Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design

Henry Athiany; Anthony Wanjoya; George Orwa; Samuel Mwalili

doi:doi:10.11648/j.ijdsa.20200606.12

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Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design

Henry Athiany, Anthony Wanjoya, George Orwa, Samuel Mwalili

Published in International Journal of Data Science and Analysis (Volume 6, Issue 6)

Received: 12 October 2020 Accepted: 28 October 2020 Published: 4 November 2020

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Abstract

A Bayesian Self-Controlled Case-Series (BSCCS) method is proposed and used to estimate the relative risk of an adverse drug event (ADE) given transient exposure to a drug or vaccine. Markov Chain Monte Carlo (MCMC) methods through WinBUGS are used to estimate parameters of the model given different settings and sample sizes. The method explores full posterior distribution for the model to obtain the relative risk estimates which at times is a challenge in likelihood analysis of complex models. Data was simulated for 10, 20 or 50 children aged between 365 and 730 days, and received their first dose of the measles, mumps, and rubella (MMR) vaccine within this follow-up period. Each child had the outcome event – viral-meningitis, in the follow-up period. Results of the data analysis indicated an increased risk of viral meningitis within 14-35 days post vaccination. Results of Bayesian approach are quite similar to the MLE risk estimates, assuming a non-informative prior. However, with more informative priors, BSCCS method produced better results with narrow credible intervals. For the real data, children aged 365 and 730 days, exposed to MMR vaccine, with viral meningitis (single exposure) were considered. While the frequentist approach estimated the incidence rate ratio (IRR) as IRR 12.037 (95% CI (3.002 - 48.259)), the Bayesian estimate was IRR 8.971 (95% CI 2.869 - 27.994). This is similar to the MLE results but with narrow credible intervals. In all cases, there is significantly higher risk of viral meningitis within 14-35 days post MMR vaccination. Results from the simulation study and real data revealed that the BSCCS model fitted better than the SCCS model.

Published in	International Journal of Data Science and Analysis (Volume 6, Issue 6)
DOI	10.11648/j.ijdsa.20200606.12
Page(s)	170-182
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), 2020. Published by Science Publishing Group

Keywords

Zero-truncated Poisson Distribution, Case-series, Bayesian Self-controlled Case Series, MMR Vaccine, Viral Meningitis

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APA Style

Henry Athiany, Anthony Wanjoya, George Orwa, Samuel Mwalili. (2020). Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design. International Journal of Data Science and Analysis, 6(6), 170-182. https://doi.org/10.11648/j.ijdsa.20200606.12

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ACS Style

Henry Athiany; Anthony Wanjoya; George Orwa; Samuel Mwalili. Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design. Int. J. Data Sci. Anal. 2020, 6(6), 170-182. doi: 10.11648/j.ijdsa.20200606.12

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AMA Style

Henry Athiany, Anthony Wanjoya, George Orwa, Samuel Mwalili. Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design. Int J Data Sci Anal. 2020;6(6):170-182. doi: 10.11648/j.ijdsa.20200606.12

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@article{10.11648/j.ijdsa.20200606.12,
  author = {Henry Athiany and Anthony Wanjoya and George Orwa and Samuel Mwalili},
  title = {Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {6},
  pages = {170-182},
  doi = {10.11648/j.ijdsa.20200606.12},
  url = {https://doi.org/10.11648/j.ijdsa.20200606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200606.12},
  abstract = {A Bayesian Self-Controlled Case-Series (BSCCS) method is proposed and used to estimate the relative risk of an adverse drug event (ADE) given transient exposure to a drug or vaccine. Markov Chain Monte Carlo (MCMC) methods through WinBUGS are used to estimate parameters of the model given different settings and sample sizes. The method explores full posterior distribution for the model to obtain the relative risk estimates which at times is a challenge in likelihood analysis of complex models. Data was simulated for 10, 20 or 50 children aged between 365 and 730 days, and received their first dose of the measles, mumps, and rubella (MMR) vaccine within this follow-up period. Each child had the outcome event – viral-meningitis, in the follow-up period. Results of the data analysis indicated an increased risk of viral meningitis within 14-35 days post vaccination. Results of Bayesian approach are quite similar to the MLE risk estimates, assuming a non-informative prior. However, with more informative priors, BSCCS method produced better results with narrow credible intervals. For the real data, children aged 365 and 730 days, exposed to MMR vaccine, with viral meningitis (single exposure) were considered. While the frequentist approach estimated the incidence rate ratio (IRR) as IRR 12.037 (95% CI (3.002 - 48.259)), the Bayesian estimate was IRR 8.971 (95% CI 2.869 - 27.994). This is similar to the MLE results but with narrow credible intervals. In all cases, there is significantly higher risk of viral meningitis within 14-35 days post MMR vaccination. Results from the simulation study and real data revealed that the BSCCS model fitted better than the SCCS model.},
 year = {2020}
}

