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., 2018; Tchetgen Tchetgen et al., 2020). For nonparametric point identification of causal effects, the framework leverages a pair of so-called treatment and outcome confounding proxy variables, in order to identify a bridge function that matches the dependence of potential outcomes or treatment variables on the hidden factors to corresponding functions of observed proxies. Unique identification of a causal effect via a bridge function crucially requires that proxies are sufficiently relevant for hidden factors, a requirement that has previously been formalized as a completeness condition. However, completeness is well-known not to be empirically testable, and although a bridge function may be well-defined in a given setting, lack of completeness, sometimes manifested by availability of a single type of proxy, may severely limit prospects for identification of a bridge function and thus a causal effect; 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：近端因果推断是近年来提出的一种框架，用于在存在未测量混杂因素的情况下评估处理变量对结果变量的因果效应（Miao 等，2018；Tchetgen Tchetgen 等，2020）。该框架通过利用一对所谓的处理代理变量和结果代理变量，识别出能够将潜在结果或处理变量对隐藏因子的依赖关系与观测到的代理变量的对应函数相匹配的桥函数，从而实现对因果效应的非参数点识别。通过桥函数唯一识别因果效应的关键前提是代理变量与隐藏因子具有充分的相关性，这一要求此前被形式化为完备性条件。然而，完备性在经验上不可检验，尽管桥函数在特定场景下可能定义良好，但缺乏完备性（有时表现为仅可获取单一类型的代理变量）可能严重限制桥函数乃至因果效应的识别前景，从而制约近端因果框架的应用。本文提出无需完备性且无需识别桥函数的部分识别方法。具体而言，我们证明即使现有信息不足以识别桥函数或相应的目标因果效应，仍可借助未观测混杂因素的代理变量推导出处理变量对结果变量因果效应的界限。此外，我们进一步确立了在相关场景中的类比部分识别结果：当识别依赖于存在可用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目标因果效应的点识别时，上述方法同样适用。