It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from built-in selection bias as, over time, the individuals at risk in the exposed and unexposed are no longer exchangeable. In this work, we formalize how the observed hazard ratio evolves and deviates from the causal hazard ratio of interest in the presence of heterogeneity of the hazard of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty, and categorical (harming, beneficial or neutral) effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio can not be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands such as contrasts of the survival probabilities.
翻译:众所周知,危险比率缺乏有用的因果解释。即使对随机控制的试验数据来说,危险比率也存在内在选择偏差,因为长期以来,暴露和未暴露的风险个人不再可以互换。在这项工作中,我们正式确定观察到的危险比率如何演变,并偏离在未暴露个人(脆弱)和实际上的异质(个人改变)危险情况下的利益因果危险比率。关于效果异性的情况,我们定义了因果危险比率。我们表明,观察到的危险比率相当于潜在变数(脆弱和变异)的期望比率,其条件分别是以受暴露和没有暴露生存为条件。以伽马为反戈斯和普瓦森化合物为例,其特点是虚弱和绝对(损害、有利或中性)效果改变为示例。这组例子表明,观察到的危险比率可能为所有因果危险比率的价值产生一种特定价值。因此,危险比率不能分别以活性(脆弱和变异性)的预期比值作为适当的因果效果衡量标准,因此,不能使用危险比率作为适当的因果效果的比值。