IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v26y2020i4d10.1007_s10985-020-09501-5.html
   My bibliography  Save this article

Subtleties in the interpretation of hazard contrasts

Author

Listed:
  • Torben Martinussen

    (University of Copenhagen)

  • Stijn Vansteelandt

    (Ghent University
    London School of Hygiene and Tropical Medicine)

  • Per Kragh Andersen

    (University of Copenhagen)

Abstract

The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by Hernán (Epidemiology (Cambridge, Mass) 21(1):13–15, 2010) in a commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individuals who survived a given period of time, populations that will typically fail to be comparable—even in a randomised trial—as a result of different pressures or intensities acting on different populations. The commentary has been very influential, but also a source of surprise and confusion. In this note, we aim to provide more insight into the subtle interpretation of hazard ratios and differences, by investigating in particular what can be learned about a treatment effect from the hazard ratio becoming 1 (or the hazard difference 0) after a certain period of time. We further define a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio, and we also define a causal hazard difference. These quantities are of theoretical interest only, however, since they rely on assumptions that cannot be empirically evaluated. Throughout, we will focus on the analysis of randomised experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:4:d:10.1007_s10985-020-09501-5
    DOI: 10.1007/s10985-020-09501-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-020-09501-5
    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/s10985-020-09501-5?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. 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.
    2. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    3. Bartolucci, Francesco & Grilli, Leonardo, 2011. "Modeling Partial Compliance Through Copulas in a Principal Stratification Framework," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 469-479.
    4. S. Vansteelandt & T. Martinussen & E. J. Tchetgen Tchetgen, 2014. "On adjustment for auxiliary covariates in additive hazard models for the analysis of randomized experiments," Biometrika, Biometrika Trust, vol. 101(1), pages 237-244.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rachel Axelrod & Daniel Nevo, 2023. "A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2743-2756, September.
    2. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.
    3. Benjamin R. Baer & Robert L. Strawderman & Ashkan Ertefaie, 2023. "Discussion on “Instrumental variable estimation of the causal hazard ratio,” by Linbo Wang, Eric Tchetgen Tchetgen, Torben Martinussen, and Stijn Vansteelandt," Biometrics, The International Biometric Society, vol. 79(2), pages 554-558, June.
    4. Chengyuan Lu & Jelle Goeman & Hein Putter, 2023. "Maximum likelihood estimation in the additive hazards model," Biometrics, The International Biometric Society, vol. 79(3), pages 1646-1656, September.
    5. Tat-Thang Vo & Hilary Davies-Kershaw & Ruth Hackett & Stijn Vansteelandt, 2022. "Longitudinal mediation analysis of time-to-event endpoints in the presence of competing risks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 380-400, July.
    6. Richard A. J. Post & Edwin R. den Heuvel & Hein Putter, 2024. "The built-in selection bias of hazard ratios formalized using structural causal models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(2), pages 404-438, April.
    7. Mats J. Stensrud & Miguel A. Hernán & Eric J Tchetgen Tchetgen & James M. Robins & Vanessa Didelez & Jessica G. Young, 2021. "A generalized theory of separable effects in competing event settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 588-631, October.
    8. Lu Mao, 2023. "Study design for restricted mean time analysis of recurrent events and death," Biometrics, The International Biometric Society, vol. 79(4), pages 3701-3714, December.
    9. Mariam O. Adeleke & Gianluca Baio & Aidan G. O'Keeffe, 2022. "Regression discontinuity designs for time‐to‐event outcomes: An approach using accelerated failure time models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1216-1246, July.
    10. 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.

    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. von Hinke, Stephanie & Davey Smith, George & Lawlor, Debbie A. & Propper, Carol & Windmeijer, Frank, 2016. "Genetic markers as instrumental variables," Journal of Health Economics, Elsevier, vol. 45(C), pages 131-148.
    2. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1615-1635, October.
    3. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy," Papers 2005.09130, arXiv.org, revised Jun 2020.
    4. Corwin M. Zigler & Thomas R. Belin, 2012. "A Bayesian Approach to Improved Estimation of Causal Effect Predictiveness for a Principal Surrogate Endpoint," Biometrics, The International Biometric Society, vol. 68(3), pages 922-932, September.
    5. Fan Yang & Peng Ding, 2018. "Using survival information in truncation by death problems without the monotonicity assumption," Biometrics, The International Biometric Society, vol. 74(4), pages 1232-1239, December.
    6. Laura Forastiere & Fabrizia Mealli & Tyler J. VanderWeele, 2016. "Identification and Estimation of Causal Mechanisms in Clustered Encouragement Designs: Disentangling Bed Nets Using Bayesian Principal Stratification," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 510-525, April.
    7. Michael R. Elliott & Anna Conlon & Yun Li, 2013. "Discussion on “Surrogate Measures and Consistent Surrogates”," Biometrics, The International Biometric Society, vol. 69(3), pages 565-569, September.
    8. 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.
    9. Bubb, Ryan & Kaufman, Alex, 2014. "Securitization and moral hazard: Evidence from credit score cutoff rules," Journal of Monetary Economics, Elsevier, vol. 63(C), pages 1-18.
    10. German Blanco & Carlos A. Flores & Alfonso Flores-Lagunes, 2013. "Bounds on Average and Quantile Treatment Effects of Job Corps Training on Wages," Journal of Human Resources, University of Wisconsin Press, vol. 48(3), pages 659-701.
    11. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.
    12. Jincheng Zhou & James S. Hodges & Haitao Chu, 2020. "Rejoinder to “CACE and meta‐analysis (letter to the editor)” by Stuart Baker," Biometrics, The International Biometric Society, vol. 76(4), pages 1385-1389, December.
    13. Jennifer Hill & Jane Waldfogel & Jeanne Brooks-Gunn, 2002. "Differential effects of high-quality child care," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 21(4), pages 601-627.
    14. Giovanni Mellace & Roberto Rocci, 2011. "Principal Stratification in sample selection problems with non normal error terms," CEIS Research Paper 194, Tor Vergata University, CEIS, revised 02 May 2011.
    15. Michael E. Sobel & Bengt Muthén, 2012. "Compliance Mixture Modelling with a Zero-Effect Complier Class and Missing Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1037-1045, December.
    16. Legge, Stefan & Schmid, Lukas, 2013. "Rankings, Random Successes, and Individual Performance," Economics Working Paper Series 1340, University of St. Gallen, School of Economics and Political Science.
    17. Tianmeng Lyu & Björn Bornkamp & Guenther Mueller‐Velten & Heinz Schmidli, 2023. "Bayesian inference for a principal stratum estimand on recurrent events truncated by death," Biometrics, The International Biometric Society, vol. 79(4), pages 3792-3802, December.
    18. Andrea Mercatanti & Fan Li, 2017. "Do debit cards decrease cash demand?: causal inference and sensitivity analysis using principal stratification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 759-776, August.
    19. 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.
    20. Stephens Alisa & Keele Luke & Joffe Marshall, 2016. "Generalized Structural Mean Models for Evaluating Depression as a Post-treatment Effect Modifier of a Jobs Training Intervention," Journal of Causal Inference, De Gruyter, vol. 4(2), pages 1-17, September.

    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:26:y:2020:i:4:d:10.1007_s10985-020-09501-5. 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.