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Abstract:Proximal causal inference is a framework for evaluating the causal effects in the presence of unmeasured confounding. For point identification, it leverages a pair of proxy variables 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 requires that proxies are sufficiently relevant for hidden factors, a requirement that has previously been formalized as a completeness condition. However, completeness is not 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 framework. In this paper, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function. We establish that proxies can be leveraged to obtain bounds on the causal effect even if available information does not suffice to identify either a bridge function or a corresponding causal effect of interest. Our bounds are non-smooth functionals of the underlying distribution. For inference, we employ LogSumExp approximations that yield smooth lower and upper bounds, and we derive the efficient influence functions of the resulting bound functionals which enable analytic variance estimation, while bootstrap confidence intervals remain available for regular plug-in implementations. We further establish analogous 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.

Submission history

From: AmirEmad Ghassami [view email]
[v1] Mon, 10 Apr 2023 04:18:27 UTC (173 KB)
[v2] Sun, 23 Apr 2023 00:36:32 UTC (170 KB)
[v3] Sun, 28 Jan 2024 20:42:34 UTC (32 KB)
[v4] Wed, 5 Aug 2026 15:03:47 UTC (34 KB)