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