Tuberculosis

Tuberculosis (TB) is a chronic infectious disease caused by a bacillus belonging to a group of bacteria grouped in the mycobacterium tuberculosis complex and remains an important public health problem of the 21st century (WHO, 2017). It remains a high-priority communicable disease that causes an enormous burden of morbidity and mortality. Tuberculosis (TB) control and elimination rely on an early detection of active TB cases, prompt anti-TB treatment, identification of persons in risk of exposure and infection and prevention of secondary TB cases. (Lönnroth et al., 2015).

Globally, in 2016 alone, approximately 10.4 million new cases (range from 8.8 million to 12.2 million) which is equivalent to 140 cases per 100000 have been occurred worldwide. According to the reports of WHO (2017), the most estimated number of TB cases are in the WHO South-East Asia Region (45%), the WHO African Region (25%) and the WHO Western Pacific Region (17%); similarly, smaller proportions of cases occurred in the WHO Eastern Mediterranean Region (7%), the WHO European Region (3%) and the WHO Region of the Americas (3%)and 1.8 million deaths of tuberculosis were reported worldwide; of which 11% of new cases and 0.4 million deaths were people with co- infected of human immunodeficiency virus (HIV) which makes the TB disease more serious top causes of mortality and morbidity (WHO, 2017; Asemahagn et al., 2018).

Likewise, there were worsened burden of TB with the estimated 600 000 (range, 540 000–660 000) incident cases of Multi Drug Resistant Tuberculosis (MDR-TB) with cases accounting for 82% (490 000). For the same report, the globally number of notified TB cases is estimated to be 350 000 (range, 330 000–370 000) MDR/RR-TB cases among notified TB patients (WHO, 2017). Thus, in 1991 the world health assembly resolution recognized TB as a major global public health problem and aimed to achieve 70% case detection and 85% treatment success in 2000. Considering the burden of this infection, world health organization (WHO) has recognized TB as a global public health emergence and launched direct observation therapy strategy (DOTS) in 1994 (WHO, 2017; Deribew et al., 2012; FMoH, 2015; ) because of a number of peoples exposed to this disease and many deaths was registered.

From the identified WHO regions worldwide, the WHO Africa region took the second most regions of with high TB cases. TB preventive treatment is expanding, especially in the two priority risk groups of people living with HIV and children under 5. However, most people eligible for TB preventive treatment are not accessing it well. It shares estimated cases of 25%. Similarly the most death of TB cases with HIV co-infected is also accounted for this region which is found to be 82% in 2016 that increase for the same cases of 2015 which was 81% ; Asemahagn et al., 2018).

The (WHO, 2017)) report revealed that Africa is not among the regions registered to have decline in TB mortality rates. There is considerable country variation in the CFR, from under 5% in a few countries to more than 20% in most countries in the WHO African Region. This shows considerable inequalities among countries in access to TB diagnosis and treatment that need to be addressed. The summary of WHO report indicated that the incidence rate of TB and HIV co-infected in WHO Africa region is estimated to be 41 (34-48) per 100000 population whereas mortality for the same cases is 31(27-36). In 2016, the total notified TB cases in this region was 1 303 483 with 84% of pulmonary cases which intake an estimated MDR/RR-TB cases of 40000 (ranging from 36000 to 44000) among notified pulmonary TB cases. The estimated TB treatment coverage in the WHO Africa region is only 49% (WHO, 2017).

Different results ascertain that although Ethiopia has only limited resources to spend on combating tuberculosis and multidrug-resistant tuberculosis, its innovative, community-based approach demonstrates that a poor country which lacks sophisticated healthcare systems and medical specialists can nevertheless respond aggressively in the battle against TB and MDR TB. It is ranked the ninth among the world most TB burden country and is one of 27 MDR TB high burden countries. In 2016 only 182 (ranging, 128-245) thousand TB incidence of which 14 (9.6-19) was related to HIV co-infection have been occurred in Ethiopia and the estimated notified co-infected people was 103330 (81%). The rate incidence of the cases for the same year is found to be 177/100000. In other way the number of deaths due to TB cases without HIV co-infection was estimated to be 26 thousands where the death rate is 25/100000 and whereas 4 (2.7-5.4) thousands of HIV co-infected were died (WHO, 2017).

