Empirical bayesInterval estimates: An application to geographical epidemiology

Summary Empirical Bayes estimates have been advocated as an improvement for mapping rare diseases or health events aggregated in small areas. In particular different parametric approaches have been proposed for dealing with non-normal data, assuming that disease occurrencies follow non-homogeneous Poisson law, whose parameters are treated as random variables. This paper shows how to conduct a complete Empirical Bayes analysis under an exchangeable model in the context of Geographical Epidemiology. Three different approaches for defining confidence limits obtained using a parametric bootstrap are compared: method 1 relies only on the first and second moment of the bootstrapped posterior distributions; method 2 computes the centiles of the bootstrapped posteriors; method 3 equates to α the average of the probabilities derived from the estimated bootstrapped cumulative posterior distributions. The simple Poisson-Gamma formulation was used to model mortality data on Larynx Cancer in the Local Health Units of Tuscany (1980–82 males). Two areas of significant elevated risk are identified.