Fine-Gray competing risks model with high-dimensional covariates: estimation and Inference
This addresses a gap in methodological and theoretical literature for biomedical applications, such as analyzing non-cancer mortality in prostate cancer patients, but is incremental as it builds on existing models with new techniques.
The paper tackles the problem of constructing confidence intervals for regression coefficients in the Fine-Gray competing risks model with high-dimensional covariates, where the number of covariates can exceed the sample size, by developing a one-step bias-correction method based on regularized estimation and presenting theoretical results and numerical experiments.
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.