Identifying Areas with Elevated Disease Incidence Rates Using Empirical Bayes Estimators

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Abstract
Using maps of observed disease incidence rates to identify regions with potentially elevated risk may be misleading due to the instability of the observed rates in regions with small populations. We use a simulation study to examine the use of maps based on observed incidence rates in identifying such high‐risk areas as compared to maps based on empirical Bayes and constrained empirical Bayes rate estimates. In addition, because the existence of clusters of areas with elevated risk violates the usual distributional assumptions underlying the empirical Bayes approach, we also examine the robustness of the estimates and the impact of incorrect assumptions on identification of high‐risk regions. The simulation results indicate that the observed incidence rates were quite sensitive in terms of identifying areas with truly elevated rates. However, due to the instability of the observed rates, maps based on observed incidence incorrectly identified areas as high risk more frequently than did maps based on the estimators. The standard and constrained empirical Bayes estimates were more stable than the observed rates even when based on incorrect distributional assumptions. The standard empirical Bayes estimates, however, were oversmoothed in that too few areas were identified as having elevated risk. The constrained empirical Bayes approach provided sensitivity closer to that of the observed rates yet with the percentage of areas incorrectly identified as high risk equal to that of the standard empirical Bayes estimates. We illustrate an application of these results with an analysis of the geographic distribution of brain cancer mortality among counties in Ohio.