  With the availability of high dimensional genetic biomarkers, it is of
interest to identify heterogeneous effects of these predictors on patients'
survival, along with proper statistical inference. Censored quantile regression
has emerged as a powerful tool for detecting heterogeneous effects of
covariates on survival outcomes. To our knowledge, there is little work
available to draw inference on the effects of high dimensional predictors for
censored quantile regression. This paper proposes a novel procedure to draw
inference on all predictors within the framework of global censored quantile
regression, which investigates covariate-response associations over an interval
of quantile levels, instead of a few discrete values. The proposed estimator
combines a sequence of low dimensional model estimates that are based on
multi-sample splittings and variable selection. We show that, under some
regularity conditions, the estimator is consistent and asymptotically follows a
Gaussian process indexed by the quantile level. Simulation studies indicate
that our procedure can properly quantify the uncertainty of the estimates in
high dimensional settings. We apply our method to analyze the heterogeneous
effects of SNPs residing in lung cancer pathways on patients' survival, using
the Boston Lung Cancer Survival Cohort, a cancer epidemiology study on the
molecular mechanism of lung cancer.
