Subtleties in the interpretation of hazard contrasts
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Subtleties in the interpretation of hazard contrasts Torben Martinussen1
· Stijn Vansteelandt2,3 · Per Kragh Andersen1
Received: 4 April 2019 / Accepted: 23 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Causality · Cox regression · Hazard difference · Hazard ratio · Randomised study · Survival analysis
1 Introduction The popularity of the Cox regression model has contributed to the enormous success of the hazard ratio as a concise summary of the effect of a randomised treatment on a survival endpoint. Notwithstanding this, use of the hazard ratio has been criticised over recent years. Hernán (2010) argued that selection effects caused by unobserved
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10985020-09501-5) contains supplementary material, which is available to authorized users.
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Torben Martinussen [email protected]
Extended author information available on the last page of the article
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heterogeneity (“frailty”) render a causal interpretation of the hazard ratio difficult when treatment affects outcome. While the treated and untreated people are comparable by design at baseline, the treated people who survive a given time t may then tend to be more “frail” (as a result of lower mortality if treatment is beneficial) than the untreated people who survive the given time t, so that the crucial comparability of both groups is lost at that time. Aalen et al. (2015) re-iterated Hernán’s concern. They viewed the problem more as one of non-collapsibility (Martinussen and Vansteelandt 2013), which is a concern about the interpretation of the hazard ratio, though not about its justification as a causal contrast. In particular, they arg
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