Four-Way Decomposition

The four-way decomposition, introduced by Tyler VanderWeele in 2014, unifies the two great themes of effect analysis — mediation and interaction — into a single, exhaustive partition of a total causal effect. Any total effect of an exposure on an outcome can be split into exactly four pieces: a controlled direct effect (neither mediation nor interaction), a reference interaction (interaction but no mediation), a mediated interaction (both mediation and interaction at once), and a pure indirect effect (mediation but no interaction). These four components are mutually exclusive and add up to the total effect, and they nest the familiar two-way and three-way decompositions as special cases. Formalized in counterfactual notation and developed at book length in VanderWeele's 2015 Explanation in Causal Inference, the method gives social epidemiologists a precise vocabulary for asking how much of an exposure's effect runs through a mediator, how much depends on the exposure and mediator acting together, and how much is direct.