Directed Acyclic Graphs, Sufficient Causes, and the Properties of Conditioning on a Common Effect

Abstract

In this paper, the authors incorporate sufficient-component causes into the directed acyclic graph (DAG) causal framework in order to make apparent several properties of conditioning on a common effect. By incorporating sufficient causes on a graph, it is possible to detect conditional independencies within strata of the conditioning variable which are not evident on DAGs without the representation of sufficient causes. It is also possible to determine the sign of the conditional covariance of two causes when conditioning on their common effect if some knowledge of the sufficient-cause mechanisms for the common effect is available. The incorporation of sufficient causes within the DAG framework also allows for the representation of interactions on DAGs and for the unification of several different causal frameworks. For illustration, the results are applied to an example concerning the familial coaggregation of two disorders.

Familial Liability for Eating Disorders and Suicide Attempts

“…If the ORs remained significant after adjustment, the contribution of common familial risk factors to eating disorders and suicide attempts would be further supported (explained in eFigure in the Supplement). 28 We also adjusted for MDD, anxiety disorder, and substance use disorder in index individuals and in relatives to further test whether the comorbidities were associated with the familial liability. Data analysis was conducted from October 5, 2014, to April 28, 2015.…”

Empirical and counterfactual conditions for sufficient cause interactions

“…Rothman & Greenland (1998), Greenland & Brumback (2002) and Flanders (2006) provide some further discussion. VanderWeele & Robins (2007) relate the su¢ cientcomponent cause framework to the directed acyclic graph causal framework and develop theory concerning the graphical representation of su¢ cient causes on directed acyclic graphs. To develop conditions for su¢ cient cause interactions we will need only one result concerning the relationship between the su¢ cientcomponent cause framework and potential outcomes which is given in Theorem 1.…”

Missing Confounding Data in Marginal Structural Models: A Comparison of Inverse Probability Weighting and Multiple Imputation

“…DAGs are acyclic, that is, one cannot begin at a variable and follow the arrows through the graph to return to that variable; that is, information flows in one direction rather than in cycles. DAGs encode the conditional dependencies between variables and may be used to determine the variables on which to condition in order to achieve unbiased effect estimation (see, for example Greenland et al (1999); VanderWeele and Robins (2007)). Specifically, we assume a simple longitudinal setting in which there are two discrete time points, T = 0, 1, and we consider a single confounding variable L C (T ), treatment A(T ), and response Y .…”