[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Jianhui Zhou (University of Virginia)
Abstract: Quantile regression has been getting more attention recently in survival analysis due to its robustness and interpretability, and is considered as a powerful alternative to Cox proportional hazards model and accelerated failure time (AFT) model. Allowing a nonlinear relationship between survival time and risk factors, we study a single index model for censored quantile regression, and employ B-spline approximation for estimation. To avoid estimation bias cause by censoring, we consider the redistribution-of-mass to obtain a weighted quantile regression estimator. For high dimensional covariates, dimension reduction approach is adopted to alleviate the “curse of dimensionality". Furthermore, we penalize the developed estimator for variable selection. The proposed methods can be efficiently implemented using the existing weighted linear quantile regression algorithm. The asymptotic properties of the developed estimators are investigated, and their numerical performance is evaluated in simulation studies. We apply the proposed methods to dataset from a kidney transplant study.