Hybrid Censored Quantile Regression Forest to Assess the Heterogeneous Effects

Abstract: In many applications, heterogeneous treatment effects on a censored response variable are of primary interest, and it is natural to evaluate the effects at different quantiles (e.g., median). The large number of potential effect modifiers, the unknown structure of the treatment effects, and the presence of right censoring pose significant challenges. In this paper, we develop a hybrid forest approach called Hybrid Censored Quantile Regression Forest (HCQRF) to assess the heterogeneous effects varying with high-dimensional variables. The hybrid estimation approach takes advantage of the random forests and the censored quantile regression. We propose a doubly-weighted estimation procedure that consists of a redistribution-of-mass weight to handle censoring and an adaptive nearest neighbor weight derived from the forest to handle high-dimensional effect functions. We propose a variable importance decomposition to measure the impact of a variable on the treatment effect function. Extensive simulation studies demonstrate the efficacy and stability of HCQRF. The result of the simulation study also convinces us of the effectiveness of the variable importance decomposition. We apply HCQRF to a clinical trial of colorectal cancer. We achieve insightful estimations of the treatment effect and meaningful variable importance results. The result of the variable importance also confirms the necessity of the decomposition.