TY - JOUR

T1 - Subtleties in the interpretation of hazard contrasts

AU - Martinussen, Torben

AU - Vansteelandt, Stijn

AU - Andersen, Per Kragh

PY - 2020

Y1 - 2020

N2 - 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 Hernan (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.

AB - 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 Hernan (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.

KW - Causality

KW - Cox regression

KW - Hazard difference

KW - Hazard ratio

KW - Randomised study

KW - Survival analysis

KW - PRINCIPAL STRATIFICATION

KW - SURVIVAL

KW - COX

U2 - 10.1007/s10985-020-09501-5

DO - 10.1007/s10985-020-09501-5

M3 - Journal article

C2 - 32654089

VL - 26

SP - 833

EP - 855

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

ER -