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Inference for High-Dimensional Censored Quantile Regression.

Zhe Fei1, Qi Zheng2, Hyokyoung G Hong3

  • 1Department of Biostatistics, University of California, Los Angeles.

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Summary

This study introduces a new statistical method for analyzing high-dimensional genetic data to understand how different genetic factors affect patient survival over time. The method provides reliable inference for complex survival analyses, especially in cancer research.

Keywords:
Conditional QuantilesFused-HDCQRHigh Dimensional PredictorsStatistical InferenceSurvival Analysis

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Area of Science:

  • Biostatistics
  • Genomics
  • Cancer Epidemiology

Background:

  • High-dimensional genetic biomarkers offer insights into patient survival.
  • Censored quantile regression is effective for detecting heterogeneous covariate effects on survival.
  • Inference for high-dimensional predictors in censored quantile regression is underexplored.

Purpose of the Study:

  • To develop a novel procedure for statistical inference on high-dimensional predictors in global censored quantile regression.
  • To investigate covariate-response associations across a range of quantile levels.
  • To address the gap in methods for high-dimensional censored quantile regression.

Main Methods:

  • A novel procedure combining low-dimensional model estimates from multi-sample splittings and variable selection.
  • Global censored quantile regression framework to analyze associations over a quantile interval.
  • Theoretical analysis showing estimator consistency and asymptotic Gaussian process behavior.

Main Results:

  • The proposed estimator is consistent under regularity conditions.
  • The estimator asymptotically follows a Gaussian process indexed by the quantile level.
  • Simulation studies demonstrate accurate uncertainty quantification in high-dimensional settings.

Conclusions:

  • The developed method provides a robust tool for inference in high-dimensional censored quantile regression.
  • The approach is applicable to analyzing complex genetic data, such as Single Nucleotide Polymorphisms (SNPs) in cancer survival studies.
  • This work advances the statistical methodology for understanding the molecular mechanisms of diseases like lung cancer.