Efficient estimation for case-cohort studies

In this paper we consider time-to-event data from case-cohort designs. In view of the fact that the existing methods are either inefficient or requiring particular censoring assumptions, we develop a semiparametrically efficient estimator under the usual assumptions for Cox regression models. The estimator is obtained by one iteration of the Newton-Raphson algorithm that solves the efficient score equations with initial values being obtained from existing methods, and shown to be consistent, asymptotically efficient and normally distributed. Simulations show that the proposed estimators perform well in finite samples, and considerably improve the efficiency of the existing pseudo-likelihood estimators when a correlate of the missing covariate is available. We focus on the situation where covariates are discrete, and also explore how to apply the method to models with continuous covariates.