Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times

New methods and theory have recently been developed to nonparametrically estimate cumulative incidence functions for competing risks survival data subject to current status censoring. In particular, the limiting distribution of the nonparametric maximum likelihood estimator and a simplified "naive estimator" have been established under certain smoothness conditions. In this paper, we establish the large-sample behavior of these estimators in two additional models, namely when the observation time distribution has discrete support and when the observation times are grouped. These asymptotic results are applied to the construction of confidence intervals in the three different models. The methods are illustrated on two data sets regarding the cumulative incidence of (i) different types of menopause from a cross-sectional sample of women in the United States and (ii) subtype-specific HIV infection from a sero-prevalence study in injecting drug users in Thailand.