Additive versus multiplicative models in ecologic regression

Abstract

Much research in environmental epidemiology relies on aggregate-level information on exposure to potentially toxic substances and on relevant covariates. We compare the use of additive (linear) and multiplicative (log-linear) regression models for the analysis of such data. We illustrate how both additive and multiplicative models can be fit to aggregate-level data sets in which disease incidence is the dependent variable, and contrast these results with similar models fitted to individual-level data. We find (1) that for aggregate-level data, multiplicative models are more likely than additive models to introduce bias into the estimation of rates, an effect not found with individual-level data; and (2) that under many circumstances multiplicative models reduce the precision of the estimates, an effect also not found in individual-level models. For both additive and multiplicative models of aggregate-level data, we find that, in the presence of covariates, narrow confidence interval are obtained only when two or more antecedent factors are strongly related to the measured covariate and/or the exposure of primary substantive interest. We conclude that the equivalency of fitting additive versus multiplicative models in studies with individual-level binary data does not carry over to studies that analyze aggregate-level information. For aggregate data, we strongly recommend use of additive models.