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doi: 10.1097/EDE.0000000000000121

A Unification of Mediation and Interaction: A 4-Way Decomposition

VanderWeele, Tyler J.

Supplemental Author Material


On p. 8 and on p. 12 of the Supplemental Digital Content to the paper A unification of mediation and interaction: a 4-way decomposition1, there was a mistake in the expression for the component due to the reference interaction for the case of a binary mediator and a binary outcome. On p. 8, the expression for

should have been given by

rather than by

Likewise, on p. 12, the SAS code should have reflected the former expression rather than the latter. A new PDF of the Supplemental Digital Content has been posted with these mistakes corrected and is available at http://links.lww.com/EDE/A797. The author thanks Ronnie Pingel of Uppsala University for catching this error.

Epidemiology. 27(5):e36, September 2016.

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The overall effect of an exposure on an outcome, in the presence of a mediator with which the exposure may interact, can be decomposed into 4 components: (1) the effect of the exposure in the absence of the mediator, (2) the interactive effect when the mediator is left to what it would be in the absence of exposure, (3) a mediated interaction, and (4) a pure mediated effect. These 4 components, respectively, correspond to the portion of the effect that is due to neither mediation nor interaction, to just interaction (but not mediation), to both mediation and interaction, and to just mediation (but not interaction). This 4-way decomposition unites methods that attribute effects to interactions and methods that assess mediation. Certain combinations of these 4 components correspond to measures for mediation, whereas other combinations correspond to measures of interaction previously proposed in the literature. Prior decompositions in the literature are in essence special cases of this 4-way decomposition. The 4-way decomposition can be carried out using standard statistical models, and software is provided to estimate each of the 4 components. The 4-way decomposition provides maximum insight into how much of an effect is mediated, how much is due to interaction, how much is due to both mediation and interaction together, and how much is due to neither.

© 2014 by Lippincott Williams & Wilkins, Inc

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