IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v27y2021i2d10.1007_s10985-021-09517-5.html
   My bibliography  Save this article

Testing equivalence of survival before but not after end of follow-up

Author

Listed:
  • Julie K. Furberg

    (Novo Nordisk A/S)

  • Christian B. Pipper

    (LEO Pharma A/S)

  • Thomas Scheike

    (University of Cophenagen)

Abstract

For equivalence trials with survival outcomes, a popular testing approach is the elegant test for equivalence of two survival functions suggested by Wellek (Biometrics 49: 877–881, 1993). This test evaluates whether or not the difference between the true survival curves is practically irrelevant by specifying an equivalence margin on the hazard ratio under the proportional hazards assumption. However, this approach is based on extrapolating the behavior of the survival curves to the whole time axis, whereas in practice survival times are only observed until the end of follow-up. We propose a modification of Welleks test that only addresses equivalence until end of follow-up and derive the large sample properties of this test. Another issue is the proportional hazards assumption which may not be realistic. If this assumption is violated, one may severely misjudge the actual treatment effect with a hazard ratio quantification and wrongly declare equivalence. We suggest a non-parametric test for assessing survival equivalence within the follow-up period. We derive the large sample properties of this test and provide an approximation to the limiting distribution under some mild assumptions on the functional form of the difference between the two survival curves. Both suggestions are investigated by simulation and applied to a clinical trial on survival of gastric cancer patients.

Suggested Citation

  • Julie K. Furberg & Christian B. Pipper & Thomas Scheike, 2021. "Testing equivalence of survival before but not after end of follow-up," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 216-243, April.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:2:d:10.1007_s10985-021-09517-5
    DOI: 10.1007/s10985-021-09517-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-021-09517-5
    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/s10985-021-09517-5?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. Holger Dette & Kathrin Möllenhoff & Stanislav Volgushev & Frank Bretz, 2018. "Equivalence of Regression Curves," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 711-729, April.
    2. Lihui Zhao & Brian Claggett & Lu Tian & Hajime Uno & Marc A. Pfeffer & Scott D. Solomon & Lorenzo Trippa & L. J. Wei, 2016. "On the restricted mean survival time curve in survival analysis," Biometrics, The International Biometric Society, vol. 72(1), pages 215-221, March.
    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. Chi Hyun Lee & Jing Ning & Yu Shen, 2018. "Analysis of restricted mean survival time for length†biased data," Biometrics, The International Biometric Society, vol. 74(2), pages 575-583, June.
    2. Kathrin Möllenhoff & Frank Bretz & Holger Dette, 2020. "Equivalence of regression curves sharing common parameters," Biometrics, The International Biometric Society, vol. 76(2), pages 518-529, June.
    3. Iván Díaz & Elizabeth Colantuoni & Daniel F. Hanley & Michael Rosenblum, 2019. "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 439-468, July.
    4. Ross L. Prentice, 2022. "On the targets of inference with multivariate failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 546-559, October.
    5. Zijing Yang & Chengfeng Zhang & Yawen Hou & Zheng Chen, 2023. "Analysis of dynamic restricted mean survival time based on pseudo‐observations," Biometrics, The International Biometric Society, vol. 79(4), pages 3690-3700, December.
    6. Yingchao Zhong & Douglas E. Schaubel, 2022. "Restricted mean survival time as a function of restriction time," Biometrics, The International Biometric Society, vol. 78(1), pages 192-201, March.
    7. Larry F. León & Ray Lin & Keaven M. Anderson, 2020. "On Weighted Log-Rank Combination Tests and Companion Cox Model Estimators," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 225-245, July.
    8. Torben Martinussen & Stijn Vansteelandt & Per Kragh Andersen, 2020. "Subtleties in the interpretation of hazard contrasts," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 833-855, October.
    9. Lu Mao, 2023. "On restricted mean time in favor of treatment," Biometrics, The International Biometric Society, vol. 79(1), pages 61-72, March.
    10. Lu Mao, 2023. "Nonparametric inference of general while‐alive estimands for recurrent events," Biometrics, The International Biometric Society, vol. 79(3), pages 1749-1760, September.
    11. Lu Tian & Hua Jin & Hajime Uno & Ying Lu & Bo Huang & Keaven M. Anderson & LJ Wei, 2020. "On the empirical choice of the time window for restricted mean survival time," Biometrics, The International Biometric Society, vol. 76(4), pages 1157-1166, December.
    12. Bastian, P. & Dette, H. & Koletzko, L., 2024. "Testing equivalence of multinomial distributions — A constrained bootstrap approach," Statistics & Probability Letters, Elsevier, vol. 206(C).
    13. Kathrin Möllenhoff & Kirsten Schorning & Franziska Kappenberg, 2023. "Identifying alert concentrations using a model‐based bootstrap approach," Biometrics, The International Biometric Society, vol. 79(3), pages 2076-2088, 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. Godwin Yung & Yi Liu, 2020. "Sample size and power for the weighted log‐rank test and Kaplan‐Meier based tests with allowance for nonproportional hazards," Biometrics, The International Biometric Society, vol. 76(3), pages 939-950, September.
    16. Yasuhiro Hagiwara & Tomohiro Shinozaki & Yutaka Matsuyama, 2020. "G‐estimation of structural nested restricted mean time lost models to estimate effects of time‐varying treatments on a failure time outcome," Biometrics, The International Biometric Society, vol. 76(3), pages 799-810, September.
    17. Eustasio del Barrio & Hristo Inouzhe & Carlos Matrán, 2020. "Box-Constrained Monotone Approximations to Lipschitz Regularizations, with Applications to Robust Testing," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 65-87, October.
    18. Chenyang Zhang & Guosheng Yin, 2023. "Bayesian nonparametric analysis of restricted mean survival time," Biometrics, The International Biometric Society, vol. 79(2), pages 1383-1396, June.
    19. Mihai C. Giurcanu & Theodore G. Karrison, 2022. "Nonparametric inference in the accelerated failure time model using restricted means," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 23-39, January.
    20. Xin Wang & Douglas E. Schaubel, 2018. "Modeling restricted mean survival time under general censoring mechanisms," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 176-199, January.

    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:2:d:10.1007_s10985-021-09517-5. 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.

    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.