A fast divide-and-conquer sparse Cox regression. (23rd September 2019)

• Record Type: Journal Article
• Authors: Wang, Yan; Hong, Chuan; Palmer, Nathan; Di, Qian; Schwartz, Joel; Kohane, Isaac; Cai, Tianxi
• Is Part Of: Biostatistics. Volume 22:Number 2(2021)
• Page Start: 381
• Page End: 401
• Publication Date: 2019-09-23
• Subjects: Cox proportional hazards model -- Distributed learning -- Divide-and-conquer -- Least square approximation -- Shrinkage estimation -- Variable selection; Medical statistics -- Periodicals; Biometry -- Periodicals; Health risk assessment -- Periodicals; Medicine -- Research -- Statistical methods -- Periodicals; 610.727
• DOI: 10.1093/biostatistics/kxz036
• Languages: English
• ISSNs: 1465-4644

Abstract

Summary: We propose a computationally and statistically efficient divide-and-conquer (DAC) algorithm to fit sparse Cox regression to massive datasets where the sample size $n_0$ is exceedingly large and the covariate dimension $p$ is not small but $n_0\gg p$ . The proposed algorithm achieves computational efficiency through a one-step linear approximation followed by a least square approximation to the partial likelihood (PL). These sequences of linearization enable us to maximize the PL with only a small subset and perform penalized estimation via a fast approximation to the PL. The algorithm is applicable for the analysis of both time-independent and time-dependent survival data. Simulations suggest that the proposed DAC algorithm substantially outperforms the full sample-based estimators and the existing DAC algorithm with respect to the computational speed, while it achieves similar statistical efficiency as the full sample-based estimators. The proposed algorithm was applied to extraordinarily large survival datasets for the prediction of heart failure-specific readmission within 30 days among Medicare heart failure patients.