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Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters

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Abstract

In regression models with a grouping structure among the explanatory variables, variable selection at the group and within group individual variable level is important to improve model accuracy and interpretability. In this article, we propose a hierarchical bi-level variable selection approach for censored survival data in the linear part of a partially linear additive hazards model where the covariates are naturally grouped. The proposed method is capable of conducting simultaneous group selection and individual variable selection within selected groups. Computational algorithms are developed, and the asymptotic rates and selection consistency of the proposed estimators are established. Simulation results indicate that our proposed method outperforms several existing penalties, for example, LASSO, SCAD, and adaptive LASSO. Application of the proposed method is illustrated with the Mayo Clinic primary biliary cirrhosis (PBC) data.

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Acknowledgements

Lu’s research was partially supported by a Discovery Grant (RG/PIN06466-2018) from Natural Sciences and Engineering Research Council (NSERC) of Canada. Yang’s research was supported by the National Natural Science Foundation of China (Grant 11801168), the Natural Science Foundation of Hunan Province (Grant 2018JJ3322), the Scientific Research Fund of Hunan Provincial Education Department (Grant 18B024), and the support of China Scholarship Council for his visiting to University of California, Riverside. The authors are also grateful to the associate editor and the referees for their insightful comments and suggestions that have greatly improved the paper.

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  1. Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada

    Arfan Raheen Afzal & Xuewen Lu

  2. Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

    Jing Yang

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  1. Arfan Raheen Afzal
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Afzal, A.R., Yang, J. & Lu, X. Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters. Comput Stat 36, 829–855 (2021). https://doi.org/10.1007/s00180-020-01062-3

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