On the Non-Monotonicity of a Non-Differentially Mismeasured Binary Confounder

TL;DR

This paper investigates how adjusting for a binary proxy of an unobserved confounder affects the estimation of causal effects, revealing non-monotonic relationships without assuming consistent confounder effects across treatment groups.

Contribution

It identifies conditions where adjusting for a non-differential binary proxy improves causal effect estimation, even when the confounder's effect direction varies.

Findings

Adjusting for the proxy can improve causal estimates under certain conditions.

The relationship between adjustment and accuracy is non-monotonic.

No assumption of same effect direction of confounder among treated and untreated.

Abstract

Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a non-differential binary proxy of it is observed. We identify conditions under which adjusting for the proxy comes closer to the incomputable true average causal effect than not adjusting at all. Unlike other works, we do not assume that the average causal effect of the confounder on the outcome is in the same direction among treated and untreated.