IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v47y2020i9p1511-1528.html
   My bibliography  Save this article

On maximum likelihood estimation of the semi-parametric Cox model with time-varying covariates

Author

Listed:
  • Mark Thackham
  • Jun Ma

Abstract

Including time-varying covariates is a popular extension to the Cox model and a suitable approach for dealing with non-proportional hazards. However, partial likelihood (PL) estimation of this model has three shortcomings: (i) estimated regression coefficients can be less accurate in small samples with heavy censoring; (ii) the baseline hazard is not directly estimated and (iii) a covariance matrix for both the regression coefficients and the baseline hazard is not easily produced.We address these by developing a maximum likelihood (ML) approach to jointly estimate regression coefficients and baseline hazard using a constrained optimisation ensuring the latter's non-negativity. We demonstrate asymptotic properties of these estimates and show via simulation their increased accuracy compared to PL estimates in small samples and show our method produces smoother baseline hazard estimates than the Breslow estimator.Finally, we apply our method to two examples, including an important real-world financial example to estimate time to default for retail home loans. We demonstrate using our ML estimate for the baseline hazard can give much clearer corroboratory evidence of the ‘humped hazard’, whereby the risk of loan default rises to a peak and then later falls.

Suggested Citation

  • Mark Thackham & Jun Ma, 2020. "On maximum likelihood estimation of the semi-parametric Cox model with time-varying covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(9), pages 1511-1528, June.
  • Handle: RePEc:taf:japsta:v:47:y:2020:i:9:p:1511-1528
    DOI: 10.1080/02664763.2019.1681946
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2019.1681946
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664763.2019.1681946?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. Medina-Olivares, Victor & Calabrese, Raffaella & Crook, Jonathan & Lindgren, Finn, 2023. "Joint models for longitudinal and discrete survival data in credit scoring," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1457-1473.
    2. Yuegang Song & Ruibing Wu, 2022. "The Impact of Financial Enterprises’ Excessive Financialization Risk Assessment for Risk Control based on Data Mining and Machine Learning," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1245-1267, December.
    3. Li Li & Yu Lu & Miaojuan Peng, 2022. "Deterioration Model for Reinforced Concrete Bridge Girders Based on Survival Analysis," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    4. Ondřej Dvouletý & Ivana Svobodová & Nina Bočková & Jarmila Duháček Šebestová, 2024. "Becoming a First-time Entrepreneur in 40s and Older: Lessons from Survival Analysis," Working Papers 0076, Silesian University, School of Business Administration.

    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:japsta:v:47:y:2020:i:9:p:1511-1528. 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/CJAS20 .

    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.