Title: On the monotonicity of a binary confounder
Authors: Jose M Pena - Linkoping University (Sweden) [presenting]
Abstract: The focus is on the average causal effect of a binary treatment on an outcome when a binary confounder confounds this relationship. Suppose that the confounder is unobserved, but a nondifferential proxy of it is observed. We will 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. We will also show through experiments that most random parameterizations result in a proxy-adjusted effect that lies between the unadjusted and the true ones. However, only half of them satisfy the monotonicity condition named above. Therefore, the condition is sufficient but not necessary. This result should be interpreted with caution because we are seldom interested in a random parameterization. Therefore, we will also discuss some nonmonotonic cases (albeit empirically untestable) where the proxy-adjusted effect still lies between the unadjusted and the true ones.