Conjugation of Generalized Gamma Prior With Poisson and Generalized Poisson Likelihoods for Disease Mapping
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Date
2021
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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.
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Keywords
Disease mapping, Dispersion, Empirical bayes, Generalized gamma, Relative risk