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The purpose of this paper is to construct confidence intervals for theregression coefficients in the Fine-Gray model for competing risks data withrandom censoring, where the number of covariates can be larger than the samplesize. Despite strong motivation from biomedical applications, ahigh-dimensional Fine-Gray model has attracted relatively little attentionamong the methodological or theoretical literature. We fill in this gap bydeveloping confidence intervals based on a one-step bias-correction for aregularized estimation. We develop a theoretical framework for the partiallikelihood, which does not have independent and identically distributed entriesand therefore presents many technical challenges. We also study theapproximation error from the weighting scheme under random censoring forcompeting risks and establish new concentration results for time-dependentprocesses. In addition to the theoretical results and algorithms, we presentextensive numerical experiments and an application to a study of non-cancermortality among prostate cancer patients using the linked Medicare-SEER data.

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