Bias Formulas for Violations of Proximal Identification Assumptions

TL;DR

This paper derives bias formulas for proximal inference estimators under linear models, aiding sensitivity and bias analysis of causal effect estimates when assumptions may be violated.

Contribution

It provides the first bias formulas for proximal inference estimators under a linear structural equation model, enabling sensitivity analysis.

Findings

Bias formulas quantify the impact of assumption violations.

Results offer insights into estimator behavior under model misspecification.

Facilitates quantitative bias analysis for proximal inference.

Abstract

Causal inference from observational data often rests on the unverifiable assumption of no unmeasured confounding. Recently, Tchetgen Tchetgen and colleagues have introduced proximal inference to leverage negative control outcomes and exposures as proxies to adjust for bias from unmeasured confounding. However, some of the key assumptions that proximal inference relies on are themselves empirically untestable. Additionally, the impact of violations of proximal inference assumptions on the bias of effect estimates is not well understood. In this paper, we derive bias formulas for proximal inference estimators under a linear structural equation model data generating process. These results are a first step toward sensitivity analysis and quantitative bias analysis of proximal inference estimators. While limited to a particular family of data generating processes, our results may offer some more general insight into the behavior of proximal inference estimators.