  Random forests are powerful non-parametric regression method but are severely
limited in their usage in the presence of randomly censored observations, and
naively applied can exhibit poor predictive performance due to the incurred
biases. Based on a local adaptive representation of random forests, we develop
its regression adjustment for randomly censored regression quantile models.
Regression adjustment is based on a new estimating equation that adapts to
censoring and leads to quantile score whenever the data do not exhibit
censoring. The proposed procedure named {\it censored quantile regression
forest}, allows us to estimate quantiles of time-to-event without any
parametric modeling assumption. We establish its consistency under mild model
specifications. Numerical studies showcase a clear advantage of the proposed
procedure.
