IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v127y2014icp56-71.html
   My bibliography  Save this article

Sufficient dimension reduction on marginal regression for gaps of recurrent events

Author

Listed:
  • Zhao, Xiaobing
  • Zhou, Xian

Abstract

A semiparametric linear transformation of gap time is proposed to model recurrent event data with high-dimensional covariates and informative censoring. It is derived from a proportional hazards model for the conditional intensity function of a renewal process. To overcome the difficulty arising from high-dimensional covariates, we develop a modified sliced regression for censored data and use a sufficient dimension reduction procedure to transform them to a lower dimensional space. Simulation studies are performed to confirm and evaluate the theoretical findings, and to compare the proposed method with existing methods in the literature. An example of application on a set of medical data is demonstrated as well. The proposed model together with the dimension reduction method offers an effective alternative for the analysis of recurrent event with high-dimensional covariates and informative censoring.

Suggested Citation

  • Zhao, Xiaobing & Zhou, Xian, 2014. "Sufficient dimension reduction on marginal regression for gaps of recurrent events," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 56-71.
  • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:56-71
    DOI: 10.1016/j.jmva.2014.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000165
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2014.01.008?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.

    References listed on IDEAS

    as
    1. Michel Delecroix & Olivier Lopez & Valentin Patilea, 2008. "Nonlinear Censored Regression Using Synthetic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 248-265, June.
    2. Cook, R. Dennis & Forzani, Liliana, 2009. "Likelihood-Based Sufficient Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 197-208.
    3. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    4. van Wieringen, Wessel N. & Kun, David & Hampel, Regina & Boulesteix, Anne-Laure, 2009. "Survival prediction using gene expression data: A review and comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1590-1603, March.
    5. Douglas E. Schaubel, 2004. "Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data," Biometrika, Biometrika Trust, vol. 91(2), pages 291-303, June.
    6. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    7. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    8. Xia, Yingcun & Zhang, Dixin & Xu, Jinfeng, 2010. "Dimension Reduction and Semiparametric Estimation of Survival Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 278-290.
    9. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    10. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    11. Xuelin Huang & Lei Liu, 2007. "A Joint Frailty Model for Survival and Gap Times Between Recurrent Events," Biometrics, The International Biometric Society, vol. 63(2), pages 389-397, June.
    12. Engler David & Li Yi, 2009. "Survival Analysis with High-Dimensional Covariates: An Application in Microarray Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-24, February.
    13. Wenbin Lu & Lexin Li, 2011. "Sufficient Dimension Reduction for Censored Regressions," Biometrics, The International Biometric Society, vol. 67(2), pages 513-523, June.
    14. Xingwei Tong & Xin He & Liuquan Sun & Jianguo Sun, 2009. "Variable Selection for Panel Count Data via Non‐Concave Penalized Estimating Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 620-635, December.
    15. Chen, Xiaolin & Wang, Qihua, 2013. "Variable selection in the additive rate model for recurrent event data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 491-503.
    16. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
    17. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaobing Zhao & Xian Zhou, 2020. "Partial sufficient dimension reduction on additive rates model for recurrent event data with high-dimensional covariates," Statistical Papers, Springer, vol. 61(2), pages 523-541, April.
    2. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    3. Dongxiao Han & Xiaogang Su & Liuquan Sun & Zhou Zhang & Lei Liu, 2020. "Variable selection in joint frailty models of recurrent and terminal events," Biometrics, The International Biometric Society, vol. 76(4), pages 1330-1339, December.
    4. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    5. Xue, Yuan & Yin, Xiangrong & Jiang, Xiaolin, 2016. "Ensemble sufficient dimension folding methods for analyzing matrix-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 193-205.
    6. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    7. Tao, Chenyang & Feng, Jianfeng, 2017. "Canonical kernel dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 131-148.
    8. Eliana Christou, 2020. "Robust dimension reduction using sliced inverse median regression," Statistical Papers, Springer, vol. 61(5), pages 1799-1818, October.
    9. Kang, Fangyuan & Sun, Liuquan & Zhao, Xingqiu, 2015. "A class of transformed hazards models for recurrent gap times," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 151-167.
    10. Jieli Ding & Liuquan Sun, 2017. "Additive mixed effect model for recurrent gap time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 223-253, April.
    11. Wu, Runxiong & Chen, Xin, 2021. "MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    12. Zeng, Bilin & Yu, Zhou & Wen, Xuerong Meggie, 2015. "A note on cumulative mean estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 322-327.
    13. Changrong Yan & Dixin Zhang, 2013. "Sparse dimension reduction for survival data," Computational Statistics, Springer, vol. 28(4), pages 1835-1852, August.
    14. Sheng, Wenhui & Yin, Xiangrong, 2013. "Direction estimation in single-index models via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 148-161.
    15. Kapla, Daniel & Fertl, Lukas & Bura, Efstathia, 2022. "Fusing sufficient dimension reduction with neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    16. Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.
    17. Qin Wang & Yuan Xue, 2023. "A structured covariance ensemble for sufficient dimension reduction," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 777-800, September.
    18. Xinchao Luo & Lixing Zhu & Hongtu Zhu, 2016. "Single‐index varying coefficient model for functional responses," Biometrics, The International Biometric Society, vol. 72(4), pages 1275-1284, December.
    19. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    20. Sankaran, P.G. & Anisha, P., 2012. "Additive hazards models for gap time data with multiple causes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1454-1462.

    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:eee:jmvana:v:127:y:2014:i:c:p:56-71. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.