Non-parametric Maximum Likelihood Estimation for Case-Cohort and Nested Case-Control Designs with Competing Risks Data

Assuming cause-specific hazards given by Cox’s regression model, we provide non-parametric maximum likelihood estimator (NPMLEs) in the nested case-control or case-cohort design with competing risks data. We propose an iterative algorithm based on self-consistency equations derived from score functions to compute NPMLE and compute the predicted cumulative incidence function with their corresponding confidence intervals and bands. Consistency and asymptotic normality are established, together with a consistent estimator of the asymptotic variance based on the observed profile likelihood. Simulation studies show that the numerical performance of NPMLE approach is satisfactory and compares well with that of weighted partial likelihood. Our method is applied to the Taiwan National Health Insurance Research Database (NHIRD) to analyze the occurrences of liver and lung cancers in type 2 diabetic mellitus patients.