Hazards of Hazard Ratios in Survival Analysis
LJ Wei, PhD
Professor in the Department of Biostatistics, Harvard T.H. Chan School of Public Health
Senior Statistician, Statistical and Data Analysis Center
In a longitudinal clinical study to compare two groups, the primary end point is often the time to a specific event (for example, disease progression, death). The hazard ratio estimate is routinely used to empirically quantify the between-group difference under the assumption that the ratio of the two hazard functions being approximately constant over time. Even when this assumption is plausible, such a ratio estimate may not give us a clinically meaningful summary of the group contrast due to lack of a reference value of hazard function from the control arm. Moreover, the clinical meaning of such a ratio estimate is difficult, if not impossible, to interpret when the underlying proportional hazards assumption is violated (namely, the hazard ratio is not constant over time). For this case, the hazard ratio-based tests may not have power to detect the group difference. In this talk, we summarize several critical concerns regarding this conventional practice and discuss alternatives (e.g., via the t-year mean survival time) for quantifying the differences between groups with respect to a time-to-event end point. The data from several recent cancer and cardiovascular clinical trials, which reflect a variety of scenarios, are used throughout to illustrate our discussions. In this talk, we are mostly interested in estimation the treatment effect beyond the hypothesis testing paradigm. An estimation procedure can also be used as a test statistic. On the other hand, most tests in survival analysis, such as the weighted logrank tests, do not have appropriate estimation counterparts. We also discuss other relevant issues in clinical studies, for example, estimating the duration of response, quantifying long term survival, et al.
Alternatives to Hazard Ratios for Comparing the Efficacy or Safety of Therapies in Non-inferiority Studies.
Uno H, Wittes J, Fu H, Solomon SD, Claggett B, Tian L, Cai T, Pfeffer MA, Evans SR, Wei LJ.
Ann Intern Med. 2015 Jul 21;163(2):127-34. doi: 10.7326/M14-1741.
Applying Evidence-Based Medicine to Shared Decision Making: Value of Restricted Mean Survival Time.
McCaw ZR, Orkaby AR, Wei LJ, Kim DH, Rich MW.
Am J Med. 2019 Jan;132(1):13-15. doi: 10.1016/j.amjmed.2018.07.026. Epub 2018 Aug 1. No abstract available.
Interpretability of Cancer Clinical Trial Results Using Restricted Mean Survival Time as an Alternative to the Hazard Ratio.
Pak K, Uno H, Kim DH, Tian L, Kane RC, Takeuchi M, Fu H, Claggett B, Wei LJ.
JAMA Oncol. 2017 Dec 1;3(12):1692-1696. doi: 10.1001/jamaoncol.2017.2797.
Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis.
Uno H, Claggett B, Tian L, Inoue E, Gallo P, Miyata T, Schrag D, Takeuchi M, Uyama Y, Zhao L, Skali H, Solomon S, Jacobus S, Hughes M, Packer M, Wei LJ.
J Clin Oncol. 2014 Aug 1;32(22):2380-5. doi: 10.1200/JCO.2014.55.2208. Epub 2014 Jun 30.