On Which Variable(s) Should We Condition to Remove Confounding Bias?

Abstract

Using causal diagrams and an axiomatization of causality, we examined the well-known claim that conditioning on confounders (“adjustment” for confounders) is sufficient to remove confounding bias. We show that this advice is poorly stated and is incomplete. To remove confounding bias, it is necessary to condition on three types of variables, none of which is a confounder. Conditioning on one of them, however, leads to an interesting form of colliding bias, which in turn, can be removed by conditioning on two other types of variables.