General theory for interactions in sufficient cause models with dichotomous exposures

TL;DR

This paper develops a comprehensive theoretical framework for understanding interactions in sufficient cause models with binary causes and outcomes, including conditions for interactions and singular causes, and relates these to statistical models.

Contribution

It introduces a general theory for interactions in sufficient cause models with dichotomous exposures, providing empirical conditions and linking to statistical and causal inference frameworks.

Findings

Conditions for sufficient cause interactions are established.

Criteria for singular interactions are derived.

Relations to linear models and Pearl's causation are discussed.

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.