On the Monotonicity of a Nondifferentially Mismeasured Binary Confounder
This work addresses causal inference challenges in statistics and epidemiology by providing a theoretical guarantee for proxy adjustment, but it is incremental as it builds on existing methods with a specific assumption.
The paper tackles the problem of estimating the average causal effect of a binary treatment when confounded by an unobserved binary confounder, using a nondifferential proxy. It shows that under a verifiable monotonicity assumption, adjusting for the proxy yields an effect measure bounded between the unadjusted and true values.
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.