Proximal causal inference is a recently proposed framework for evaluating the causal effect of a treatment on an outcome variable in the presence of unmeasured confounding (Miao et al., 2018a; Tchetgen Tchetgen et al., 2020). For nonparametric point identification, the framework leverages proxy variables of unobserved confounders, provided that such proxies are sufficiently relevant for the latter, a requirement that has previously been formalized as a completeness condition. Completeness is key to connecting the observed proxy data to hidden factors via a so-called confounding bridge function, identification of which is an important step towards proxy-based point identification of causal effects. However, completeness is well-known not to be empirically testable, therefore potentially restricting the application of the proximal causal framework. In this paper, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function. That is, we establish that proxies of unobserved confounders can be leveraged to obtain bounds on the causal effect of the treatment on the outcome even if available information does not suffice to identify either a bridge function or a corresponding causal effect of interest. We further establish analogous partial identification results in related settings where identification hinges upon hidden mediators for which proxies are available, however such proxies are not sufficiently rich for point identification of a bridge function or a corresponding causal effect of interest.

翻译：近端因果推断是一种近期提出的框架，用于在存在未测量混杂因素的情况下评估处理对结局变量的因果效应（Miao等，2018a；Tchetgen Tchetgen等，2020）。对于非参数点识别，该框架利用了未观测混杂因素的代理变量，前提是这些代理变量与后者充分相关，这一要求先前已被形式化为完备性条件。完备性是通过所谓的混杂桥函数将观测到的代理数据与隐藏因素联系起来的关键，而识别该桥函数是基于代理变量实现因果效应点识别的重要步骤。然而，众所周知完备性无法通过经验验证，因此可能限制近端因果框架的应用。本文提出了无需完备性且无需识别桥函数的部分识别方法。即，我们证明即使现有信息不足以识别桥函数或相应的感兴趣因果效应，仍可利用未观测混杂因素的代理变量来获取处理对结局因果效应的界限。我们进一步在相关场景中建立了类似的部分识别结果——当识别依赖于存在代理变量的隐藏中介变量，但这些代理变量不足以实现桥函数或相应感兴趣因果效应的点识别时，该方法同样适用。