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August 2012 General theory for interactions in sufficient cause models with dichotomous exposures
Tyler J. VanderWeele, Thomas S. Richardson
Ann. Statist. 40(4): 2128-2161 (August 2012). DOI: 10.1214/12-AOS1019

Abstract

The sufficient-component cause framework assumes the existence of sets of sufficient causes that bring about an event. For a binary outcome and an arbitrary number of binary causes any set of potential outcomes can be replicated by positing a set of sufficient causes; typically this representation is not unique. A sufficient cause interaction is said to be present if within all representations there exists a sufficient cause in which two or more particular causes are all present. A singular interaction is said to be present if for some subset of individuals there is a unique minimal sufficient cause. Empirical and counterfactual conditions are given for sufficient cause interactions and singular interactions between an arbitrary number of causes. Conditions are given for cases in which none, some or all of a given set of causes affect the outcome monotonically. The relations between these results, interactions in linear statistical models and Pearl’s probability of causation are discussed.

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Tyler J. VanderWeele. Thomas S. Richardson. "General theory for interactions in sufficient cause models with dichotomous exposures." Ann. Statist. 40 (4) 2128 - 2161, August 2012. https://doi.org/10.1214/12-AOS1019

Information

Published: August 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1257.62006
MathSciNet: MR3059079
Digital Object Identifier: 10.1214/12-AOS1019

Subjects:
Primary: 62A01
Secondary: 62J99 , 68T30

Keywords: Causal inference , counterfactual , epistasis , interaction , potential outcomes , synergism

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 4 • August 2012
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