On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder

TL;DR

This paper investigates how adjusting for a nondifferential proxy of an unobserved binary confounder affects causal effect estimates, showing it yields a measure between unadjusted and true effects under verifiable monotonicity.

Contribution

It introduces a monotonicity assumption that allows bounding the causal effect when only a proxy for an unobserved confounder is available.

Findings

Adjusted effect lies between unadjusted and true effects

Monotonicity assumption is empirically verifiable

Provides bounds for causal effect estimation

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 nondifferential proxy of it is observed. We show that, under certain monotonicity assumption that is empirically verifiable, adjusting for the proxy produces a measure of the effect that is between the unadjusted and the true measures.