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Interactions With Income

Kaufman, Jay S.

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doi: 10.1097/01.ede.0000208474.84947.80
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To the Editor:

In their recent article in this journal, Stjärne and colleagues1 describe socioeconomic gradients in the incidence of myocardial infarction (MI) using population-based data from Sweden. An additional goal of the article was to assess departure from additivity for the joint relations between individual income and neighborhood income in determining MI risk. This analysis is summarized in Figure 3 and Table 5 from which the authors conclude that joint effects are roughly additive for men and superadditive for women. It is important to note from the nearly parallel log(OR) lines in the lower panel of Figure 3, however, that the joint effects for men are also approximately what would be expected under multiplicativity. This similarity can perhaps be better appreciated by consideration of the interaction contrast ratio (ICR) for the median-split data in Table 5, which shows that the joint effects incidence rate ratio (IRR) expected under additivity for men in the adjusted data in Table 5 would be (1.01 + 1.37 − 1) = 1.38, whereas the IRR expected under exact multiplicativity would be (1.01 × 1.37) = 1.38.2(pp. 340–341.) The observed point estimate of 1.48 for men is therefore actually supermultiplicative, just as it is for women, but negligibly so. It is the essentially null value for the adjusted effect of individual income for men (IRR = 1.01) that constrains the expected values under additivity and multiplicativity to be nearly identical. In light of this negligible effect for one of the 2 interacting factors, the distinction between values expected under additivity and multiplicativity becomes trivial. Note further that Figure 3 exaggerates this interaction pattern somewhat by plotting predicted values from a model that requires exact log-linearity. Thus, the odds ratios shown here range from above 1.0 to less than 0.20, a degree of heterogeneity in cluster-specific odds ratios that presumably is much greater than would be estimated by the second-stage variance of a hierarchical model of these same data.

Moreover, additivity is the benchmark for assessing joint effects because of a model of independent action that relates statistical interaction to biologic mechanisms through latent potential outcome types.2(pp. 332–336.) Even under the best of conditions, the inference gleaned is weak, because although absence of interacting latent types implies additivity of effects, the converse is not true. When considering binary variables that are formed from arbitrary median splits rather than naturally discrete events, the model becomes even more tenuous for insights into mechanism. The authors interpret the results as indicating that women who are jointly exposed to individual low income and low income context are at higher risk than one might expect if these 2 factors were operating in complete mechanistic independence. However, is this statistical null hypothesis really plausible in substantive terms? Both individual and community income surely affect health by providing various resources for medical care and healthy lifestyle. There would therefore be little justification for giving any a priori credibility to the null hypothesis that 2 measures of material disadvantage operate on entirely different etiologic pathways.

Jay S. Kaufman

Department of Epidemiology

School of Public Health

University of North Carolina

Chapel Hill, NC

[email protected]


1. Stjärne MK, Fritzell J, Ponce de Leon A, et al. SHEEP Study Group. Neighborhood socioeconomic context, individual income and myocardial infarction. Epidemiology. 2006;17:14–23.
2. Greenland S, Rothman KJ. Concepts of interaction. In: Rothman KJ, Greenland S, eds. Modern Epidemiology, 2nd ed. Philadelphia: Lippincott Williams & Wilkins; 1998:329–342.
© 2006 Lippincott Williams & Wilkins, Inc.