Mathematical modeling of directed acyclic graphs to explore competing causal mechanisms underlying epidemiological study data

1 Accurately estimating the effect of an exposure on an outcome requires understanding how variables relevant to a study question are causally related to each other. Directed acyclic graphs (DAGs) are used in epidemiology to understand causal processes and determine appropriate statistical approaches to obtain unbiased measures of effect. Compartmental models (CMs) are also used to represent different causal mechanisms, by depicting flows between disease states on the population level. In this paper, we extend a mapping between DAGs and CMs to show how DAG–derived CMs can be used to compare competing causal mechanisms by simulating epidemiological studies and conducting statistical analyses on the simulated data. Through this framework, we can evaluate how robust simulated epidemiological study results are to different biases in study design and underlying causal mechanisms. As a case study, we simulated a longitudinal cohort study to examine the obesity paradox: the apparent protective effect of obesity on mortality among diabetic ever-smokers, but not among diabetic never-smokers. Our simulations illustrate how study design bias (e.g., reverse causation), can lead to the obesity paradox. Ultimately, we show the utility of transforming DAGs into in silico laboratories within which researchers can systematically evaluate bias, and inform analyses and study design.