IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v76y2022i1p37-43.html
   My bibliography  Save this article

Reconstructing the Kaplan–Meier Estimator as an M-estimator

Author

Listed:
  • Jiaqi Gu
  • Yiwei Fan
  • Guosheng Yin

Abstract

The Kaplan–Meier (KM) estimator, which provides a nonparametric estimate of a survival function for time-to-event data, has broad applications in clinical studies, engineering, economics and many other fields. The theoretical properties of the KM estimator including its consistency and asymptotic distribution have been well established. From a new perspective, we reconstruct the KM estimator as an M-estimator by maximizing a quadratic M-function based on concordance, which can be computed using the expectation–maximization (EM) algorithm. It is shown that the convergent point of the EM algorithm coincides with the traditional KM estimator, which offers a new interpretation of the KM estimator as an M-estimator. As a result, the limiting distribution of the KM estimator can be established using M-estimation theory. Application on two real datasets demonstrates that the proposed M-estimator is equivalent to the KM estimator, and the confidence intervals and confidence bands can be derived as well.

Suggested Citation

  • Jiaqi Gu & Yiwei Fan & Guosheng Yin, 2022. "Reconstructing the Kaplan–Meier Estimator as an M-estimator," The American Statistician, Taylor & Francis Journals, vol. 76(1), pages 37-43, January.
    • Handle: RePEc:taf:amstat:v:76:y:2022:i:1:p:37-43
    DOI: 10.1080/00031305.2021.1947376
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2021.1947376
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2021.1947376?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.

    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:amstat:v:76:y:2022:i:1:p:37-43. 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/UTAS20 .

    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.