On measures of uncertainty of empirical Bayes small-area estimators

A common index of disease incidence and mortality is the standardized mortality ratio (SMR). The SMR is a reliable measure of relative risk for large geographical regions such as countries or states, but may be unreliable for small areas such as counties. This paper reviews several empirical Bayes methods for producing smoothed estimates of the SMR as well as the conditional autoregressive procedure which accounts for spatial correlation. A multi-level Poisson model with covariates is developed, and estimating functions are used to estimate model parameters as in Lahiri and Maiti (University of Nebraska Technical Report, 2000). A hybrid of parametric bootstrap and delta methods is used to estimate the MSE. The proposed measure captures all sources of uncertainty in approximating the MSE of the proposed empirical Bayes estimator of the SMR.