Martinussen Torben, Vansteelandt Stijn, Andersen Per Kragh
Section of Biostatistics, University of Copenhagen, Øster Farimagsgade 5B, 1014, Copenhagen K, Denmark.
Department of Applied Mathematics, Computer Sciences and Statistics, Ghent University, Krijgslaan 281 (S9), 9000, Gent, Belgium.
Lifetime Data Anal. 2020 Oct;26(4):833-855. doi: 10.1007/s10985-020-09501-5. Epub 2020 Jul 11.
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.
风险比是随机试验中最常报告的治疗效果衡量指标之一，但也是诸多误解的根源。埃尔南在一篇评论文章（《流行病学》（马萨诸塞州剑桥）21(1):13 - 15，2010年）中明确指出了这一点，该评论强调风险比对比的是在给定时间段内存活的治疗组和未治疗组个体群体，由于不同群体受到不同压力或强度的影响，这些群体通常无法进行比较——即使在随机试验中也是如此。这篇评论极具影响力，但也引发了惊讶与困惑。在本笔记中，我们旨在通过特别研究在一段时间后风险比变为1（或风险差为0）时能从治疗效果中学到什么，从而更深入地洞察风险比及差异的微妙解释。我们进一步定义了一个具有因果解释的风险比，并研究其与考克斯风险比的关系，还定义了因果风险差。然而，这些量仅具有理论意义，因为它们依赖于无法通过实证评估的假设。自始至终，我们将专注于随机试验的分析。
