Inference for High-Dimensional Censored Quantile Regression

Zhe Fei, Qi Zheng, Hyokyoung G. Hong and Yi Li

Journal of the American Statistical Association, 2023, vol. 118, issue 542, 898-912

Abstract: 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 inferences on the effects of high-dimensional predictors for censored quantile regression (CQR). This article proposes a novel procedure to draw inference on all predictors within the framework of global CQR, 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.

Date: 2023
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DOI: 10.1080/01621459.2021.1957900

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