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Abstract:
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Censored quantile regression has emerged as a powerful tool for detecting heterogeneous effects of covariates on survival outcomes. However, few works are available to draw inferences on the effects of high dimensional predictors for censored quantile regression. This paper proposes a novel fused estimator for statistical inferences on all predictors within the framework of ``global'' censored quantile regression, where the quantile level is over an interval, instead of several discrete values. The proposed estimator is fused from a sequence of low dimensional estimations based on multi-sample splitting and variable selection for dimension reduction. We show that the estimator is consistent and asymptotically follows a Gaussian process indexed by the quantile level. Simulation studies indicate that our procedure properly quantifies the uncertainty of effect estimates in high dimensional settings. We apply our method to analyze the heterogeneous effects of SNPs residing in the lung cancer pathways on patients' survival, using the Boston Lung Cancer Survivor Cohort, a cancer epidemiology study investigating the molecular mechanism of lung cancer.
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