Regularized linear censored quantile regression

For right-censored survival data, censored quantile regression is emerging as an attractive alternative to the Cox’s proportional hazards and the accelerated failure time models. Censored quantile regression has been considered as a robust and flexible alternative in the sense that it can capture a variety of treatment effects at different quantile levels of survival function. In this paper, we present a novel regularized estimation and variable selection procedure for censored quantile regression model. Statistical inference on censored quantile regression is often based on a martingale-based estimating function that may require a strict linearity assumption and a grid-search procedure. Instead, we employ a local kernel-based Kaplan–Meier estimator and modify the quantile loss function to facilitate censored observations. This approach allows us to assume the linearity condition only at the particular quantile level of interest. Our proposed method is then regularized by using LASSO and adaptive LASSO, along with sufficient dimension reduction, to select a subset of informative covariates in a high-dimension setting. The asymptotic properties of the proposed estimators are rigorously studied. Their finite-sample properties and practical utility are explored via simulation studies and application to PBC data.