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A Three-way Decomposition of a Total Effect into Direct, Indirect, and Interactive Effects

VanderWeele, Tyler J.

doi: 10.1097/EDE.0b013e318281a64e

Recent theory in causal inference has provided concepts for mediation analysis and effect decomposition that allow one to decompose a total effect into a direct and an indirect effect. Here, it is shown that what is often taken as an indirect effect can in fact be further decomposed into a “pure” indirect effect and a mediated interactive effect, thus yielding a three-way decomposition of a total effect (direct, indirect, and interactive). This three-way decomposition applies to difference scales and also to additive ratio scales and additive hazard scales. Assumptions needed for the identification of each of these three effects are discussed and simple formulae are given for each when regression models allowing for interaction are used. The three-way decomposition is illustrated by examples from genetic and perinatal epidemiology, and discussion is given to what is gained over the traditional two-way decomposition into a direct and an indirect effect.

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Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA.

Submitted 28 February 2012; accepted 5 December 2012.

Supported by National Institutes of Health grants HD060696 and ES017876.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article ( This content is not peer-reviewed or copy-edited; it is the sole responsibility of the author.

Correspondence: Tyler J. VanderWeele, Harvard School of Public Health, Departments of Epidemiology and Biostatistics, 677 Huntington Avenue, Boston, MA 02115. E-mail:

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