Bayesian hierarchical models in estimating Relative risk of HIV prevalence in Ilocos Region

• Main Authors: Garcia, Daniel Bezalel A., Addawe, Rizavel C.
• Format: Conference Proceeding
• Language: English
• Subjects: Bayesian analysis; Estimation; HIV; Human immunodeficiency virus; Infectious diseases; Poisson distribution; Probability distribution functions; Risk; Statistical analysis
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0192483

This paper used Bayesian Hierarchical Models, particularly the usual Poisson-Gamma model and the Poisson-Gamma model with Covariates in estimating the relative risk of HIV prevalence in Ilocos Region instead of using the Standardized Incidence Ratio (SIR) which is a frequentist approach. The study in the relative risk of HIV prevalence is significant due to its present nature of being incurable. The use of Poisson distribution as likelihood in relative risk estimation is appropriate because HIV prevalence is independent, that is, when the infection occurs, it does not affect the probability of another infection occurring in the same area. The appropriateness of Gamma distribution as the prior distribution is due to the fact Poisson and Gamma distributions are from the same family of distributions. Covariates are considered in this study to possibly improve the precision of results and to prohibit alternative explanations for the results due to the population of sexually active males and the number of diagnosed tuberculosis patients per municipality or city. It is confirmed that the application of Bayesian Poisson-Gamma and Poisson-Gamma with Covariates hierarchical models exhibit more stable HIV relative risk estimates and shrinkage when compared to SIR. There is no implication of a significant difference between the two Bayesian Hierarchical Models after the application of Deviance Information Criterion (DIC). It is recommended when applying the Poisson-Gamma model with Covariates to consider other fixed effects related to HIV prevalence to further improve the model. Lastly, the Bayesian Hierarchical Models presented in this paper can be utilized in estimating the posterior relative risk of other rare or infectious diseases.