IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v108y2013i501p247-264.html
   My bibliography  Save this article

High-Dimensional Sparse Additive Hazards Regression

Author

Listed:
  • Wei Lin
  • Jinchi Lv

Abstract

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of regularization methods for simultaneous variable selection and estimation in the additive hazards model, by combining the nonconcave penalized likelihood approach and the pseudoscore method. In a high-dimensional setting where the dimensionality can grow fast, polynomially or nonpolynomially, with the sample size, we establish the weak oracle property and oracle property under mild, interpretable conditions, thus providing strong performance guarantees for the proposed methodology. Moreover, we show that the regularity conditions required by the L 1 method are substantially relaxed by a certain class of sparsity-inducing concave penalties. As a result, concave penalties such as the smoothly clipped absolute deviation, minimax concave penalty, and smooth integration of counting and absolute deviation can significantly improve on the L 1 method and yield sparser models with better prediction performance. We present a coordinate descent algorithm for efficient implementation and rigorously investigate its convergence properties. The practical use and effectiveness of the proposed methods are demonstrated by simulation studies and a real data example.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:247-264
    DOI: 10.1080/01621459.2012.746068
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2012.746068
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2012.746068?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    2. Zhang Haixiang & Zheng Yinan & Yoon Grace & Zhang Zhou & Gao Tao & Joyce Brian & Zhang Wei & Schwartz Joel & Vokonas Pantel & Colicino Elena & Baccarelli Andrea & Hou Lifang & Liu Lei, 2017. "Regularized estimation in sparse high-dimensional multivariate regression, with application to a DNA methylation study," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(3), pages 159-171, August.
    3. Yingying Fan & Jinchi Lv, 2013. "Asymptotic Equivalence of Regularization Methods in Thresholded Parameter Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1044-1061, September.
    4. Yan, Xiaodong & Wang, Hongni & Wang, Wei & Xie, Jinhan & Ren, Yanyan & Wang, Xinjun, 2021. "Optimal model averaging forecasting in high-dimensional survival analysis," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1147-1155.
    5. Jianglin Fang, 2021. "Feature screening for ultrahigh-dimensional survival data when failure indicators are missing at random," Statistical Papers, Springer, vol. 62(3), pages 1141-1166, June.
    6. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    7. Xiaobo Wang & Jiayu Huang & Guosheng Yin & Jian Huang & Yuanshan Wu, 2023. "Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 115-141, January.
    8. Lv, Shaogao & You, Mengying & Lin, Huazhen & Lian, Heng & Huang, Jian, 2018. "On the sign consistency of the Lasso for the high-dimensional Cox model," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 79-96.
    9. 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.
    10. Ping-Shou Zhong & Tao Hu & Jun Li, 2015. "Tests for Coefficients in High-dimensional Additive Hazard Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 649-664, September.
    11. Yingying Fan & Jinchi Lv, 2014. "Asymptotic properties for combined L1 and concave regularization," Biometrika, Biometrika Trust, vol. 101(1), pages 57-70.
    12. Arfan Raheen Afzal & Jing Yang & Xuewen Lu, 2021. "Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters," Computational Statistics, Springer, vol. 36(2), pages 829-855, June.
    13. Xiaolin Chen & Yi Liu & Qihua Wang, 2019. "Joint feature screening for ultra-high-dimensional sparse additive hazards model by the sparsity-restricted pseudo-score estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1007-1031, October.
    14. Jiang Dandan & Sun Jianguo, 2017. "Group Tests for High-dimensional Failure Time Data with the Additive Hazards Models," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-10, May.
    15. Wang, Lu & Shen, Jincheng & Thall, Peter F., 2014. "A modified adaptive Lasso for identifying interactions in the Cox model with the heredity constraint," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 126-133.
    16. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:247-264. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.