Modeling correlated data in epidemiology: mixed or marginal model?

Correlated observations (within centers, families, subjects,...) are common in epidemiology. Even when one is only interested in the modeling of means according to risk factors, it is also necessary to model the variance-cova riance matrix of the observations in order to make correct inferences on th e parameters of interest. All the more so when the aim of the survey is the measurement of these correlations or of the variance of the random effects from which they are assumed to originate. We discuss, within the framework of the linear and of the logistic models, the implications of two choices for the modeling of covariances. The mixed model shows the unobserved eleme nts responsible for the similarity between certain observations. In a longi tudinal survey, for instance, one can use a random effect, specific to each subject expressing how much a subject's trajectory is translated as compar ed to what is expected according to its characteristics (age, sex,...). The marginal approach leads To modeling separately the means and the covarianc e matrix of the observations. The distinction between these two approaches is important for non linear models, in particular the logistic one. We insi st on rite interconnection between a mixed model formulation and a marginal one, as well as on the implication of the choice in terms of the parameter s' interpretation.