IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v27y2021i3d10.1007_s10985-021-09522-8.html
   My bibliography  Save this article

OptBand: optimization-based confidence bands for functions to characterize time-to-event distributions

Author

Listed:
  • T. Chen

    (Harvard Medical School and Harvard Pilgrim Health Care)

  • S. Tracy

    (Harvard T.H. Chan School of Public Health
    Dana-Faber Cancer Institute)

  • H. Uno

    (Dana-Faber Cancer Institute)

Abstract

Classical simultaneous confidence bands for survival functions (i.e., Hall–Wellner, equal precision, and empirical likelihood bands) are derived from transformations of the asymptotic Brownian nature of the Nelson–Aalen or Kaplan–Meier estimators. Due to the properties of Brownian motion, a theoretical derivation of the highest confidence density region cannot be obtained in closed form. Instead, we provide confidence bands derived from a related optimization problem with local time processes. These bands can be applied to the one-sample problem regarding both cumulative hazard and survival functions. In addition, we present a solution to the two-sample problem for testing differences in cumulative hazard functions. The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies. The proposed bands are applied to clinical trial data to assess survival times for primary biliary cirrhosis patients treated with D-penicillamine.

Suggested Citation

  • T. Chen & S. Tracy & H. Uno, 2021. "OptBand: optimization-based confidence bands for functions to characterize time-to-event distributions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 481-498, July.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:3:d:10.1007_s10985-021-09522-8
    DOI: 10.1007/s10985-021-09522-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-021-09522-8
    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/s10985-021-09522-8?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. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
    2. Lu Tian & Rui Wang & Tianxi Cai & Lee-Jen Wei, 2011. "The Highest Confidence Density Region and Its Usage for Joint Inferences about Constrained Parameters," Biometrics, The International Biometric Society, vol. 67(2), pages 604-610, 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. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    2. Robert Drake & Apratim Guha, 2014. "A mutual information-based k -sample test for discrete distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 2011-2027, September.
    3. Zhao, Yichuan & Zhao, Meng, 2011. "Empirical likelihood for the contrast of two hazard functions with right censoring," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 392-401, March.
    4. Bin Dong & David E. Matthews, 2012. "Empirical Likelihood for Cumulative Hazard Ratio Estimation with Covariate Adjustment," Biometrics, The International Biometric Society, vol. 68(2), pages 408-418, June.
    5. Ben O’Neill, 2022. "Smallest covering regions and highest density regions for discrete distributions," Computational Statistics, Springer, vol. 37(3), pages 1229-1254, July.
    6. Jimin Lee & Seunggeun Hyun, 2011. "Confidence bands for the difference of two survival functions under the additive risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 785-797, February.
    7. Qin, Gengsheng & Zhao, Yichuan, 2007. "Empirical likelihood inference for the mean residual life under random censorship," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 549-557, March.
    8. Subramanian, Sundarraman, 2022. "Simultaneous confidence bands for survival functions from twice censorship," Statistics & Probability Letters, Elsevier, vol. 186(C).
    9. Wei Wang & Shou‐En Lu & Jerry Q. Cheng & Minge Xie & John B. Kostis, 2022. "Multivariate survival analysis in big data: A divide‐and‐combine approach," Biometrics, The International Biometric Society, vol. 78(3), pages 852-866, September.
    10. Guanghui Wei & Douglas E. Schaubel, 2008. "Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards," Biometrics, The International Biometric Society, vol. 64(3), pages 724-732, September.
    11. Shen, Junshan & He, Shuyuan, 2006. "Empirical likelihood for the difference of two survival functions under right censorship," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 169-181, January.
    12. David R. Bickel, 2014. "Small-scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison," International Statistical Review, International Statistical Institute, vol. 82(3), pages 457-476, December.
    13. Sundarraman Subramanian, 2020. "Function-based hypothesis testing in censored two-sample location-scale models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 183-213, January.
    14. McKeague, Ian W. & Zhao, Yichuan, 2006. "Width-scaled confidence bands for survival functions," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 327-339, February.
    15. Yichuan Zhao & Song Yang, 2008. "Empirical likelihood inference for censored median regression with weighted empirical hazard functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 441-457, June.
    16. Zhou, Mai & Zhu, Shihong, 2015. "Empirical likelihood confidence band for the difference of survival functions under proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 228-235.
    17. Zhao, Meng & Zhao, Yichuan & McKeague, Ian W., 2015. "Empirical likelihood inference for the odds ratio of two survival functions under right censoring," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 304-312.
    18. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.
    19. Shihong Zhu & Yifan Yang & Mai Zhou, 2015. "A note on the empirical likelihood confidence band for hazards ratio with covariate adjustment," Biometrics, The International Biometric Society, vol. 71(3), pages 859-563, September.
    20. Nubyra Ahmed & Sundarraman Subramanian, 2016. "Semiparametric simultaneous confidence bands for the difference of survival functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 504-530, October.

    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:lifeda:v:27:y:2021:i:3:d:10.1007_s10985-021-09522-8. 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.