Bayesian Hierarchical Approach in Latent Gaussian Modeling for Tuberculosis Cases in Jimma Zone: Using INLA Method

Abstract

Introduction: Tuberculosis is the long-lasting infectious disease caused by bacteria called Mycobacterium tuberculosis. Globally, in 2016 alone, approximately 10.4 million new cases have occurred worldwide. Africa has shared around 25% of the incidence and specifically in Ethiopia around 82 thousand was caught by Tuberculosis. Objectives: This study has been aimed to model the counts of Tuberculosis cases using Bayesian hierarchical approach of Latent Gaussian Model (LGM) with Integrated Nested Laplace Approximation method. It is also designed to determine the predictors and see the variation of Tuberculosis incidences across districts of Jimma zone. Moreover, the researcher intends to compare the inbuilt R-INLA default priors and penalized complexity priors so that to assure the robustness of the priors for which Bayesian hierarchical approach of latent Gaussian model was applied. Methods: The study has been conducted in Jimma zone of entire districts and the data is basically secondary which is obtained from Jimma zone health office. The counts of Tuberculosis cases have been analyzed with factors like gender, HIV co-infection, Population density and age of patients. The Integrated Nested Laplace Approximation (INLA) method of Bayesian approach which is fast, deterministic and promising alternative to MCMC method was used to determine posterior marginal. Results: The latent Gaussian model of Poisson distributional assumption of Tuberculosis cases that includes both fixed and random effects with penalized complexity priors appeared to be the best model to fit the data based on the Watanabe Akaike Information Criteria and other supportive criteria. Using Kullback-Leibler Divergence criteria, the under-used simplified Laplace approximation indicated that posterior marginal was well approximated by normal distribution. The predictive value of the best model is not far deviated from the actual data based on the Conditional Predictive Ordinate and the probability integral transform. Conclusions: The hierarchical level of Latent Gaussian Model with Penalized Complexity was found to be the appropriate model. All the variables were significant under this model and the posterior marginal was well approximated by standard Gaussian. The PIT indicated that predictive distribution was less affected by outliers and the model was reasonably well.