Ann Stat. 2013 Feb;41(1):196-220. doi: 10.1214/12-aos1058.
Annals of statistics
Tyler J VanderWeele, Ilya Shpitser
PMID: 25544784 PMCID: PMC4276366 DOI: 10.1214/12-aos1058
The causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence. The causal inference literature has not, however, produced a clear formal definition of a confounder, as it has given priority to the concept of confounding over that of a confounder. We consider a number of candidate definitions arising from various more informal statements made in the literature. We consider the properties satisfied by each candidate definition, principally focusing on (i) whether under the candidate definition control for all "confounders" suffices to control for "confounding" and (ii) whether each confounder in some context helps eliminate or reduce confounding bias. Several of the candidate definitions do not have these two properties. Only one candidate definition of those considered satisfies both properties. We propose that a "confounder" be defined as a pre-exposure covariate
Keywords: Adjustment; causal diagrams; causal inference; confounder; counterfactuals; minimal sufficiency
