A Bayesian conditional autoregressive with INLA: A case study of tuberculosis in Java, Indonesia

Abstract

Most disease risk mapping models are modeled by using the Bayesian approach. In this approach, the posterior distribution is typically estimated by using Markov Chain Monte Carlo (MCMC) method. However, it is known that the MCMC method suffers from convergence issues and requires a high demand for computational resources. This study aims to identify potential covariates in tuberculosis reduction and to map the relative risk of tuberculosis disease in the Java region by using Bayesian Conditional Autoregressive (CAR) with Integrated Nested Laplace Approximation (INLA). The posterior distribution of Bayes was estimated analytically using INLA that resulting in a more efficient, fast, and accurate inference. The results showed that Besag York Mollié (BYM) has the smallest Deviance Information Criterion (DIC) and Mean Absolute Deviance (MAD), so this model gives the best prediction. The significant covariates in reducing the number of TB cases in Java are percentages of healthy homes, household clean and healthy behavior, non-smokers, and complete tuberculosis treatment. In addition, 52.1% of districts/cities in Java were found to have a relative risk greater than one, and most of them were located in West Java.