How hazard ratios can mislead and why it matters in practice

Robins J. A new approach to causal inference in mortality studies with a sustained exposure period-application to control of the healthy worker survivor effect. Math Modell. 1986;7:1393–512.

Google Scholar 

Hernán MA. The hazards of hazard ratios. Epidemiology. 2010;21:13–5.

PubMed  PubMed Central  Google Scholar 

Post RAJ, van den Heuvel ER, Putter H. The built-in selection bias of hazard ratios formalized using structural causal models. Lifetime Data Anal. 2024;30:404–38.

PubMed  PubMed Central  Google Scholar 

Didelez V, Stensrud MJ. On the logic of collapsibility for causal effect measures. Biometr J. 2022;64:235–42.

Google Scholar 

Huitfeldt A, Stensrud MJ, Suzuki E. On the collapsibility of measures of effect in the counterfactual causal framework. Emerg Themes Epidemiol. 2019;16:1.

PubMed  PubMed Central  Google Scholar 

Sjölander A, Dahlqwist E, Zetterqvist J. A note on the noncollapsibility of rate differences and rate ratios. Epidemiology. 2016;27:356–9.

PubMed  Google Scholar 

Stensrud MJ, Hernàn MA. Invited Commentary: Why use methods that require proportional hazards? Am J Epidemiol. 2025; kwae361.

Stensrud MJ, Hernán MA. Why test for proportional hazards? JAMA. 2020;323:1401–2.

PubMed  PubMed Central  Google Scholar 

Sjölander A, Dickman PW. Why test for proportional hazards-or any other model assumptions? Am J Epidemiol. 2024;193:926–7.

PubMed  PubMed Central  Google Scholar 

Prentice RL, Aragaki AK. Intention-to-treat comparisons in randomized trials. Stat Sci. 2022;37:380–93.

Google Scholar 

Ying A, Xu R. On Defense of the Hazard Ratio, 2023. arXiv:2307.11971 [math].

Strobel A, Wienke A, Kuss O. How hazardous are hazard ratios? An empirical investigation of individual patient data from 27 large randomized clinical trials. Eur J Epidemiol. 2023;38:859–67.

PubMed  Google Scholar 

Abrahamowicz M, Beauchamp ME, Roberts EK, Taylor JMG, Revisiting the hazards of hazard ratios through simulations and case studies, Eur J Epidemiol, 2025.

Saad ED, Zalcberg JR, Péron J, Coart E, Burzykowski T, Buyse M. Understanding and communicating measures of treatment effect on survival: can we do better? JNCI J Natl Cancer Instit. 2018;110:232–40.

Google Scholar 

Dao QL, Phung Q, Liu MA. Limitations of the hazard ratio as a summary measure in cancer clinical trials. J Thoracic Oncol. 2021;16(10):e86–7.

Google Scholar 

Stensrud MJ, Aalen JM, Aalen OO, Valberg M. Limitations of hazard ratios in clinical trials. Eur Heart J. 2019;40:1378–83.

PubMed  Google Scholar 

Thompson MG, Burgess JL, Naleway AL, Tyner H, Yoon SK, Meece J, Olsho LEW, Caban-Martinez AJ, Fowlkes AL, Lutrick K, Groom HC, Dunnigan K, Odean MJ, Hegmann K, Stefanski E, Edwards LJ, Schaefer-Solle N, Grant L, Ellingson K, Kuntz JL, Zunie T, Thiese MS, Ivacic L, Wesley MG, Lamberte JM, Sun X, Smith ME, Phillips AL, Groover KD, Yoo YM, Gerald J, Brown RT, Herring MK, Joseph G, Beitel S, Morrill TC, Mak J, Rivers P, Poe BP, Lynch B, Zhou Y, Zhang J, Kelleher A, Li Y, Dickerson M, Hanson E, Guenther K, Tong S, Bateman A, Reisdorf E, Barnes J, Azziz-Baumgartner E, Hunt DR, Arvay ML, Kutty P, Fry AM, Gaglani M. Prevention and attenuation of Covid-19 with the NT162b2 and mRNA-1273 vaccines. New Engl J Med. 2021;385:320–9.

CAS  PubMed  Google Scholar 

Arbel R, Hammerman A, Sergienko R, Friger M, Peretz A, Netzer D, Yaron S. BNT162b2 Vaccine Booster and Mortality Due to Covid-19. N Engl J Med. 2021;385(26):2413–20. https://doi.org/10.1056/NEJMoa211564.

Fox RJ, Bar-Or A, Traboulsee A, Oreja-Guevara C, Giovannoni G, Vermersch P, Syed S, Li Y, Vargas WS, Turner TJ, Wallstroem E, Reich DS. Tolebrutinib in Nonrelapsing Secondary Progressive Multiple Sclerosis. N Engl J Med 2025;392:1883–92. https://doi.org/10.1056/NEJMoa2415988

Giaquinto AN, Sung H, Newman LA, Freedman RA, Smith Star J, Jemal A, Siegel RL. Breast cancer statistics 2024. CA Cancer J Clinic. 2024;74(6):477–95.

Google Scholar 

Howlader N, Cronin KA, Kurian AW, Andridge R. Differences in Breast Cancer Survival by Molecular Subtypes in the United States, Cancer epidemiology, biomarkers and prevention: a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology, vol. 27. Cancer Epidemiol Biomarkers Prev: Publisher; 2018.

