Dependence of confounding on the target population: a modification of causal graphs to account for co-action

Directed acyclic graphs (DAGs) are useful tools for assessing confounding. However, the basic approach to detecting confounding in DAGs does not distinguish among various forms of interaction between the exposure and covariates and between different target populations for which effects are estimated. We propose a simple modification of DAG rules to overcome this limitation.

Using fundamental concepts and DAGs, we show that the basic approach can suggest confounding even when absent if the covariate has no effect in the reference population being used as the comparator for the target population, as occurs when the target population is the exposed and the covariate acts only when the exposure is present.

We present three examples that illustrate this scenario and propose a simple revision to the basic approach to detecting confounding in DAGs that makes confounding in the presence of causal interaction easier to evaluate visually. This revision extends to other scenarios involving other target populations and variables with multiple levels.

A simple modification of the basic approach to identifying confounding in DAGs allows more frequent exclusion of confounding when it is absent.