[Epidemiologic and statistical interaction models and consequences for regression analysis]

Different ways to define interaction between exposition factors in epidemiological studies as well as the choice between additive and multiplicative no interaction leads frequently to confusion during data analysis. In their standard form methods of event data analysis such as Poisson or logistic regression assume a multiplicative parameterization of no interaction. However, evidence from empirical investigations as well as causal models of disease etiology, e.g. the simple independent action model of Finney or the sufficient-component-causes model of Rothman, suggest additive or other kinds of non-multiplicative concepts of no interaction. For additive structured data we illustrate the asymptotic bias ("interaction-bias") of main effect estimates which are based on inappropriate data analysis using multiplicative models and omitting significant or non-significant interaction terms. We show that both the epidemiological study design as well as the underlying causal model are determinants of the interaction structure of the data and should be considered in the model selection process. The definition of interaction should distinguish between risk, rate and odds if risks are not very small. Using generalized linear models with parametrical link functions we are able to analyze non-multiplicative interaction structures.