The GMLE based Buckley–James estimator with modified case–cohort data

We consider the estimation problem under the linear regression model with the modified case–cohort design. The extensions of the Buckley–James estimator (BJE) under the case–cohort designs have been studied under an additional assumption that the censoring variable and the covariate are independent. If this assumption is violated, as is the case in a typical real data set in the literature, our simulation results suggest that those extensions are not consistent and we propose a new extension. Our estimator is based on the generalized maximum likelihood estimator (GMLE) of the underlying distributions. We propose a self-consistent algorithm, which is quite different from the one for multivariate interval-censored data. We also show that under certain regularity conditions, the GMLE and the BJE are consistent and asymptotically normally distributed. Some simulation results are presented. The BJE is also applied to the real data set in the literature.