Empirical bayes estimation of small area prevalence of non-rare conditions

Geographical studies are becoming increasingly common in epidemiology. The problems of small area investigations are well known, and several methods are available for the estimation and mapping of disease risk across small areas, with the emphasis mainly on applications concerning rare disease incidence or mortality. An empirical Bayes method is proposed for small area estimation of the prevalence of non-rare conditions, whose variability is binomial and cannot be approximated by a Poisson model. It is the direct equivalent of a semi-parametric non-iterative moment estimation method proposed in the Poisson case. As an example, the geographical distribution of the prevalence of respiratory symptoms in schoolchildren across 71 small areas in Huddersfield, Northern England is studied. Whereas random variability causes the crude area-specific prevalences to be unstable, the posterior estimates, corrected towards overall or local means, are capable of highlighting genuine extra-binomial variability. The method is very simple and can readily be applied to the study of a number of common conditions.