Bayesian Poisson-gamma and Log-normal models for estimating the relative risks of health insurance claims due to dengue disease in Bandung

Abstract

Dengue disease is one of the most dangerous diseases and it is commonly found in Bandung, one of the most populous cities in Indonesia. Some patients who need more intensive care at hospital certainly require high fare of treatment. The risk of high fare to spend can be covered by health insurance. As a direct consequence, it is important for insurance companies to anticipate the relative risk of claims filed by health insurance holders due to this disease. In this study, the relative risk of claims that may be filed by health insurance holders is estimated by implementing frequentist approach, i.e. SMR (Standardized Mortality/Morbidity Ratio) model, and Bayesian approach, i.e. Poisson-Gamma and Log-normal models. Based on the implementation on the data of health insurance holders and the number of dengue cases in Bandung in 2013 and 2014 and the analysis of the results, it can be concluded that Bayesian inference is more suitable to be applied than frequentist inference because the estimation of the relative risk of claims in industrial insurance is often related to random variables which have non constant parameters. From one of the goodness of fit methods, i.e. DIC, it can be concluded that Poisson-Gamma model is the best model which suits the data better. From these models, sub-districts that have the highest relative risk estimates are specified to provide an overview for insurance companies to anticipate the possibility of health insurance claims resulting from dengue disease from particular critical sub-districts. More accurate results are expected to be obtained once more complete data can be collected.