Statistical modeling and estimation for heterogeneous censored survival data is of great practical importance, as exemplified by applications in bio-medicine. Censored quantile and expectile regression methods offer useful tools to capture heterogeneity in the set of covariates at different locations of the survival distribution. The former is computationally challenging due to the non-smooth nature of the check loss, and the later employs the inverse probability of censoring weighting (IPW) technique, which involves the unknown survival function of censored times and is designed for right-censored data. In this article, we investigate the expectile regression for censored data to capture its heterogeneity and develop a novel and unified estimation method for various types of censoring mechanisms. To handle the censoring, we employ the data augmentation approach instead of IPW, without estimating the survival function of the censored times. Extensive simulation studies are carried out to evaluate the performance of the proposed approach and also two real datasets are analyzed, obtaining some intriguing findings. The proposed algorithm has been implemented into an R function, DAer.
Cao et al. (Wed,) studied this question.