Waks AG, Winer EP. Breast cancer treatment: a review. JAMA. 2019;321:288–300.

CAS  PubMed  Google Scholar 

Dumas E, Laot L, Coussy F, Grandal Rejo B, Daoud E, Laas E, Kassara A, Majdling A, Kabirian R, Jochum F, Gougis P, Michel S, Houzard S, Le Bihan-Benjamin C, Bousquet PJ, Hotton J, Azencott CA, Reyal F, Hamy AS. The French early breast cancer cohort (FRESH): a resource for breast cancer research and evaluations of oncology practices based on the French national healthcare system database (SNDS). Cancers. 2022;14:2671.

CAS  PubMed  PubMed Central  Google Scholar 

Greenland S. Absence of confounding does not correspond to collapsibility of the rate ratio or rate difference. Epidemiology. 1996;7:498–501.

CAS  PubMed  Google Scholar 

Stovitz SD, Banack HR, Kaufman JS. Depletion of the susceptibles’ taught through a story, a table and basic arithmetic. BMJ Evid Based Med. 2018;23(5);199

Google Scholar 

Fireman B, Gruber S, Zhang Z, Wellman R, Nelson JC, Franklin J, Maro J, Murray CR, Toh S, Gagne J, Schneeweiss S, Amsden L, Wyss R. Consequences of depletion of susceptibles for hazard ratio estimators based on propensity scores. Epidemiology. 2020;31:806.

PubMed  PubMed Central  Google Scholar 

Renoux C, Dell’Aniello S, Brenner B, Suissa S. Bias from depletion of susceptibles: the example of hormone replacement therapy and the risk of venous thromboembolism. Pharmacoepidemiol Drug Saf. 2017;26(5):554–60. https://doi.org/10.1002/pds.4197.

Article  CAS  PubMed  Google Scholar 

Sashegyi A, Ferry D. On the interpretation of the hazard ratio and communication of survival benefit. Oncologist. 2017;22:484–6.

PubMed  PubMed Central  Google Scholar 

De Neve J, Gerds TA. On the interpretation of the hazard ratio in Cox regression. Biom J. 2020;62(3):742–50.

PubMed  Google Scholar 

Sormani MP, Bruzzi P. Estimating a treatment effect: choosing between relative and absolute measures. Mult Scler J. 2017;23:197–200.

Google Scholar 

Moynihan R, Bero L, Ross-Degnan D, Henry D, Lee K, Watkins J, Mah C, Soumerai SB. Coverage by the news media of the benefits and risks of medications. N Engl J Med. 2000;342(22):1645–50. https://doi.org/10.1056/NEJM20000603422206.

Murray EJ, Caniglia EC, Swanson SA, Hernández-Díaz S, Hernán MA. Patients and investigators prefer measures of absolute risk in subgroups for pragmatic randomized trials. J Clin Epidemiol. 2018;103:10–21.

PubMed  PubMed Central  Google Scholar 

Noordzij M, van Diepen M, Caskey FC, Jager KJ. Relative risk versus absolute risk: one cannot be interpreted without the other. Nephrol Dial Transplant. 2017;32:ii13–8.

PubMed  Google Scholar 

Kaplan EL, Meier P. Nonparametric Estimation from Incomplete Observations. J. Am. Stat. Assoc.ASA Website; 1958. p. 457–81 (https://www.tandfonline.com/doi/pdf/10.1080/01621459.1958.10501452.).

Xie J, Liu C. Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data. Stat Med. 2005;24(20):3089–110. https://doi.org/10.1002/sim.2174.

Article  PubMed  Google Scholar 

Wang J. A simple, doubly robust, efficient estimator for survival functions using pseudo observations. Pharm Stat. 2018;17(1):38–48.

CAS  PubMed  Google Scholar 

Shahar E, Shahar DJ. More on selection bias. Epidemiology. 2010;21:429.

PubMed  Google Scholar 

Lin J-C, Lee W-C. Hazard ratio bias in cohort studies. Epidemiology. 2013;24:777.

PubMed  Google Scholar 

Stensrud MJ, Valberg M, Røysland K, Aalen OO. Exploring selection bias by causal frailty models: the magnitude matters. Epidemiology. 2017;28(3):379–86.

PubMed  Google Scholar 

Colnet B, Josse J, Varoquaux G, Scornet E. Risk ratio, odds ratio, risk difference... Which causal measure is easier to generalize?, 2023. arXiv:2303.16008 [stat].

Liu Y, Wang B, Yang M, Hui J, Xu H, Kil S, Hsu JC. Correct and logical causal inference for binary and time-to-event outcomes in randomized controlled trials. Biometr J. 2022;64:198–224.

Google Scholar 

Daniel R, Zhang J, Farewell D. Making apples from oranges: comparing noncollapsible effect estimators and their standard errors after adjustment for different covariate sets. Biom J. 2021;63(3):528–57. https://doi.org/10.1002/bimj.20190027.

Article  PubMed  Google Scholar 

Cox DR. Journal of the Royal Statistical Society. Series B (Methodological). Royal Statistical Society, Oxford University Press. 1972. p. 187–220.

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