On Which Variable(s) Should We Condition to Remove Confounding Bias?
Eyal Shahar *
Department of Epidemiology and Biostatistics, Mel and Enid Zuckerman College of Public Health, University of Arizona, USA.
Doron J. Shahar
Department of Mathematics, College of Science, University of Arizona, USA.
*Author to whom correspondence should be addressed.
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.
Keywords: Causal diagrams, axioms of causality, confounding bias, colliding bias, conditioning