Mediation analysis aims at disentangling the effects of a treatment on an outcome through alternative causal mechanisms and has become a popular practice in biomedical and social science applications. The causal framework based on counterfactuals is currently the standard approach to mediation, with important methodological advances introduced in the literature in the last decade, especially for simple mediation, that is with one mediator at the time. Among a variety of alternative approaches, Imai et al. showed theoretical results and developed an R package to deal with simple mediation as well as with multiple mediation involving multiple mediators conditionally independent given the treatment and baseline covariates. This approach does not allow to consider the often encountered situation in which an unobserved common cause induces a spurious correlation between the mediators. In this context, which we refer to as mediation with uncausally related mediators, we show that, under appropriate hypothesis, the natural direct and joint indirect effects are non-parametrically identifiable. Moreover, we adopt the quasi-Bayesian algorithm developed by Imai et al. and propose a procedure based on the simulation of counterfactual distributions to estimate not only the direct and joint indirect effects but also the indirect effects through individual mediators. We study the properties of the proposed estimators through simulations. As an illustration, we apply our method on a real data set from a large cohort to assess the effect of hormone replacement treatment on breast cancer risk through three mediators, namely dense mammographic area, nondense area and body mass index.

中文翻译：

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存在多个非因果相关的中介因素时的因果中介分析

中介分析旨在通过替代因果机制解开治疗对结果的影响，并已成为生物医学和社会科学应用中的流行实践。基于反事实的因果框架是目前调解的标准方法，在过去十年的文献中引入了重要的方法学进步，特别是对于当时只有一名调解人的简单调解。在各种替代方法中，Imai 等人。展示了理论结果并开发了一个 R 包来处理简单调解以及涉及多个调解员的多重调解，这些调解员在给定治疗和基线协变量的情况下条件独立。这种方法不允许考虑经常遇到的情况，其中未观察到的共同原因导致中介之间的虚假相关性。在这种情况下，我们将其称为与非因果相关中介的中介，我们表明，在适当的假设下，自然直接和联合间接影响是非参数可识别的。此外，我们采用由 Imai 等人开发的准贝叶斯算法。并提出一个基于反事实分布模拟的程序，不仅可以估计直接和联合间接影响，还可以估计通过个体中介的间接影响。我们通过模拟研究了所提出的估计器的特性。作为例证，