Tennant et al. make the bold claim that ‘analyses of “change scores” do not estimate causal effects in observational data’.¹ However, it seems to me that this claim is related to the definition of the effect of interest (the estimand) and not the estimation. It is well established, under the potential outcomes framework, that ‘the causal effect is the comparison of the potential outcomes, for the same unit, at the same moment in time post-treatment. In particular, the causal effect is not defined in terms of comparisons of outcomes at different times as in a before and after comparison’ (p. 6, original emphasis).² The authors’ estimand for the change score is defined by the outcome at baseline and follow-up so, by definition, they are correct that the change score from baseline is not a causal estimand, and this is well established. I am quoting from a major textbook on the subject co-authored by Donald Rubin who extended the potential outcomes framework from randomized–controlled trials to observational studies. However, the same book makes it clear that for the estimation of causal effects, as opposed to their definition, we can, with assumptions, use outcomes at different times to estimate missing potential outcomes, as it is not possible to observe all potential outcomes—the fundamental problem of causal inference. To quote Imbens and Rubin again, ‘a before-and-after comparison of the same physical object involves distinct units in our framework, and also the comparison of two different physical objects at the same time involves distinct units. Such comparisons are critical for estimating causal effects, but they do not define causal effects in our approach’ (p. 7, original emphasis).² Hence, estimating causal effects using pre-intervention observations to inform missing potential outcomes is very well established in many disciplines including public health.³ It would seem a shame if readers were put off such methods by the ambiguous title of Tennant et al.’s paper.

中文翻译：

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定义是，分析否：对“变化分数的分析不估计观察数据中的因果效应”的评论

坦南特等人。大胆宣称“对“变化分数”的分析不估计观测数据中的因果效应。¹然而，在我看来，这种说法与利益效应（估计值）的定义有关，而不是估计值。众所周知，在潜在结果框架下，“因果效应是治疗后同一单位、同一时间点潜在结果的比较”。特别是，因果效应不是根据不同时间的结果比较来定义的，就像之前和之后的比较一样”（第 6 页，最初的重点）。²作者对变化分数的估计是由基线和随访的结果定义的，因此，根据定义，他们是正确的，即基线的变化分数不是因果估计，这是公认的。我引用了唐纳德·鲁宾（Donald Rubin）合着的一本关于该主题的主要教科书，他将潜在结果框架从随机对照试验扩展到观察性研究。然而，同一本书清楚地表明，对于因果效应的估计，与它们的定义相反，我们可以通过假设，使用不同时间的结果来估计缺失的潜在结果，因为不可能观察到所有潜在结果——因果推理的基本问题。再次引用 Imbens 和 Rubin 的话，“同一物理对象的前后比较涉及我们框架中的不同单元，同时比较两个不同的物理对象也涉及不同的单位。这样的比较对于估计因果效应，但它们没有在我们的方法中定义因果效应”（第 7 页，原始重点）。²因此，在包括公共卫生在内的许多学科中，使用干预前观察来估计因果关系以告知缺失的潜在结果已经非常成熟。³如果读者因 Tennant等人的模棱两可的标题而对这种方法感到厌烦，那将是一种耻辱。的纸。