  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.
