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American Journal of Epidemiology Advance Access published online on August 16, 2007
American Journal of Epidemiology, doi:10.1093/aje/kwm179
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American Journal of Epidemiology © The Author 2007. Published by the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

PRACTICE OF EPIDEMIOLOGY

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

Tyler J. VanderWeele1 and James M. Robins2

1 Department of Health Studies, Division of Biological Sciences, University of Chicago, Chicago, IL
2 Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA

Correspondence to Dr. Tyler J. VanderWeele, Department of Health Studies, University of Chicago, 5841 South Maryland Avenue, MC 2007, Chicago, IL 60637 (e-mail: vanderweele{at}uchicago.edu).

Received for publication October 27, 2006. Accepted for publication May 22, 2007.

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.

causality; collider stratification; directed acyclic graphs; epidemiologic methods; independence; interaction; sufficient causes

Abbreviations: DAG, directed acyclic graph; SCC, sufficient-component cause


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