A Single Index Model for Censored Quantile Regression

Quantile regression, which is a valuable alternative to the commonly used Cox proportional hazards model and accelerated failure time (AFT) model in survival analysis, has been getting more attention recently due to its robustness and interpretability. By allowing nonlinear relationship between survival time and risk factors, we study a single index model for censored quantile regression, and employ the B-spline approximation for estimation. To account for censoring, we consider the redistribution-of-mass to obtain a weighted quantile regression estimator. In addition, dimension reduction approach is adopted to deal with the "curse of dimensionality". Furthermore, we penalize the developed estimator for variable selection purpose. The proposed methods are easy to implement using the existing weighted linear quantile regression algorithm compared to available methods, and can be generalized to multiple index models. The asymptotic properties of the developed estimator are investigated and the estimator's numerical performance is illustrated in simulation studies. We also apply the proposed methods to Boston housing data and kidney transplant study.