  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.
