Empirical Bayes Estimators Under Nonparametric Priors for Disease Mapping of HIV/AIDS

Empirical Bayes (EB) method is a statistical technique in which the prior distribution by Bayesian rule is estimated from the data. This paper focuses on generation of the prior distribution from previously informative data to improve the efficiency of estimation on the standardized morbidity ratio (SMR) of newly diagnostic HIV/ AIDS infected cases. Data source of newly diagnosed HIV/AIDS infection is provided by the NAP (National AIDS program) project, collected by the National Health Security Office (NHSO) in Thailand 2008 to 2013. After constructing and testing empirical prior distribution of previous SMR data during 2010-2012, we found that the distribution of prior followed a normal distribution at approximately 0.1 p-value. The further results of EB estimation indicated that in Thailand 2013, the mean of SMREB overall the country was 0.85 that decreases slightly in HIV infection, compared with the past five years from 2008 to 2012 as the national standard reference. The maximum SMREB of 3.26 found in Nong Bua Lamphu, and the minimum value of 0.14 in Roi Et. Empirical Bayes estimates with normal prior perform well with smaller variance, leading to the narrow width of the credible interval (CI).