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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
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    References listed on IDEAS

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    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.
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