We consider semiparametric analysis of competing risks data subject to mixed case interval censoring. The Fine–Gray model () is used to model the cumulative incidence function and is coupled with sieve semiparametric maximum likelihood estimation based on univariate or multivariate likelihood. The univariate likelihood of cause-specific data enables separate estimation of cumulative incidence function for each competing risk, in contrast with the multivariate likelihood of full data which estimates cumulative incidence functions for multiple competing risks jointly. Under both likelihoods and certain regularity conditions, we show that the regression parameter estimator is asymptotically normal and semiparametrically efficient, although the spline-based sieve estimator of the baseline cumulative subdistribution hazard converges at a rate slower than root-n. The proposed method is evaluated by simulation studies regarding its finite sample performance and is illustrated by a competing risk analysis of data from an dementia cohort study.
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