Empirical Bayes Methods for Stabilizing Incidence Rates before Mapping

Abstract

The epidemiologic utility of mapping and ranking incidence rates is often questioned owing to instability of the observed incidence values in areas with small populations. Spurious fluctuations in the observed rates caused by this instability can mask true spatial and temporal trends in risk. To produce maps with the required level of geographic resolution, yet based on reliable estimates, it is desirable to reduce the random variation in the observed rates before mapping. In this paper, we describe the empirical Bayes approach for obtaining stabilized incidence estimates. We begin by deriving Bayes rate estimators and then illustrate how using the observed rates to estimate unknown distributional information leads to the empirical Bayes formulation. A drawback of the approach is that the histogram of the empirical Bayes rate estimates may be narrower than the true distribution of risk. We outline a constrained empirical Bayes approach that produces improved estimators for the true distribution of the unknown rates. We include discussions of relevant previous applications of empirical Bayes methods to rate mapping problems and an evaluation of the strengths and weaknesses of the approach.