CONJUGATION OF GENERALIZED GAMMA PRIOR WITH POISSON ANDGENERALIZED POISSON LIKELIHOODS FOR DISEASE MAPPING

Abstract

This article focused on the use of generalized Gamma distribution as
conjugate prior with Poisson and generalized Poisson likelihoods to handle dispersion in small samples. Based on this conjugacy, Poisson-Generalized Gamma model (PGG) and Generalized Poisson-Generalized Gamma model (GPGG) are developed for Bayesian disease mapping and compared with the existing Poisson-Gamma model.
The efficiency of these models was investigated using both simulated and real data applications. The deviance information criterion (DIC), dispersion test (DT), Monte Carlo error (MCE) and relative efficiency (reff) were used for comparison. All indicated that GPGG model provided the best precision and model efficiency to handle dispersion and relative risk estimation for disease mapping in small and large samples under uncontaminated and contaminated data. Thus, GPGG and PGG models served as alternative models in providing reliable mapping of disease.