The Annals of Statistics

General theory for interactions in sufficient cause models with dichotomous exposures

Tyler J. VanderWeele and Thomas S. Richardson

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 40, Number 4 (2012), 2128-2161.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1358951378

Digital Object Identifier
doi:10.1214/12-AOS1019

Mathematical Reviews number (MathSciNet)
MR3059079

Zentralblatt MATH identifier
1257.62006

Subjects
Primary: 62A01: Foundations and philosophical topics
Secondary: 68T30: Knowledge representation 62J99: None of the above, but in this section

Keywords
Causal inference counterfactual epistasis interaction potential outcomes synergism

Citation

VanderWeele, Tyler J.; Richardson, Thomas S. General theory for interactions in sufficient cause models with dichotomous exposures. Ann. Statist. 40 (2012), no. 4, 2128--2161. doi:10.1214/12-AOS1019. https://projecteuclid.org/euclid.aos/1358951378


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