Empirical Bayes and Fully Bayes procedures to detect high-risk areas in disease mapping

Disease mapping studies have experienced an enormous development in the last twenty years. Both an Empirical Bayes (EB) and a Fully Bayes (FB) approach have been used for smoothing purposes. However, an excess of smoothing might hinder the detection of true high-risk areas. Identifying these extreme regions minimizing the misclassification of background or normal areas, and then, avoiding false alarms is crucial in epidemiology. Bayesian decision rules, based on the posterior distribution of the relative risks, have been investigated for this task, but no similar studies have been conducted under the EB approach. Within this framework, second order correct estimators of the MSE of the log-relative risk predictor can be used to build appropriate confidence intervals for the relative risks. Their ability to detect high-risk areas is investigated through a simulation study using the geographical structure of the well-known Scottish lip cancer data. Bayesian credibility intervals and decision rules, based on the posterior distribution of the relative risks, are also investigated to check if any of the approaches outperforms the others when classifying high-risk regions. The conclusion is that Bayesian decision rules, exploiting the posterior distribution of the relative risks, are more powerful to detect high-risk areas than EB confidence intervals, but no general rules can be defined as a global criterion to be routinely applied in every real setting.