Poisson-generalized gamma empirical Bayes model for disease mapping

Abstract

In spatial disease mapping, the use of Bayesian models of estimation technique is becoming popular for smoothing relative risks estimates for disease mapping. The most common Bayesian conjugate model for disease mapping is the Poisson-Gamma Model (PG). To explore further the activity of smoothing of relative risk estimates for Bayesian disease mapping, this study focused on the use of generalized gamma distribution as conjugate priors with respect to Poisson likelihood. Two new empirical Bayesian (EB) models are developed; these include Poisson-Generalized Gamma model (PGG) and modified Poisson-Generalized Gamma model (MPGG). The model simulation results indicated that PGG and MPGG models are more likely to handle dispersion in zero-deflated data, contaminated data and zero-inflated data for small and large sample data. Hence, the new EB models are highly competitive to improve the efficiency of relative risk estimation for disease mapping.

Keywords: Disease Mapping, Empirical Bayes, Generalized Gamma, Dispersion, Poisson