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

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 biostatistics applications, high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literatures. We fill in this blank by proposing first a consistent regularized estimator and then the confidence intervals based on the one-step bias-correcting estimator. We are able to generalize the partial likelihood approach for the Fine-Gray model under random censoring despite many technical difficulties. We lay down a methodological and theoretical framework for the one-step bias-correcting estimator with the partial likelihood, which does not have independent and identically distributed entries. We also handle for our theory the approximation error from the inverse probability weighting (IPW), proposing novel 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.