title: Sieve estimation of Cox models with latent structures.
abstract: This article considers sieve estimation in the Cox model with an unknown regression structure based on right-censored data. We propose a semiparametric pursuit method to simultaneously identify and estimate linear and nonparametric covariate effects based on B-spline expansions through a penalized group selection method with concave penalties. We show that the estimators of the linear effects and the nonparametric component are consistent. Furthermore, we establish the asymptotic normality of the estimator of the linear effects. To compute the proposed estimators, we develop a modified blockwise majorization descent algorithm that is efficient and easy to implement. Simulation studies demonstrate that the proposed method performs well in finite sample situations. We also use the primary biliary cirrhosis data to illustrate its application.
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, China.|School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, China.
authors.forename: Yongxiu
authors.initials: Y
authors.lastname: Cao
authors.affiliation: Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa, U.S.A.|School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China.
authors.forename: Jian
authors.initials: J
authors.lastname: Huang
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, China.
authors.forename: Yanyan
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong.
authors.forename: Xingqiu
authors.initials: X
authors.lastname: Zhao
mesh_terms: D000465:Algorithms; D006801:Humans; D016013:Likelihood Functions; D008105:Liver Cirrhosis, Biliary; D015233:Models, Statistical; D016016:Proportional Hazards Models; D012044:Regression Analysis; D018709:Statistics, Nonparametric
keywords: Group selection; Model-pursuit consistency; Modified blockwise majorization descent algorithm; Partially linear Cox model; Penalized partial likelihood