This paper contrasts the concepts of interaction and effect modification using a series of examples. Interaction and effect modification are formally defined within the counterfactual framework. Interaction is defined in terms of the effects of 2 interventions whereas effect modification is defined in terms of the effect of one intervention varying across strata of a second variable. Effect modification can be present with no interaction; interaction can be present with no effect modification. There are settings in which it is possible to assess effect modification but not interaction, or to assess interaction but not effect modification. The analytic procedures for obtaining estimates of effect modification parameters and interaction parameters using marginal structural models are compared and contrasted. A characterization is given of the settings in which interaction and effect modification coincide.
From the Department of Epidemiology and Biostatistics, Harvard University, Boston, MA.
Submitted 11 November 2008; accepted 31 July 2009.
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Correspondence: Tyler J. VanderWeele, Department of Epidemiology and Biostatistics, Harvard School of Public Health, 677 Huntington Ave, Boston, MA 02115. E-mail: email@example.com.
Erratum: On the Distinction Between Interaction and Effect Modification
When this article was published in the November 2009 issue of Epidemiology, in Equation 1 (p. 867), the subscript q in E[Deq|Q = q] was erroneous. Equation 1 for the marginal structural model for effect modification should thus have read:
E[De|Q = q] = a0+α1q +α2q+α3eq
The author thanks Alvaro Alonso for catching this error.