IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v29y2023i3d10.1007_s10985-023-09589-5.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-023-09589-5
    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/s10985-023-09589-5?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. 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.
    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. Ditzhaus, Marc & Pauly, Markus, 2019. "Wild bootstrap logrank tests with broader power functions for testing superiority," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 1-11.
    2. Xiaodong Luo & Hui Quan, 2020. "Some Meaningful Weighted Log-Rank and Weighted Win Loss Statistics," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 216-224, July.
    3. Kato, Naohiro & Kuriki, Satoshi, 2013. "Likelihood ratio tests for positivity in polynomial regressions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 334-346.
    4. Chang-Yu Liu & Xin Liu & Rong-Xian Yue, 2024. "Locally optimal designs for comparing curves in generalized linear models," Statistical Papers, Springer, vol. 65(5), pages 3181-3201, July.
    5. Nathan Cunningham & Jim E. Griffin & David L. Wild, 2020. "ParticleMDI: particle Monte Carlo methods for the cluster analysis of multiple datasets with applications to cancer subtype identification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 463-484, June.
    6. Dette, Holger & Schorning, Kirsten & Konstantinou, Maria, 2017. "Optimal designs for comparing regression models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 273-286.
    7. Zhang Qingyang, 2023. "A nonparametric test for comparing survival functions based on restricted distance correlation," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-15.
    8. Lu Tian & Haoda Fu & Stephen J. Ruberg & Hajime Uno & Lee†Jen Wei, 2018. "Efficiency of two sample tests via the restricted mean survival time for analyzing event time observations," Biometrics, The International Biometric Society, vol. 74(2), pages 694-702, June.
    9. Grzegorz Wyłupek, 2021. "A permutation test for the two-sample right-censored model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1037-1061, October.
    10. Sanyu Zhou, 2018. "An exact method for the multiple comparison of several polynomial regression models with applications in dose-response study," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 413-429, July.
    11. Liu, Xin & Ye, Min & Yue, Rong-Xian, 2021. "Optimal designs for comparing population curves in hierarchical models," Statistics & Probability Letters, Elsevier, vol. 178(C).
    12. Deborah Plana & Geoffrey Fell & Brian M. Alexander & Adam C. Palmer & Peter K. Sorger, 2022. "Cancer patient survival can be parametrized to improve trial precision and reveal time-dependent therapeutic effects," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    13. Sanyu Zhou & Defa Wang & Jingjing Zhu, 2020. "Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region," Statistical Papers, Springer, vol. 61(3), pages 1335-1346, June.
    14. Emura, Takeshi & Hsu, Jiun-Huang, 2020. "Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    15. Marc Buyse & Everardo D. Saad & Tomasz Burzykowski & Julien Péron, 2020. "Assessing Treatment Benefit in Immuno-oncology," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 83-103, July.
    16. Yukun Liu & Guosheng Yin, 2017. "Partitioned log-rank tests for the overall homogeneity of hazard rate functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 400-425, July.
    17. Jimmy T. Efird, 2023. "The Inverse Log-Rank Test: A Versatile Procedure for Late Separating Survival Curves," IJERPH, MDPI, vol. 20(24), pages 1-23, December.
    18. Kristin McCullough & Tatiana Dmitrieva & Nader Ebrahimi, 2022. "New approximate Bayesian computation algorithm for censored data," Computational Statistics, Springer, vol. 37(3), pages 1369-1397, July.
    19. Tamara Fernández & Nicolás Rivera, 2021. "A reproducing kernel Hilbert space log‐rank test for the two‐sample problem," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1384-1432, December.
    20. Jinhui Zhang & Yanlin Shi & Guogui Huang, 2023. "Expected length of stay at residential aged care facilities in Australia: current and future," Journal of Population Research, Springer, vol. 40(4), pages 1-30, December.

    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:29:y:2023:i:3:d:10.1007_s10985-023-09589-5. 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.