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TY - JOUR
T1 - Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design
AU - Henry Athiany
AU - Anthony Wanjoya
AU - George Orwa
AU - Samuel Mwalili
Y1 - 2020/11/04
PY - 2020
N1 - https://doi.org/10.11648/j.ijdsa.20200606.12
DO - 10.11648/j.ijdsa.20200606.12
T2 - International Journal of Data Science and Analysis
JF - International Journal of Data Science and Analysis
JO - International Journal of Data Science and Analysis
SP - 170
EP - 182
PB - Science Publishing Group
SN - 2575-1891
UR - https://doi.org/10.11648/j.ijdsa.20200606.12
AB - A Bayesian Self-Controlled Case-Series (BSCCS) method is proposed and used to estimate the relative risk of an adverse drug event (ADE) given transient exposure to a drug or vaccine. Markov Chain Monte Carlo (MCMC) methods through WinBUGS are used to estimate parameters of the model given different settings and sample sizes. The method explores full posterior distribution for the model to obtain the relative risk estimates which at times is a challenge in likelihood analysis of complex models. Data was simulated for 10, 20 or 50 children aged between 365 and 730 days, and received their first dose of the measles, mumps, and rubella (MMR) vaccine within this follow-up period. Each child had the outcome event – viral-meningitis, in the follow-up period. Results of the data analysis indicated an increased risk of viral meningitis within 14-35 days post vaccination. Results of Bayesian approach are quite similar to the MLE risk estimates, assuming a non-informative prior. However, with more informative priors, BSCCS method produced better results with narrow credible intervals. For the real data, children aged 365 and 730 days, exposed to MMR vaccine, with viral meningitis (single exposure) were considered. While the frequentist approach estimated the incidence rate ratio (IRR) as IRR 12.037 (95% CI (3.002 - 48.259)), the Bayesian estimate was IRR 8.971 (95% CI 2.869 - 27.994). This is similar to the MLE results but with narrow credible intervals. In all cases, there is significantly higher risk of viral meningitis within 14-35 days post MMR vaccination. Results from the simulation study and real data revealed that the BSCCS model fitted better than the SCCS model.
VL - 6
IS - 6
ER -

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Author Information

Henry Athiany

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
George Orwa

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Samuel Mwalili

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Henry Athiany, Anthony Wanjoya, George Orwa, Samuel Mwalili. (2020). Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design. International Journal of Data Science and Analysis, 6(6), 170-182. https://doi.org/10.11648/j.ijdsa.20200606.12

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ACS Style

Henry Athiany; Anthony Wanjoya; George Orwa; Samuel Mwalili. Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design. Int. J. Data Sci. Anal. 2020, 6(6), 170-182. doi: 10.11648/j.ijdsa.20200606.12

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AMA Style

Henry Athiany, Anthony Wanjoya, George Orwa, Samuel Mwalili. Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design. Int J Data Sci Anal. 2020;6(6):170-182. doi: 10.11648/j.ijdsa.20200606.12

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@article{10.11648/j.ijdsa.20200606.12,
  author = {Henry Athiany and Anthony Wanjoya and George Orwa and Samuel Mwalili},
  title = {Bayesian Analysis of Zero-Truncated Poisson Model: Application to the Self-Controlled Case-series Design},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {6},
  pages = {170-182},
  doi = {10.11648/j.ijdsa.20200606.12},
  url = {https://doi.org/10.11648/j.ijdsa.20200606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200606.12},
  abstract = {A Bayesian Self-Controlled Case-Series (BSCCS) method is proposed and used to estimate the relative risk of an adverse drug event (ADE) given transient exposure to a drug or vaccine. Markov Chain Monte Carlo (MCMC) methods through WinBUGS are used to estimate parameters of the model given different settings and sample sizes. The method explores full posterior distribution for the model to obtain the relative risk estimates which at times is a challenge in likelihood analysis of complex models. Data was simulated for 10, 20 or 50 children aged between 365 and 730 days, and received their first dose of the measles, mumps, and rubella (MMR) vaccine within this follow-up period. Each child had the outcome event – viral-meningitis, in the follow-up period. Results of the data analysis indicated an increased risk of viral meningitis within 14-35 days post vaccination. Results of Bayesian approach are quite similar to the MLE risk estimates, assuming a non-informative prior. However, with more informative priors, BSCCS method produced better results with narrow credible intervals. For the real data, children aged 365 and 730 days, exposed to MMR vaccine, with viral meningitis (single exposure) were considered. While the frequentist approach estimated the incidence rate ratio (IRR) as IRR 12.037 (95% CI (3.002 - 48.259)), the Bayesian estimate was IRR 8.971 (95% CI 2.869 - 27.994). This is similar to the MLE results but with narrow credible intervals. In all cases, there is significantly higher risk of viral meningitis within 14-35 days post MMR vaccination. Results from the simulation study and real data revealed that the BSCCS model fitted better than the SCCS model.},
 year = {2020}
}

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