Bayesian Spatial Modelling of Tuberculosis Incidence in Meru County, Kenya Using Conditional Autoregressive(CAR) and Poisson Lognormal(PLN) Models

Kithaka Gilbert Mucheri^1, , Peter Kinyua Gachoki¹ and Kilai Mutua¹

¹Department of Pure and Applied Sciences, Kirinyaga University

Cite this paper:
Kithaka Gilbert Mucheri, Peter Kinyua Gachoki and Kilai Mutua. Bayesian Spatial Modelling of Tuberculosis Incidence in Meru County, Kenya Using Conditional Autoregressive(CAR) and Poisson Lognormal(PLN) Models. American Journal of Applied Mathematics and Statistics. 2024; 12(3):55-65. doi: 10.12691/ajams-12-3-3

Abstract

Establishing the patterns of a disease or disease mapping is very important in disease control and prevention. The level of accuracy that is achieved at this stage determines the effectiveness of control measures to be developed. Disease mapping has been widely done using the frequentist approach which is limited in that it does not consider prior probability distribution of a phenomenon. This limitation leads to lower levels of accuracy and validity. This study proposed a Bayesian Approach for mapping tuberculosis incidence in Meru County, Kenya. Correlational research design was utilized to determine association between TB cases and geographical locations where the cases were positively identified. Secondary data from the Meru County Health Records was used for this study. Spatial autocorrelation was performed to determine patterns of TB incidence. The study applied Conditional Autoregressive (CAR) model and Poisson Lognormal (PLN) model under the Bayesian Approach to model TB incidence in order to determine spatial temporal trends. Parameter estimation for the models was done using GIBBs Sampling under Markov Chain Monte-Carlo (MCMC). The two models (PLN and CAR) were compared using Deviance Information Criteria (DIC) to determine the one that had a better fit. Morans's I statistic was -0.3150 (p>0.05) meaning that there was no spatial autocorrelation for TB incidence in Meru County. Model results further indicated that there was no spacial dependence for TB incidence in Meru County. Deviance Information Criterion (DIC) values obtained were 0.22541 for CAR model and 0.56723 for PLN model meaning that CAR model had outperformed the PLN model. The study concluded that CAR model is more effective for disease mapping since it incorporates information from neighboring regions directly into the model to increase accuracy of estimates. Therefore, the study recommended use of Bayesian modelling for disease mapping as it incorporates prior information to stabilize the parameter estimates.

Keywords:
tuberculosis bayesian spatial models spatial dependency conditional autoregressive model poisson lognormal model poisson gamma model

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