Model pursuit and variable selection in the additive accelerated failure time model
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Model pursuit and variable selection in the additive accelerated failure time model Li Liu1
· Hao Wang1 · Yanyan Liu1
· Jian Huang2
Received: 12 January 2020 / Revised: 29 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we propose a new semiparametric method to simultaneously select important variables, identify the model structure and estimate covariate effects in the additive AFT model, for which the dimension of covariates is allowed to increase with sample size. Instead of directly approximating the non-parametric effects as in most existing studies, we take a linear effect out to weak the condition required for model identifiability. To compute the proposed estimates numerically, we use an alternating direction method of multipliers algorithm so that it can be implemented easily and achieve fast convergence rate. Our method is proved to be selection consistent and possess an asymptotic oracle property. The performance of the proposed methods is illustrated through simulations and the real data analysis. Keywords Additive AFT model · Model pursuit · Variable selection · Penalization · ADMM algorithm Mathematics Subject Classification 62B10 · 62G20 · 62N01
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Yanyan Liu [email protected] Li Liu [email protected] Hao Wang [email protected] Jian Huang [email protected]
1
School of Mathematics and Statistics, Wuhan University, Wuhan, China
2
Department of Statistics and Actuarial Science, University of Iowa, Iowa City, USA
123
L. Liu et al.
1 Introduction The rapid development of technology and information drives high dimensional data collection in practical study areas such as genomic and health sciences. Under the sparsity assumption, various variable selection methods have been proposed to improve the accuracy of the estimation. Among them, penalized methods have been studied extensively for uncensored response. Examples include LASSO (Tibshirani 1996), adaptive LASSO (Zou 2006), SCAD (Fan and Li 2001), the Dantizg selector (Candes and Tao 2007) and MCP (Zhang 2010). Some of these methods have been adapted to analyze censored data based on classical Cox model. For example, Tibshirani (1997) and Fan and Li (2002) extended the LASSO and nonconcave penalized likelihood methods to the Cox model, respectively. Zhang and Lu (2007) developed the adaptive LASSO for Cox model. In the literature of survival analysis, a useful alternative to the Cox model is the accelerated failure time (AFT) model (Wei 1992), which assumes the linear relationship between the logarithm of survival time and covariates of interest. Compared with the Cox model, estimated parameters in the AFT model can be easily interpreted in practice. Inference procedures for the AFT model include the inverse probability weighting (IPW) method (Stute 1993, 1996), Buckley–James iterative method (BJ) and rank-based method (Buckley and James 1979; Zeng and Lin 2007). Some researchers developed variable selection methods for fitting semiparametric AFT models in high dimensional data setti
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