Primary Submission Category: Causal Inference and Bias/Discrimination
Regression-Based Proximal Causal Inference
Authors: Jiewen Liu, Chan Park, Kendrick Li, Eric Tchetgen Tchetgen,
Presenting Author: Jiewen Liu*
A recently proposed framework to account for known but unmeasured sources of confounding is so-called proximal causal inference (PCI). The approach leverages negative controls, more broadly termed treatment and outcome confounding proxies, a priori known to have null associations with the primary treatment and outcome, respectively, conditional on measured and hidden confounders which they proxy. While formal statistical inference has been developed for PCI, its implementation is hindered by complex, ill-posed integral equations. Our paper introduces a regression-based PCI approach, obviating solving integral equations. Our method employs two-stage regression through generalized linear models (GLMs). In the first stage, one fits a GLM for an outcome proxy in terms of the treatment proxy. In the second stage, one fits a GLM for the primary outcome using the predicted value of the first stage regression model as a regressor that accounts for residual confounding. The proposed approach has merit in that (i) it is applicable to continuous, count, and binary outcomes, making it relevant to a wide range of real-world applications, and (ii) it is easy to implement by using off-the-shelf software. We establish statistical inference theory for regression-based PCI and illustrate their performance in both synthetic and real-world empirical applications.