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Biometrika Advance Access published online on January 24, 2008
Biometrika, doi:10.1093/biomet/asm090
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© 2008 Biometrika Trust

Articles

Empirical and counterfactual conditions for sufficient cause interactions

Tyler J. Vanderweele

Department of Health Studies, University of Chicago, 5841 South Maryland Avenue, MC 2007, Chicago, Illinois 60637, U.S.A. vanderweele{at}uchicago.edu

James M. Robins

Departments of Epidemiology and Biostatistics, Harvard School of Public Health, 677 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. robins{at}hsph.harvard.edu

Received for publication 1 September 2006. Revision received 1 July 2007.
  Abstract

Sufficient-component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of sufficient causes, synergism and sufficient cause interactions. Doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of sufficient cause interactions. The conditions are novel in that, unlike other conditions in the literature, they make no assumption about monotonicity. The conditions can also be generalized and the conditions for three-way sufficient cause interactions are given explicitly. The statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models.

Key Words: Causal inference • Counterfactual • Interaction • Potential outcome • Risk difference • Sufficient cause • Synergism


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