A confounding bridge approach for double negative control inference on causal effects

TL;DR

This paper introduces a novel confounding bridge method using negative control variables to adjust for unmeasured confounding in causal inference, demonstrated through simulations and an air pollution study.

Contribution

It develops a new framework leveraging negative control variables and a confounding bridge function for more accurate causal effect estimation.

Findings

Standard analysis shows a significant effect of PM2.5 on mortality.

Adjusted analysis suggests the effect may be confounded and attenuated after correction.

The method effectively reduces bias from unmeasured confounders.

Abstract

Unmeasured confounding is a key challenge for causal inference. In this paper, we establish a framework for unmeasured confounding adjustment with negative control variables. A negative control outcome is associated with the confounder but not causally affected by the exposure in view, and a negative control exposure is correlated with the primary exposure or the confounder but does not causally affect the outcome of interest. We introduce an outcome confounding bridge function that depicts the relationship between the confounding effects on the primary outcome and the negative control outcome, and we incorporate a negative control exposure to identify the bridge function and the average causal effect. We also consider the extension to the positive control setting by allowing for nonzero causal effect of the primary exposure on the control outcome. We illustrate our approach with simulations and apply it to a study about the short-term effect of air pollution on mortality. Although a standard analysis shows a significant acute effect of PM2.5 on mortality, our analysis indicates that this effect may be confounded, and after double negative control adjustment, the effect is attenuated toward zero.