Analyzing Irish suicide rates with mixture models

Abstract

In the analysis of morbidity and mortality data, variance component models are commonly used to provide an improvement in the estimation of rates for small regions which typically show large variability. This article investigates Irish suicide data using Poisson mixed models. The random effect distributions are estimated using Nonparametric Maximum likelihood which allows the calculation of shrinkage estimates from the posterior probability estimates of the EM algorithm, as well as the construction of `league tables'. As these models are inefficient in the case of spatial dependency, we investigate the addition of spatial autocorrelation terms based on neighboring average crude rates and standardized mortality ratios, as well as gender-specific versions of these. We consider models for the average crude rate as well as for the relative risk. A close correspondence between fitted values from both types of models suggests that information concerning within-region variability, incorporated in the parameters of the average crude rate model, appears indirectly in the simpler relative risk model by means of the expected values used in the offset term of the latter.