Primary Submission Category: Partial Identification
Partial Identification of Causal Effects Using Proxy Variables
Authors: AmirEmad Ghassami, Ilya Shpitser, Eric Tchetgen Tchetgen,
Presenting Author: AmirEmad Ghassami*
Proximal causal inference is a recently proposed framework for evaluating causal effects in the presence of unmeasured confounding. For point identification of causal effects, it requires identification of certain nuisance functions called bridge functions using proxy variables that are sufficiently relevant to the unmeasured confounder, formalized as a completeness condition. However, completeness is not testable, and although a bridge function may exist, lack of completeness may severely limit prospects for identification of a bridge function and thus a causal effect; therefore, restricting the application of the framework. In this work, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function, i.e., we establish that proxies can be leveraged to obtain bounds on the causal effect even if available information does not suffice to identify a bridge function. Our bounds are non-smooth functionals of the underlying distribution. Hence, in the context of inference, we initially employ the LogSumExp approximation to obtain smooth approximations of our bounds. Subsequently, we leverage bootstrap confidence intervals on the approximated bounds. We further establish analogous results in related settings where identification hinges upon hidden mediators for which proxies are available, yet such proxies are not sufficiently rich for point identification of a bridge function or a corresponding causal effect.