2017/07/29 by Jue Hou, Jelena Bradic, Jelena Bradić +4
Mathematics · Medicine · #62F30 #62N03 #Applications (stat.AP) #Artificial intelligence #Censoring (clinical trials) #Computer science #Confidence interval #Covariate #Coverage probability #Econometrics #Estimator #FOS: Computer and information sciences #FOS: Mathematics #Gray (unit) #Independent and identically distributed random variables #Inference #Machine Learning (stat.ML) #Mathematics #Medicine #Methodology (stat.ME) #Random effects model #Random variable #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics #Statistics Theory (math.ST) #Weighting #math.ST #msc:62F30 #msc:62N03 #stat.AP #stat.ME #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1707.09561
63 pages
openalex publication_date 2017/07/29 · openalex created_date 2017/08/08 · arxiv created 2019/04/08 · arxiv updated 2019/04/10 · openalex updated_date 2026/08/06
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.