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In many applications, heterogeneous treatment effects on a censored responsevariable are of primary interest, and it is natural to evaluate the effects atdifferent quantiles (e.g., median). The large number of potential effectmodifiers, the unknown structure of the treatment effects, and the presence ofright censoring pose significant challenges. In this paper, we develop a hybridforest approach called Hybrid Censored Quantile Regression Forest (HCQRF) toassess the heterogeneous effects varying with high-dimensional variables. Thehybrid estimation approach takes advantage of the random forests and thecensored quantile regression. We propose a doubly-weighted estimation procedurethat consists of a redistribution-of-mass weight to handle censoring and anadaptive nearest neighbor weight derived from the forest to handlehigh-dimensional effect functions. We propose a variable importancedecomposition to measure the impact of a variable on the treatment effectfunction. Extensive simulation studies demonstrate the efficacy and stabilityof HCQRF. The result of the simulation study also convinces us of theeffectiveness of the variable importance decomposition. We apply HCQRF to aclinical trial of colorectal cancer. We achieve insightful estimations of thetreatment effect and meaningful variable importance results. The result of thevariable importance also confirms the necessity of the decomposition.

Hybrid Censored Quantile Regression Forest to Assess the Heterogeneous Effects