios. But the important problem of estimation of the cumulative intensities (CIs) in the interval-censored models has not been considered previously. We develop the NPMLE of the CI in a simple alive/dead model and of the CIs in a competing risks model. Assuming that data are generated by a discrete and finite mixed case interval censoring mechanism we provide a discussion and the simulation study of the asymptotic properties of the NPMLEs of the CIs. In particular we show that they are asymptotically unbiased; in contrast the ad hoc estimators presented in extant literature are substantially biased. We illustrate our methods with the data from a prospective cohort study on the longevity of dental veneers.