Commonalities in the classical, collapsibility and counterfactual concepts of confounding.

Objectives: Three definitions of confounding are available in the epidemiologic literature, namely, the classical, collapsibility, and counterfactual. The classical and collapsibility definitions are intuitively appealing but, especially in the case of the latter, there are shortcomings. The more recent counterfactual definition overcomes these limitations but at the cost of increased abstraction. One of the aims of this article is to demonstrate that under certain conditions the three definitions of confounding have key features in common.

Conclusions: The counterfactual definition of confounding addresses the inherent shortcomings of the classical and collapsibility definitions, and forms the basis of innovative methods of data analysis.