"Toward a clearer definition of confounding" revisited with directed acyclic graphs

In a 1993 paper (Am J Epidemiol. 1993;137(1):1-8), Weinberg considered whether a variable that is associated with the outcome and is affected by exposure but is not an intermediate variable between exposure and outcome should be considered a confounder in etiologic studies. As an example, she examined the common practice of adjusting for history of spontaneous abortion when estimating the effect of an exposure on the risk of spontaneous abortion. She showed algebraically that such an adjustment could substantially bias the results even though history of spontaneous abortion would meet some definitions of a confounder. Directed acyclic graphs (DAGs) were introduced into epidemiology several years later as a tool with which to identify confounders. The authors now revisit Weinberg's paper using DAGs to represent scenarios that arise from her original assumptions. DAG theory is consistent with Weinberg's finding that adjusting for history of spontaneous abortion introduces bias in her original scenario. In the authors' examples, treating history of spontaneous abortion as a confounder introduces bias if it is a descendant of the exposure and is associated with the outcome conditional on exposure or is a child of a collider on a relevant undirected path. Thoughtful DAG analyses require clear research questions but are easily modified for examining different causal assumptions that may affect confounder assessment.