Prediction error estimators in Empirical Bayes disease mapping

Mapping of small area mortality (or incidence) risks is a widely used technique in public health research. The standardized mortality ratio (SMR) is a common direct index of disease mortality, but it might be very inaccurate in areas or counties with low population. Hence, the use of models that borrow information from related (neighbouring) regions, smoothing the crude mortality risks, is recommended. In this work, we focus on comparing prediction error estimators used in Empirical Bayes (EB) disease mapping, which are correct up to first order, with alternative first and second-order correct proposals from the small area estimation literature. Our main interest is to check if second-order approximations of the prediction error improve confidence intervals for the relative risks. The well known Scottish lip cancer data is used for illustrative purposes. A simulation study is also conducted indicating that there is not much gain in efficiency when using second-order corrections. Copyright (c) 2007 John Wiley & Sons, Ltd.