Abstract:
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.
