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Investigating non-inferiority or equivalence in time-to-event data under non-proportional hazards

Author

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  • Kathrin Möllenhoff

    (Heinrich Heine University)

  • Achim Tresch

    (University of Cologne
    University of Cologne
    University of Cologne)

Abstract

The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan–Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards, a log-rank test is commonly performed to investigate whether there is a difference in survival or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inferiority trials, the commonly performed log-rank based tests are similarly affected by a violation of this assumption. Here we propose a parametric framework to assess equivalence or non-inferiority for survival data. We derive pointwise confidence bands for both, the hazard ratio and the difference of the survival curves. Further we propose a test procedure addressing non-inferiority and equivalence by directly comparing the survival functions at certain time points or over an entire range of time. Once the model’s suitability is proven the method provides a noticeable power benefit, irrespectively of the shape of the hazard ratio. On the other hand, model selection should be carried out carefully as misspecification may cause type I error inflation in some situations. We investigate the robustness and demonstrate the advantages and disadvantages of the proposed methods by means of a simulation study. Finally, we demonstrate the validity of the methods by a clinical trial example.

Suggested Citation

  • Kathrin Möllenhoff & Achim Tresch, 2023. "Investigating non-inferiority or equivalence in time-to-event data under non-proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 483-507, July.
  • Handle: RePEc:spr:lifeda:v:29:y:2023:i:3:d:10.1007_s10985-023-09589-5
    DOI: 10.1007/s10985-023-09589-5
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    References listed on IDEAS

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    1. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    2. Huimin Li & Dong Han & Yawen Hou & Huilin Chen & Zheng Chen, 2015. "Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-18, January.
    3. Song Yang & Ross Prentice, 2010. "Improved Logrank-Type Tests for Survival Data Using Adaptive Weights," Biometrics, The International Biometric Society, vol. 66(1), pages 30-38, March.
    4. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
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