Semiparametric Analysis of Competing Risks Data Under Missing Cause of Failure
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The cause of failure information in cohort studies that involve competing risks is frequently partially observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a novel computationally efficient pseudo-partial-likelihood estimation method under the semiparametric proportional cause-specific hazards model with missing at random cause of failure. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing causes of failure, and that the regression coefficient estimator can be substantially more efficient compared to the augmented inverse probability weighting estimator. The method is applied to an HIV cohort study with a large proportion of missing causes of failure that motivates the proposed work.
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