Proximal causal inference was recently proposed as a framework to identify causal effects from observational data in the presence of hidden confounders for which proxies are available. In this paper, we extend the proximal causal inference approach to settings where identification of causal effects hinges upon a set of mediators which are not observed, yet error prone proxies of the hidden mediators are measured. Specifically, (i) We establish causal hidden mediation analysis, which extends classical causal mediation analysis methods for identifying natural direct and indirect effects under no unmeasured confounding to a setting where the mediator of interest is hidden, but proxies of it are available. (ii) We establish hidden front-door criterion, which extends the classical front-door criterion to allow for hidden mediators for which proxies are available. (iii) We show that the identification of a certain causal effect called population intervention indirect effect remains possible with hidden mediators in settings where challenges in (i) and (ii) might co-exist. We view (i)-(iii) as important steps towards the practical application of front-door criteria and mediation analysis as mediators are almost always measured with error and thus, the most one can hope for in practice is that the measurements are at best proxies of mediating mechanisms. We propose identification approaches for the parameters of interest in our considered models. For the estimation aspect, we propose an influence function-based estimation method and provide an analysis for the robustness of the estimators.

翻译：最近提出的近端因果推断框架，可在存在可获取代理变量的隐藏混杂因素时，从观测数据中识别因果效应。本文将该方法扩展至以下场景：因果效应的识别依赖于一组未被观测的中介变量，但可通过测量其易出错的代理变量实现。具体而言：(i) 我们建立了因果隐藏中介分析，将经典因果中介分析中无需未测混杂即可识别自然直接效应与间接效应的方法，扩展至目标中介变量隐藏但可获取其代理变量的场景；(ii) 我们提出了隐藏前门准则，将经典前门准则扩展至允许存在可获取代理变量的隐藏中介变量；(iii) 我们证明，在(i)和(ii)所述挑战可能共存的场景中，仍可基于隐藏中介变量识别称为"人群干预间接效应"的特定因果效应。我们将(i)-(iii)视为前门准则与中介分析实际应用的重要进展——由于中介变量几乎总是存在测量误差，实践中最多只能期望测量值成为中介机制的代理变量。针对所考虑模型中的目标参数，我们提出了识别方法。在估计方面，我们提出了基于影响函数的估计方法，并分析了估计量的稳健性。