Semiparametric estimation for the non-mixture cure model in case-cohort and nested case-control studies

Case-cohort and nested case-control designs are widely used strategies to reduce costs of covariate measurements in epidemiological cohort studies. A unified likelihood framework for two cohort designs is constructed and two statistical procedures are presented for making inference about the effects of incomplete covariates on the cumulative incidence of clinical event time. A pseudo-maximum likelihood estimation based on the sieve method is developed for the semiparametric non-mixture cure model, which can handle missing covariates and a cure fraction occurring in censored survival data. The resulting estimators are shown to be consistent and asymptotically normal in both case-cohort and nested case-control studies. In addition, for two cohort designs, an expectation-maximization (EM) algorithm is developed to simplify the maximization of the likelihood function with the Bernstein-based smoothing technique. Such a procedure would allow one to estimate the nonparametric component of the semiparametric model in closed form and relieve the computational burden. Simulation studies demonstrate that the proposed estimators have good properties in practical situations, and a motivating application to real data is provided to illustrate the methodology.