Censored quantile regression via Box-Cox transformation under conditional independence

Abstract

We propose a new quantile regression model when data are subject to censoring. Our model does not require any global linearity assumption, or inde- pendence of the covariates and the censoring time. We develop a class of power- transformed quantile regression models such that the transformed survival time can be better characterized by linear regression quantiles. Consistency and asymptotic normality of the resulting estimators are shown. A re-sampling based approach is proposed for statistical inference. Empirically, the new estimator is shown to outperform its competitors under conditional independence, and perform similarly under unconditional independence. The proposed method is illustrated with a data analysis.