Global Quantile Learning with Censored Data Based on Random Forest

Music City Center 

Quantiles of survival time have been frequently reported in biomedical studies for their straightforward interpretation as well as superior flexibility and identifiability in the presence of censoring. Censored quantile regression has served as the main tool for predicting survival quantiles. However, existing work on censored quantile regression generally assumes linear effects of covariates and yet limited attention has been paid to the quantile prediction performance. In this work, we propose a Global Censored Quantile Random Forest (GCQRF) framework which is designed to simultaneously predict survival quantiles over of continuum of quantile indices with an inherent capacity to accommodate complex nonlinear relationships between covariates and the survival time. We quantify the prediction process's variation without assuming an infinite forest and establish the corresponding weak convergence result. As a useful by-product, feature importance ranking measures based on out-of-sample predictive accuracy are proposed. We demonstrate the superior predictive accuracy of the proposed method over a number of existing alternatives through extensive numerical studies. We illustrate the utility of the proposed importance ranking measures on both simulated and real data.

Random Forest, Censored Quantile Regression, U-processes, Variable Importance