On the Non-Monotonicity of a Non-Differentially Mismeasured Binary Confounder
This work addresses a methodological challenge in causal inference for researchers dealing with mismeasured confounders, though it appears incremental as it builds on existing proxy adjustment frameworks.
The paper tackles the problem of estimating causal effects when a binary confounder is unobserved but a non-differential proxy is available, identifying conditions where adjusting for the proxy improves accuracy over no adjustment. It shows that this adjustment can be beneficial even without assuming monotonic effects of the confounder across treatment groups.
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.