Bayesian Approach with Different Heterogeneity Variance Priors in Disease Mapping of HIV/AIDS in Thailand

The objective of this study is to compare Bayesian models and Bayesian maps under several different heterogeneity variance priors after controlling with the same data and the same mean prior in the application of standardized morbidity ratio (SMR) of HIV/AIDS infection in Thailand 2013. Three noniterative estimators of heterogeneity variance priors for SMRs as dispersion measures among areas are compared to produce the best fitting model and map. The data source of the number of newly diagnosed HIV/ AIDS cases infected out of the persons who come to receive medical treatments including blood test is provided by the National AIDS Program (NAP), collected by the National Health Security Office (NHSO). The results showed that the first heterogeneity variance prior estimate derived from the marginal variance estimator of observed number of HIV/AIDS cases performs best with the smallest deviance information criterion (DIC), the largest log-marginal-likelihood, and the highest posterior probability, leading to a suitable map with five high risk classes of SMR classification under Bayesian mapping. Practically, the prior information on the mean is the most popular use to improve Bayes estimates; however, a recommendation based upon an acceptable prior on the heterogeneity variance after controlling the same mean prior from this study result is also adopted as an alternative choice.