To the Editor:
In a recent commentary, Lawlor1 suggests dropping the term “biologic interaction.” I am not opposed to such a proposal for some of the very reasons Lawlor gives, and I have generally tried to avoid using the term in my own work. However, in abandoning the term “biologic interaction,” I think it is important that we not abandon the concept to which it once referred.
Lawlor claims that “biologic interaction” was used by Rothman2 to describe deviation from additivity in risk differences. This is not quite right. Rothman conceived of “biologic interaction” as the presence of a sufficient cause for the outcome that would operate when 2 exposures were both present. Under certain, relatively strong, assumptions, the presence of such a sufficient cause would be implied by a departure from additivity.
Conceived of in a slightly different way, we may be interested whether, for some individuals, an outcome occurs if both of 2 exposures are present but not if only one or the other is present. If we let Dij denote the outcome that would have occurred for an individual if the first exposure were i and the second exposure were j, we might want to know whether there were individuals such that D11 = 1 but D10 = D01 = 0 (referred to as a “sufficient cause interaction” in my own work3). Such a response pattern implies (but is not necessary for) synergism in the sufficient cause framework.3,4 This outcome pattern moreover does not necessarily imply that the 2 exposures interact physically in producing the outcome5; however, nor is this response pattern equivalent to a statistical interaction.6,7
A similar set of issues has arisen in the genetics literature, with the use of the word “epistasis” for gene-gene interactions. In a recent review article, Phillips8 suggests using “statistical epistasis” for interaction in a statistical model, “compositional epistasis” for settings such as when the outcome occurs if and only if both of the relevant variants are present (D11 = 1 but D10 = D01 = D00 = 0), and “functional epistasis” for the physical interaction of proteins. Some sort of similar nomenclature could be adopted within epidemiology. If we do drop the word “biologic” when discussing interactions, let us not lose sight of the relevant distinctions to which it once pointed.
In closing, I would like to make a plea for the use of the relative excess risk due to interaction (RERI)9 in assessing interaction on the additive scale from case-control studies. RERI is defined by RR11 − RR10 − RR01 + 1, where RRij is the relative risk when the first and second exposures are i and j, respectively, and where the risk ratios can be approximated by odds ratios when the outcome is rare. The additive scale is relevant for assessing the public health implications of interaction. Moreover, under the assumptions of no bias due to confounding, selection or measurement error, the additive scale (and RERI in particular) is useful in detecting the sort of response patterns for which D11 = 1 but D10 = D01 = 0 (“sufficient cause interactions”). If both exposures are never preventive for any individual, then RERI >0 implies the presence of this response pattern5,6; without this no-preventive-action assumption, RERI >1 still implies the presence of this response pattern.5,6 If we are interested in detecting the even stronger notion of interaction that D11 = 1 but D10 = D01 = D00 = 0 (individuals for whom the outcome occurs if and only if both exposures are present) then RERI >2 suffices without any assumptions about preventive action10; RERI >1 suffices if at least one of the exposures is never preventive for any individual; and RERI >0 suffices if both are never preventive. No similar set of conditions is available for the “synergy index”9,11 in all of the various cases considered above. Skrondal11 objects to the use of RERI on the grounds of what he calls the “uniqueness problem” and the “misspecification problem.” In my view, both concerns are exaggerated; moreover both are easily addressed by using a weighting approach to RERI,12 rather than logistic regression,9 to control for confounding.
Tyler J. VanderWeele
Departments of Epidemiology and Biostatistics
Harvard School of Public Health
1. Lawlor DA. Biologic interaction: time to drop the term? Epidemiology.
2. Rothman KJ. Synergy and antagonism in cause-effect relationships. Am J Epidemiol.
3. VanderWeele TJ, Robins JM. Empirical and counterfactual conditions for sufficient cause interactions. Biometrika.
4. Rothman KJ. Causes. Am J Epidemiol
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5. VanderWeele TJ, Robins JM. The identification of synergism in the suffcient-component cause framework. Epidemiology.
6. VanderWeele TJ. Sufficient cause interactions and statistical interactions. Epidemiology.
7. Rajaleid K, Janszky I, Hallqvist J. In defense of “biologic interaction.” Epidemiology.
8. Phillips PC. Epistasis-the essential role of gene interactions in the structure and evolution of genetic systems. Nat Rev Genet.
9. Hosmer DW, Lemeshow S. Confidence interval estimation of interaction. Epidemiology.
10. VanderWeele TJ. Empirical tests for compositional epistasis. Nat Rev Genet.
11. Skrondal A. Interaction as departure from additivity in case-control studies: a cautionary note. Am J Epidemiol.
12. VanderWeele TJ, Vansteelandt S. A weighting approach to causal effects and additive interaction in case-control studies: marginal structural linear odds models. Am J Epidemiol.