Efficient estimation for case‐cohort studies

The author considers time‐to‐event data from case‐cohort designs. As existing methods are either inefficient or based on restrictive assumptions concerning the censoring mechanism, he proposes a semi‐parametrically efficient estimator under the usual assumptions for Cox regression models. The estimator in question is obtained by a one‐step Newton‐Raphson approximation that solves the efficient score equations with initial value obtained from an existing method. The author proves that the estimator is consistent, asymptotically efficient and normally distributed in the limit. He also resorts to simulations to show that the proposed estimator performs well in finite samples and that it considerably improves the efficiency of existing pseudo‐likelihood estimators when a correlate of the missing covariate is available. Although he focuses on the situation where covariates are discrete, the author also explores how the method can be applied to models with continuous covariates.