Abstract: We propose a new quantile regression model when data are subject to censoring. Our model does not require any global linearity assumption, or independence 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.
Key words and phrases: Accelerated failure time model, Box-Cox transformation, censored quantile regression, empirical process, estimating equation, martingale.