Why Bayesian? Although the application of Bayesian statistics sounds the researchers, it stayed long century with its theoretical definition only because of its difficulties with integration of the denominator in Bayes theorem. Thanks to simulation based MCMC methods, the approach got valued to have numerical meaning with the efficient estimation of the application in any fields with some limitation like burden of time in approximating the posterior and convergence problem (Gelman et al. 2009; Berger, 2013). As of 2009, the other news was welcomed with very flexible and fast approximation techniques called Integrated Nested Laplace Approximation (INLA) for Latent Gaussian Model (Rue et al., 2009).

With this study, the reason why Bayesian approach is preferred over the usual frequentist technique is that the power of information obtained from the approach is much better as it is the combination of likelihood data and prior information about the distribution of the parameter. It still empowers the efficiency of the data even when the size may large enough in representing the target population by giving distribution for the unknown parameters. Thus, considering the stated advantages of Bayesian application over classical method and the interesting application of INLA with Latent Gaussian Model (LGM) method are the most key for the motivation to apply it for the data set under this study (Riebler et al., 2017; Blangiardo et al., 2015).

Latent Gaussian Models (LGMs) form a flexible subclass of Bayesian hierarchical models and are practical from a statistical modeling point of view and readily interpretable. Consequently, LGMs have become popular in many areas of statistics and various fields of applications especially in spatial and spatio-temporal model (Nzabanita, 2012). The Integrated Nested Laplace Approximation (INLA) proposed by Rue et al., (2009) is focused on providing a good approximation to the posterior marginal distributions of the parameters in the model of Bayesian hierarchical framework. In particular, this approximation has been developed for Latent Gaussian models.
Statement of the Problems

Different study reported from various parts of the country showed that the prevalence of smear-positive cases ranged from 33 to 213.4/100,000 people in Ethiopia during different year of till 2016 (Deribew et al., 2012; Asemahagn et al., 2018).

Therefore, considering the seriousness of the disease and gaps found with different studies, the researcher has fitted latent Gaussian model with Bayesian hierarchical approach using INLA method. The author of this study has filled gaps seen with previous studies; with especial weight to model gaps used by different researchers.

According to the study by different researchers on Bayesian GLMM of TB cases, the results of model comparison indicated that in most cases Bayesian approach empowered over the classical in better estimation of the parameter. However, the study was based on the application of the simulation based MCMC method which has the burdensome of time consuming, convergence problem and Monte Carlo error. Thus, with this study, the recent (as of 2009), deterministic, fast and promising alternative of MCMC called INLA to approximate the posterior marginal has been applicable. The offset variables which is used to adjust number of events and population size was ignored with those previous studies are considered under this study (Tonui et al., 2018; Ojo et al., 2017; Martins et al., 2013; Blangiardo et al., 2015; Rue et al., 2009) .

Most of the researchers have used INLA methods with default priors only which sometimes was bad and without further concise with the approximation methods of INLA. This thesis therefore, addressed the problem of prior assignment by considering the informative Penalized Complexity (PC) prior and intended on the application of different approximation methods of INLA (Riebler et al., 2017; Bivand et al., 2015; Kipruto et al., 2015 )

Thus, the study have attempted to answer the basic research questions on: whether there is variation in the distribution of TB cases among the districts of Jimma zone, whether changes in prior assignment is really affect the candidate model to be selected and answered the questions on how to apply latent Gaussian model with INLA methods under the framework Bayesian hierarchical paradigm.
Objectives

General Objective

The general objective of this study was to model the counts for TB cases in Jimma zone using Bayesian hierarchical approach of latent Gaussian model with INLA method.

Specific Objectives

To see the variation in the distribution of TB cases across districts.
To compare the R-INLA’s inbuilt default priors with the informative penalized complexity priors for robustness of the priors.
To fit latent Gaussian model with INLA methods under the framework Bayesian hierarchical paradigm.

Significance of the Study

The results of this study may help the organization as well as individuals who work on this area to get clue on to what extent TB distribution is serious across the districts of Jimma zone. It may also be an input to see the trend of TB prevalence by comparing the result of this study with existing previous study of the same case and site. The other basic significance of the study is that it may also further assist other researchers interested in this area and they may use it as a benchmark for their future works. In determining the posterior distribution, MCMC simulation technique is the most applicable methods used for a long period of time. But, recently (as of 2009) very fast, convenient and very fast representative approximation technique called INLA which designed for latent Gaussian model is availed. With this study therefore, researchers will benefit by getting familiar with the method and may further helps in advertising the approximation technique. The result of this study will also expected to help those make policy of any TB concern agendas and strategies.