Improving estimation efficiency for case-cohort studies with a cure fraction

In the studies of time-to-event outcomes, it often happens that a fraction of subjects will never experience the event of interest, and these subjects are said to be cured. The studies with a cure fraction often yield a low event rate. To reduce cost and enhance study power, 2-phase sampling designs are often adopted, especially when the covariates of interest are expensive to measure or obtain. In this paper, we consider the generalized case-cohort design for studies with a cure fraction. Under this design, the expensive covariates are measured for a subset of the study cohort, called subcohort, and for all or a subset of the remaining subjects outside the subcohort who have experienced the event during the study, called cases. We propose a 2-step estimation procedure under a class of semiparametric transformation mixture cure models. We first develop a sieve maximum weighted likelihood method based only on the complete data and also devise an Expectation-Maximization (EM) algorithm for implementation. We then update the resulting estimator via a working model between the outcome and cheap covariates or auxiliary variables using the full data. We show that the proposed update estimator is consistent and asymptotically at least as efficient as the complete-data estimator, regardless of whether the working model is correctly specified or not. We also propose a weighted bootstrap procedure for variance estimation. Extensive simulation studies demonstrate the superior performance of the proposed method in finite-sample. An application to the National Wilms' Tumor Study is provided for illustration.