Statistical Inference for Cox Proportional Hazards Models with a Diverging Number of Covariates

TL;DR

This paper introduces a debiased lasso method for Cox proportional hazards models that accurately estimates regression coefficients and confidence intervals without requiring sparsity assumptions, even as the number of covariates grows.

Contribution

It develops a novel approach to inference in high-dimensional Cox models that avoids sparsity assumptions on the inverse Fisher information matrix.

Findings

Method provides consistent estimates and confidence intervals with correct coverage.

Simulation studies confirm the method's accuracy and robustness.

Application to lung cancer data demonstrates practical utility.

Abstract

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under-coverage confidence intervals. We propose a modified debiased lasso approach, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression coefficients when the dimension of covariates diverges with the sample size. As demonstrated by extensive simulations, our proposed method provides consistent estimates and confidence intervals with nominal coverage probabilities. The utility of the method is further demonstrated by assessing the effects of genetic markers on patients' overall survival with the Boston Lung Cancer Survival Cohort, a large-scale epidemiology study investigating mechanisms underlying the lung cancer.