Interval-censored competing risks data arise when each study subject mayexperience an event or failure from one of several causes and the failure timeis not observed exactly but rather known to lie in an interval between twosuccessive examinations. We formulate the effects of possibly time-varyingcovariates on the cumulative incidence or sub-distribution function (i.e., themarginal probability of failure from a particular cause) of competing risksthrough a broad class of semiparametric regression models that captures bothproportional and non-proportional hazards structures for the sub-distribution.We allow each subject to have an arbitrary number of examinations andaccommodate missing information on the cause of failure. We considernonparametric maximum likelihood estimation and devise a fast and stableEM-type algorithm for its computation. We then establish the consistency,asymptotic normality, and semiparametric efficiency of the resulting estimatorsby appealing to modern empirical process theory. In addition, we show throughextensive simulation studies that the proposed methods perform well inrealistic situations. Finally, we provide an application to a study on HIV-1infection with different viral subtypes.
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