Inference under Fine-Gray competing risks model with high-dimensional covariates

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 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.MSC 2010 subject classifications: Primary 62N03, 62F30; secondary 62J07.

Regularized Weighted Nonparametric Likelihood Approach for High-Dimension Sparse Subdistribution Hazards Model for Competing Risk Data

“…Although, the penalized proportional subdistribution hazards model have been proposed in previous studies, this study considered more scenarios with more penalties. Other works considered only low dimension with different penalties [ 32 ] or high dimension with a few L 1 penalties with no more than 1000 variables [ 26 , 27 ]. Our findings revealed that sensitivity of all penalties were comparable, but the MCP and MCP-L 2 penalties outperformed the other methods in term of selecting less noninformative variables.…”

“…(5) The SCAD-L 2 Zeng and Xie 2020 [36] and MCP-L 2 penalties, where a L 2 penalty is appended to the SCAD and MCP penalties to induce grouping effect in variable selection Asymptotic properties of penalized estimators in different contexts have been investigated by different studies, and all the above penalties have been shown to enjoy the oracle property [26,27,32], i.e., these penalties are consistent in variable selection, and their estimators are asymptotically normal and unbiased. More explicitly, they work as well as knowing the true model in advance.…”

“…Recently, some efforts have been made related to variable selection and direct modeling of cumulative incidence function for high-dimensional competing risk data including [ 19 ], Ambrogi and Scheike [ 16 ], Hou et al [ 26 ], Hou et al [ 27 ], Tapak et al [ 28 ], Tapak et al [ 29 ], Saadati et al [ 30 ], Gilhodes et al [ 31 ], and Fu et al [ 32 ] based on different settings. None of the above approaches was likelihood-based procedures.…”

High-Dimensional Survival Analysis: Methods and Applications

“…With high-dimensional predictors, several authors (Kawaguchi et al 2019, Ha et al 2014, Ahn et al 2018 proposed regularized subdistribution hazard models for variable selection, and Hou et al (2019) further performed inference using a one-step debiased lasso estimator. For prediction, several deep learning methods for competing risks have been proposed based on CIFs.…”

High-Dimensional Survival Analysis: Methods and Applications

“…In fact, model ( 7) implies that 1 − Fc(t|Xi) = {1 − F0c(t)} exp(X i β) , where Fc(t|Xi) and F0c(t) are the CIF given Xi and the baseline CIF, respectively. With high-dimensional predictors, several authors (Kawaguchi et al 2019, Ha et al 2014, Ahn et al 2018 proposed regularized subdistribution hazard models for variable selection, and Hou et al (2019) further performed inference using a one-step debiased LASSO estimator. For prediction, several deep learning works for competing risks have been proposed based on CIFs.…”