Fine-Gray competing risks model with high-dimensional covariates: estimation and Inference

TL;DR

This paper develops a method for constructing confidence intervals for high-dimensional regression coefficients in the Fine-Gray competing risks model, addressing challenges of bias correction and theoretical guarantees.

Contribution

It introduces a one-step bias-correction approach for high-dimensional Fine-Gray models with theoretical validation and practical algorithms.

Findings

Effective confidence interval construction for high-dimensional data

Theoretical guarantees under complex censoring schemes

Successful application to prostate cancer mortality data

Abstract

The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new concentration results for time-dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.