IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v73y2021i1d10.1007_s10463-019-00739-x.html
   My bibliography  Save this article

On the proportional hazards model with last observation carried forward covariates

Author

Listed:
  • Hongyuan Cao

    (Jilin University
    Florida State University)

  • Jason P. Fine

    (University of North Carolina at Chapel Hill)

Abstract

Standard partial likelihood methodology for the proportional hazards model with time-dependent covariates requires knowledge of the covariates at the observed failure times, which is not realistic in practice. A simple and commonly used estimator imputes the most recently observed covariate prior to each failure time, which is known to be biased. In this paper, we show that a weighted last observation carried forward approach may yield valid estimation. We establish the consistency and asymptotic normality of the weighted partial likelihood estimators and provide a closed form variance estimator for inference. The estimator may be conveniently implemented using standard software. Interestingly, the convergence rate of the estimator is slower than the parametric rate achieved with fully observed covariates but the same as that obtained with all lagged covariate values. Simulation studies provide numerical support for the theoretical findings. Data from an Alzheimer’s study illustrate the practical utility of the methodology.

Suggested Citation

  • Hongyuan Cao & Jason P. Fine, 2021. "On the proportional hazards model with last observation carried forward covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 115-134, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00739-x
    DOI: 10.1007/s10463-019-00739-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-019-00739-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-019-00739-x?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. Hongyuan Cao & Mathew M. Churpek & Donglin Zeng & Jason P. Fine, 2015. "Analysis of the Proportional Hazards Model With Sparse Longitudinal Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1187-1196, September.
    2. Jane Xu & Scott L. Zeger, 2001. "Joint analysis of longitudinal data comprising repeated measures and times to events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 375-387.
    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. Lei Liu & Xuelin Huang & John O'Quigley, 2008. "Analysis of Longitudinal Data in the Presence of Informative Observational Times and a Dependent Terminal Event, with Application to Medical Cost Data," Biometrics, The International Biometric Society, vol. 64(3), pages 950-958, September.
    2. Eva Ascarza & Bruce G. S. Hardie, 2013. "A Joint Model of Usage and Churn in Contractual Settings," Marketing Science, INFORMS, vol. 32(4), pages 570-590, July.
    3. Song Zhang & Peter Müller & Kim-Anh Do, 2010. "A Bayesian Semiparametric Survival Model with Longitudinal Markers," Biometrics, The International Biometric Society, vol. 66(2), pages 435-443, June.
    4. Jian-Jian Ren & Yuyin Shi, 2024. "Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 617-648, August.
    5. Sarah J. Ratcliffe & Wensheng Guo & Thomas R. Ten Have, 2004. "Joint Modeling of Longitudinal and Survival Data via a Common Frailty," Biometrics, The International Biometric Society, vol. 60(4), pages 892-899, December.
    6. Zhuowei Sun & Hongyuan Cao & Li Chen, 2022. "Regression analysis of additive hazards model with sparse longitudinal covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 263-281, April.
    7. Erning Li & Naisyin Wang & Nae-Yuh Wang, 2007. "Joint Models for a Primary Endpoint and Multiple Longitudinal Covariate Processes," Biometrics, The International Biometric Society, vol. 63(4), pages 1068-1078, December.
    8. Philipson, Pete & Hickey, Graeme L. & Crowther, Michael J. & Kolamunnage-Dona, Ruwanthi, 2020. "Faster Monte Carlo estimation of joint models for time-to-event and multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    9. repec:jss:jstsof:35:i09 is not listed on IDEAS
    10. Yingye Zheng & Patrick J. Heagerty, 2005. "Partly Conditional Survival Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 61(2), pages 379-391, June.
    11. Zhang, Cuihong & Ning, Jing & Cai, Jianwen & Squires, James E. & Belle, Steven H. & Li, Ruosha, 2024. "Dynamic risk score modeling for multiple longitudinal risk factors and survival," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    12. Xiao Song & Yijian Huang, 2004. "A Corrected Pseudo-score Approach for Additive Hazards Model With Longitudinal Covariates Measured With Error," UW Biostatistics Working Paper Series 1049, Berkeley Electronic Press.
    13. Lei Liu & Robert A. Wolfe & Xuelin Huang, 2004. "Shared Frailty Models for Recurrent Events and a Terminal Event," Biometrics, The International Biometric Society, vol. 60(3), pages 747-756, September.
    14. Anne Eaton & Yifei Sun & James Neaton & Xianghua Luo, 2022. "Nonparametric estimation in an illness‐death model with component‐wise censoring," Biometrics, The International Biometric Society, vol. 78(3), pages 1168-1180, September.
    15. Jeremy M. G. Taylor & Yongseok Park & Donna P. Ankerst & Cecile Proust-Lima & Scott Williams & Larry Kestin & Kyoungwha Bae & Tom Pickles & Howard Sandler, 2013. "Real-Time Individual Predictions of Prostate Cancer Recurrence Using Joint Models," Biometrics, The International Biometric Society, vol. 69(1), pages 206-213, March.
    16. Yueh-Yun Chi & Joseph G. Ibrahim, 2006. "Joint Models for Multivariate Longitudinal and Multivariate Survival Data," Biometrics, The International Biometric Society, vol. 62(2), pages 432-445, June.
    17. Xiao Song & Marie Davidian & Anastasios A. Tsiatis, 2002. "A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 58(4), pages 742-753, December.
    18. Xiao Song & C. Y. Wang, 2008. "Semiparametric Approaches for Joint Modeling of Longitudinal and Survival Data with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 64(2), pages 557-566, June.
    19. Zangdong He & Wanzhu Tu & Sijian Wang & Haoda Fu & Zhangsheng Yu, 2015. "Simultaneous variable selection for joint models of longitudinal and survival outcomes," Biometrics, The International Biometric Society, vol. 71(1), pages 178-187, March.
    20. Wei, Shaoceng & Xu, Liou & Kryscio, Richard J., 2014. "Markov transition model to dementia with death as a competing event," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 78-88.
    21. Lin, Huazhen & Li, Yi & Tan, Ming T., 2013. "Estimating a unitary effect summary based on combined survival and quantitative outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 129-139.

    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:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00739-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.