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New methods and theory have recently been developed to nonparametricallyestimate cumulative incidence functions for competing risks survival datasubject to current status censoring. In particular, the limiting distributionof the nonparametric maximum likelihood estimator and a simplified "naiveestimator" have been established under certain smoothness conditions. In thispaper, we establish the large-sample behavior of these estimators in twoadditional models, namely when the observation time distribution has discretesupport and when the observation times are grouped. These asymptotic resultsare applied to the construction of confidence intervals in the three differentmodels. The methods are illustrated on two data sets regarding the cumulativeincidence of (i) different types of menopause from a cross-sectional sample ofwomen in the United States and (ii) subtype-specific HIV infection from asero-prevalence study in injecting drug users in Thailand.

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