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:近距离因果推断是一种最近提出用于在存在未观测混淆因素的情况下评估治疗对结果变量的因果效应的框架(Miao et al., 2018a;Tchetgen Tchetgen et al., 2020)。对于非参数点识别,框架利用未观察到的混淆因素的代理变量,前提是这样的代理变量足够相关于后者,该要求先前已被形式化为完备性条件。完整性对于通过所谓的混淆桥函数将观察到的代理数据与隐藏因素相连接,这是代理的点识别因果效应的重要一步。然而,众所周知,完备性不是经验检验的,因此可能限制使用近距离因果框架。在本文中,我们提出部分识别方法,不需要完整性,并且无需识别桥接函数。也就是说,我们建立了这样一种方法,即可以利用未观察到的混淆因素的代理来获得关于治疗对结果的因果效应的界限,即使所提供的信息不足以识别缺陷函数或者所需识别的感兴趣的因果效应。我们进一步在相关的设置中建立了类似的部分识别结果,其中识别依赖于可用的代理中介变量,但这样的代理对于桥函数或感兴趣的因果效应的点识别不足够丰富。