Modification of Standardized Mortality Ratio Index Corresponding to Small Population Problem

Abstract

Statistical methods to estimate geographical distribution using municipality-specific mortality data were considered. The methods are based on Poisson model with spatial smoothing by a spherical neighborhood system that is prescribed with the population size. The smoothed rates may be corrected by empirical Bayes method with gamma frailty model or crossing-over type likelihood method. The proposed method provides shrinkage estimators, in which the crude SMR is shrunk towards a local neighborhood mean value. We examined the proposed method by analyzing site-specific cancer mortality data in Japan for the period 1993-2002. The results of our study suggested that correction with gamma frailty model has a fairly good performance for grasping a general view of spatial distribution of mortality. However no remarkable improvement was obtained in comparison with the simple smoothing method.