Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model

Endale Alemayehu; Reta Habtamu; Akalu Banbeta

doi:doi:10.11648/j.bio.20200801.12

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Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model

Endale Alemayehu, Reta Habtamu, Akalu Banbeta

Received: 10 January 2020 Accepted: 26 February 2020 Published: 19 May 2020

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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. Africa has shared around 25% of the incidence and specifically in Ethiopia around 82 thousand was caught by Tuberculosis. Methods: The study has been conducted in, south west Ethiopia, Jimma zone of entire districts and the data is basically secondary which is obtained from Jimma zone health office. The counts of Tuberculosis case counts 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 of the parameters of interest. Results: The Latent Gaussian Model (LGM) 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: 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.

DOI	10.11648/j.bio.20200801.12
Published in	American Journal of Bioscience and Bioengineering (Volume 8, Issue 1, February 2020)
Page(s)	7-16
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Tuberculosis, Bayesian Approach, LGM, INLA

References

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Endale Alemayehu, Reta Habtamu, Akalu Banbeta. (2020). Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model. American Journal of Bioscience and Bioengineering, 8(1), 7-16. https://doi.org/10.11648/j.bio.20200801.12

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Endale Alemayehu; Reta Habtamu; Akalu Banbeta. Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model. Am. J. BioSci. Bioeng. 2020, 8(1), 7-16. doi: 10.11648/j.bio.20200801.12

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Endale Alemayehu, Reta Habtamu, Akalu Banbeta. Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model. Am J BioSci Bioeng. 2020;8(1):7-16. doi: 10.11648/j.bio.20200801.12

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@article{10.11648/j.bio.20200801.12,
  author = {Endale Alemayehu and Reta Habtamu and Akalu Banbeta},
  title = {Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model},
  journal = {American Journal of Bioscience and Bioengineering},
  volume = {8},
  number = {1},
  pages = {7-16},
  doi = {10.11648/j.bio.20200801.12},
  url = {https://doi.org/10.11648/j.bio.20200801.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bio.20200801.12},
  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. Africa has shared around 25% of the incidence and specifically in Ethiopia around 82 thousand was caught by Tuberculosis. Methods: The study has been conducted in, south west Ethiopia, Jimma zone of entire districts and the data is basically secondary which is obtained from Jimma zone health office. The counts of Tuberculosis case counts 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 of the parameters of interest. Results: The Latent Gaussian Model (LGM) 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: 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.},
 year = {2020}
}

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TY  - JOUR
T1  - Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model
AU  - Endale Alemayehu
AU  - Reta Habtamu
AU  - Akalu Banbeta
Y1  - 2020/05/19
PY  - 2020
N1  - https://doi.org/10.11648/j.bio.20200801.12
DO  - 10.11648/j.bio.20200801.12
T2  - American Journal of Bioscience and Bioengineering
JF  - American Journal of Bioscience and Bioengineering
JO  - American Journal of Bioscience and Bioengineering
SP  - 7
EP  - 16
PB  - Science Publishing Group
SN  - 2328-5893
UR  - https://doi.org/10.11648/j.bio.20200801.12
AB  - 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. Africa has shared around 25% of the incidence and specifically in Ethiopia around 82 thousand was caught by Tuberculosis. Methods: The study has been conducted in, south west Ethiopia, Jimma zone of entire districts and the data is basically secondary which is obtained from Jimma zone health office. The counts of Tuberculosis case counts 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 of the parameters of interest. Results: The Latent Gaussian Model (LGM) 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: 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.
VL  - 8
IS  - 1
ER  -

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Author Information

Endale Alemayehu

Department of Statistics, College of Natural Sciences, Ambo University, Ambo, Ethiopia
Reta Habtamu

Department of Statistics, College of Natural Sciences, Jimma University, Jimma, Ethiopia
Akalu Banbeta

Department of Statistics, College of Natural Sciences, Jimma University, Jimma, Ethiopia

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Endale Alemayehu, Reta Habtamu, Akalu Banbeta. (2020). Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model. American Journal of Bioscience and Bioengineering, 8(1), 7-16. https://doi.org/10.11648/j.bio.20200801.12

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Endale Alemayehu; Reta Habtamu; Akalu Banbeta. Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model. Am. J. BioSci. Bioeng. 2020, 8(1), 7-16. doi: 10.11648/j.bio.20200801.12

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AMA Style

Endale Alemayehu, Reta Habtamu, Akalu Banbeta. Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model. Am J BioSci Bioeng. 2020;8(1):7-16. doi: 10.11648/j.bio.20200801.12

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@article{10.11648/j.bio.20200801.12,
  author = {Endale Alemayehu and Reta Habtamu and Akalu Banbeta},
  title = {Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model},
  journal = {American Journal of Bioscience and Bioengineering},
  volume = {8},
  number = {1},
  pages = {7-16},
  doi = {10.11648/j.bio.20200801.12},
  url = {https://doi.org/10.11648/j.bio.20200801.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bio.20200801.12},
  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. Africa has shared around 25% of the incidence and specifically in Ethiopia around 82 thousand was caught by Tuberculosis. Methods: The study has been conducted in, south west Ethiopia, Jimma zone of entire districts and the data is basically secondary which is obtained from Jimma zone health office. The counts of Tuberculosis case counts 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 of the parameters of interest. Results: The Latent Gaussian Model (LGM) 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: 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.},
 year = {2020}
}

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TY  - JOUR
T1  - Analysis of TB Case Counts in Southwest Ethiopia Using Bayesian Hierarchical Approach of the Latent Gaussian Model
AU  - Endale Alemayehu
AU  - Reta Habtamu
AU  - Akalu Banbeta
Y1  - 2020/05/19
PY  - 2020
N1  - https://doi.org/10.11648/j.bio.20200801.12
DO  - 10.11648/j.bio.20200801.12
T2  - American Journal of Bioscience and Bioengineering
JF  - American Journal of Bioscience and Bioengineering
JO  - American Journal of Bioscience and Bioengineering
SP  - 7
EP  - 16
PB  - Science Publishing Group
SN  - 2328-5893
UR  - https://doi.org/10.11648/j.bio.20200801.12
AB  - 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. Africa has shared around 25% of the incidence and specifically in Ethiopia around 82 thousand was caught by Tuberculosis. Methods: The study has been conducted in, south west Ethiopia, Jimma zone of entire districts and the data is basically secondary which is obtained from Jimma zone health office. The counts of Tuberculosis case counts 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 of the parameters of interest. Results: The Latent Gaussian Model (LGM) 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: 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.
VL  - 8
IS  - 1
ER  -

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