In this paper, we discuss relationships between causal interactions within the counterfactual framework and interference in which the exposure of one person may affect the outcomes of another. We show that the empirical tests for causal interactions can, in fact, all be adapted to empirical tests for particular forms of interference. In the context of interference, by recoding the response as some function of the outcomes of the various persons within a cluster, a wide range of different forms of interference can potentially be detected. The correspondence between causal interactions and forms of interference extends to encompass n-way causal interactions, interference between n persons within a cluster, and multivalued exposures. The theory for causal interactions provides a complete conceptual apparatus for assessing interference as well. The results are illustrated using data from a hypothetical vaccine trial to reason about specific forms of interference and spillover effects that may be present in this vaccine setting. We discuss the implications of this correspondence for our conceptualizations of interaction and for application to vaccine trials and many other settings in which spillover effects may be present.
From the Departments of aEpidemiology and bBiostatistics, Harvard School of Public Health, Boston, MA; cDepartment of Clinical Epidemiology, Leiden University Medical Center, Leiden, The Netherlands; and dCenter for Communicable Disease Dynamics, Harvard School of Public Health, Boston, MA.
Submitted 6 July 2011; accepted 8 December 2011.
Supported by National Institutes of Health grants ES017876 and HD060696. The author reported no financial interests related to this research.
Editors' note: A commentary on this article appears on page 181.
Correspondence: Tyler J. VanderWeele, Departments of Epidemiology and Biostatistics, Harvard School of Public Health, 677 Huntington Ave, Boston, MA 02115. E-mail: firstname.lastname@example.org.