International Journal of Data Science and Analysis

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

Received: 12 October 2020    Accepted: 28 October 2020    Published: 04 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.

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

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

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

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

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya; Deputy Principal, Bomet University College, Bomet, Kenya

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

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    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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    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://download.sciencepg.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
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    DO  - 10.11648/j.ijdsa.20200606.12
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    JF  - International Journal of Data Science and Analysis
    JO  - International Journal of Data Science and Analysis
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    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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