Adaptive lasso penalised censored composite quantile regression

Abstract

To account for censoring in estimating the accelerated failure time (AFT) model with right censored data, the weighted least squares regression (WLSR) has been developed by using the inverse-censoring-probability weights. However, it is well known that the traditional ordinary least squares may fail to produce a reliable estimator for data subject to heavy-tailed errors or outliers. For robust estimation in the AFT model, we propose the weighted composite quantile regression (WCQR) method, in which the sum of weighted multiple quantile objective functions based on the inverse-censoring-probability weights is used as a loss function. As a novel regularisation method for right censored data, we further propose the adaptive lasso penalised WCQR (AWCQR) method in order to perform simultaneous estimation and variable selection. The large sample properties of the WCQR and AWCQR estimators are established under some regularity conditions. The proposed methods are evaluated through simulation studies and real data applications.