IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v9y2013i2p185-204n5.html
   My bibliography  Save this article

Exact Nonparametric Confidence Bands for the Survivor Function

Author

Listed:
  • Matthews David

    (Statistics & Actuarial Science, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada)

Abstract

A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan–Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden–Decker–Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin’s lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample.

Suggested Citation

  • Matthews David, 2013. "Exact Nonparametric Confidence Bands for the Survivor Function," The International Journal of Biostatistics, De Gruyter, vol. 9(2), pages 185-204, October.
  • Handle: RePEc:bpj:ijbist:v:9:y:2013:i:2:p:185-204:n:5
    DOI: 10.1515/ijb-2012-0046
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2012-0046
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/ijb-2012-0046?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:bpj:ijbist:v:9:y:2013:i:2:p:185-204:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.