Efficient Estimation for Censored Quantile Regression

Censored quantile regression (CQR) has received growing attention in survival analysis because of its flexibility in modeling heterogeneous effect of covariates. Advances have been made in developing various inferential procedures under different assumptions and settings. Under the conditional independence assumption, many existing CQR methods can be characterized either by stochastic integral-based estimating equations (see, e.g., Peng and Huang) or by locally weighted approaches to adjust for the censored observations (see, for instance, Wang and Wang). While there have been proposals of different apparently dissimilar strategies in terms of formulations and the techniques applied for CQR, the inter-relationships amongst these methods are rarely discussed in the literature. In addition, given the complicated structure of the asymptotic variance, there has been limited investigation on improving the estimation efficiency for censored quantile regression models. This article addresses these open questions by proposing a unified framework under which many conventional approaches for CQR are covered as special cases. The new formulation also facilitates the construction of the most efficient estimator for the parameters of interest amongst a general class of estimating functions. Asymptotic properties including consistency and weak convergence of the proposed estimator are established via the martingale-based argument. Numerical studies are presented to illustrate the promising performance of the proposed estimator as compared to existing contenders under various settings. Supplementary materials for this article are available online.