A typology of four notions of confounding in epidemiology.

Confounding is a major concern in epidemiology. Despite its significance, the different notions of confounding have not been fully appreciated in the literature, leading to confusion of causal concepts in epidemiology. In this article, we aim to highlight the importance of differentiating between the subtly different notions of confounding from the perspective of counterfactual reasoning. By using a simple example, we illustrate the significance of considering the distribution of response types to distinguish causation from association, highlighting that confounding depends not only on the population chosen as the target of inference, but also on the notions of confounding in distribution and confounding in measure. This point has been relatively underappreciated, partly because some literature on the concept of confounding has only used the exposed and unexposed groups as the target populations, while it would be helpful to use the total population as the target population. Moreover, to clarify a further distinction between confounding "in expectation" and "realized" confounding, we illustrate the usefulness of examining the distribution of exposure status in the target population. To grasp the explicit distinction between confounding in expectation and realized confounding, we need to understand the mechanism that generates exposure events, not the product of that mechanism. Finally, we graphically illustrate this point, highlighting the usefulness of directed acyclic graphs in examining the presence of confounding in distribution, in the notion of confounding in expectation.