Confidence intervals for high-dimensional Cox models

TL;DR

This paper develops methods to construct valid confidence intervals for regression coefficients in high-dimensional Cox models with censored data, addressing challenges from time-dependent covariates and large covariate sets.

Contribution

It introduces a debiased estimator tailored for high-dimensional Cox models with time-dependent covariates, extending existing methods to more complex survival analysis scenarios.

Findings

Confidence intervals are asymptotically valid under specified conditions.

The proposed method performs well in extensive numerical experiments.

Addresses challenges from time-dependent covariates and high-dimensional data.

Abstract

The purpose of this paper is to construct confidence intervals for the regression coefficients in high-dimensional Cox proportional hazards regression models where the number of covariates may be larger than the sample size. Our debiased estimator construction is similar to those in Zhang and Zhang (2014) and van de Geer et al. (2014), but the time-dependent covariates and censored risk sets introduce considerable additional challenges. Our theoretical results, which provide conditions under which our confidence intervals are asymptotically valid, are supported by extensive numerical experiments.