Efficient estimation for accelerated failure time model under case-cohort and nested case-control sampling

Case-cohort (Prentice, 1986) and nested case-control (Thomas, 1977) designs have been widely used as a cost-effective alternative to the full-cohort design. In this article, we propose an efficient likelihood-based estimation method for the accelerated failure time model under case-cohort and nested case-control designs. An EM algorithm is developed to maximize the likelihood function and a kernel smoothing technique is adopted to facilitate the estimation in the M-step of the EM algorithm. We show that the proposed estimators for the regression coefficients are consistent and asymptotically normal. The asymptotic variance of the estimators can be consistently estimated using an EM-aided numerical differentiation method. Simulation studies are conducted to evaluate the finite-sample performance of the estimators and an application to a Wilms tumor data set is also given to illustrate the methodology.