Bayesian approach using MCMC in disease mapping with standardized morbidity ratio of HIV/AIDS in Thailand

The development of health service policies has been needed the precise data information from the previous evidence. The disease mapping is an essential tool for analyzing and monitoring the disease distribution in order to allocate the needed resources of health in each areas. Statistics of interest is the standardized morbidity ratio (SMR), as similarly to relative risk, but can adjust some confounders with age-gender specific morbidity rate across areas. The purpose of this study is to apply Bayesian models with Markov Chain Monte Carlo (MCMC) to derive the posterior outcomes under the hierarchical multilevel hyper-parameters in the application of SMR on HIV/AIDS infectious mapping in Thailand 2017. Posterior distribution, which is an outcome of Bayes' approach, is balanced between observed likelihood of data and prior knowledge. Likelihoods of observed count data are based on Poisson model while the prior of SMR is initially based on Gamma. Considering hyper-parameters model, the location parameter of Gamma prior is assumed to be the lognormal distribution whereas the scale parameter of Gamma prior is based on Laplace, Inverse Gamma, and Gamma distribution. Our goal is to find the best fitting data of posterior probability among three prior candidates according to above scale parameter distributions. The data source was from the number of new cases diagnosed HIV/AIDS infection of all registry persons who enter for blood testing and treated by medical doctors in the National AIDS Program (NAP). All data were collected by the National Health Security Office, NHSO. The results indicated that the both best fitting Bayesian model and mapping of hierarchical data was Poisson likelihood with Gamma prior, coping with hyper-parameter priors of Lognormal-Laplace distributions showing the smallest deviance information criterion (DIC) and three largest values of log-marginal-likelihood (log-ML), posterior probability, and efficiency of MCMC under the smallest autocorrelation. The six top-ranking provinces with highest risk subject to SMR measure were Samut Prakan, Nakhon Nayok, Chumpon, Pathum Thani, Phuket, and Sing Buri.