In causal mediation analysis, the natural direct and indirect effects (natural effects) are nonparametrically unidentifiable in the presence of treatment-induced confounding, which motivated the development of randomized interventional analogues (RIAs) of the natural effects. The RIAs are easier to identify and widely used in practice. Applied researchers often interpret RIA estimates as if they were the natural effects, even though the RIAs could be poor proxies for the natural effects. This calls for practical and theoretical guidance on when the RIAs differ from or coincide with the natural effects, which this paper aims to address. We develop a novel empirical test for the divergence between the RIAs and the natural effects under the weak assumptions sufficient for identifying the RIAs and illustrate the test using the Moving to Opportunity Study. We also provide new theoretical insights on the relationship between the RIAs and the natural effects from a covariance perspective and a structural equation perspective. Additionally, we discuss previously undocumented connections between the natural effects, the RIAs, and estimands in instrumental variable analysis and Wilcoxon-Mann-Whitney tests.

翻译：在因果中介分析中，当存在治疗诱导的混杂时，自然直接效应与间接效应（自然效应）在非参数意义上不可识别，这促使了自然效应的随机干预对应效应的提出与发展。随机干预对应效应更易于识别，在实践中得到广泛应用。应用研究者常将随机干预对应效应的估计值解释为自然效应，尽管前者可能只是后者的不良代理。这亟需关于随机干预对应效应何时与自然效应存在差异或保持一致的实践与理论指导，本文旨在解决这一问题。我们在足以识别随机干预对应效应的弱假设下，开发了一种检验随机干预对应效应与自然效应差异的新型实证检验方法，并利用"机会迁移研究"数据进行了示例分析。此外，我们从协方差视角和结构方程视角，为随机干预对应效应与自然效应的关系提供了新的理论见解。同时，我们探讨了先前文献未充分论述的自然效应、随机干预对应效应与工具变量分析及Wilcoxon-Mann-Whitney检验中估计量之间的关联。