The Mathematics of Descriptions in Descriptive Epidemiology

Identifying patterns of disease distribution in a population is the task of descriptive epidemiology, where the patterns are descriptions of how the disease is distributed in the population. In everyday public health practice it is descriptive epidemiology that is hard at work when we inform the public about health problems, monitor its health status, gather information for planning and administrative purposes, or generate hypotheses to be tested by further analytic investigations. In this paper we pursue a formalization of the population descriptions that are the heart of descriptive epidemiology. We call attention to a fact, so far unrecognized by epidemiologists, that the set of (complete) population descriptions, suitably defined, has an associated relational and algebraic structure. This formalization allows us to access mathematical properties of this structure of an epidemiologic dataset with methods developed over the past 30 years.