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A regularized variable selection procedure in additive hazards model with stratified case-cohort design

Author

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  • Ai Ni

    (Memorial Sloan Kettering Cancer Center)

  • Jianwen Cai

    (University of North Carolina at Chapel Hill)

Abstract

Case-cohort designs are commonly used in large epidemiological studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large. An efficient variable selection method is needed for case-cohort studies where the covariates are only observed in a subset of the sample. Current literature on this topic has been focused on the proportional hazards model. However, in many studies the additive hazards model is preferred over the proportional hazards model either because the proportional hazards assumption is violated or the additive hazards model provides more relevent information to the research question. Motivated by one such study, the Atherosclerosis Risk in Communities (ARIC) study, we investigate the properties of a regularized variable selection procedure in stratified case-cohort design under an additive hazards model with a diverging number of parameters. We establish the consistency and asymptotic normality of the penalized estimator and prove its oracle property. Simulation studies are conducted to assess the finite sample performance of the proposed method with a modified cross-validation tuning parameter selection methods. We apply the variable selection procedure to the ARIC study to demonstrate its practical use.

Suggested Citation

  • Ai Ni & Jianwen Cai, 2018. "A regularized variable selection procedure in additive hazards model with stratified case-cohort design," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 443-463, July.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:3:d:10.1007_s10985-017-9402-7
    DOI: 10.1007/s10985-017-9402-7
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    References listed on IDEAS

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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Wei Lin & Jinchi Lv, 2013. "High-Dimensional Sparse Additive Hazards Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 247-264, March.
    3. Torben Martinussen & Thomas H. Scheike, 2009. "Covariate Selection for the Semiparametric Additive Risk Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 602-619, December.
    4. Ai Ni & Jianwen Cai & Donglin Zeng, 2016. "Variable selection for case-cohort studies with failure time outcome," Biometrika, Biometrika Trust, vol. 103(3), pages 547-562.
    5. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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