Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data

Vincent Moshi Ouma; Samuel Musili Mwalili; Anthony Wanjoya Kiberia

doi:doi:10.11648/j.ajtas.20160505.22

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Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data

Vincent Moshi Ouma, Samuel Musili Mwalili, Anthony Wanjoya Kiberia

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

Received: 9 September 2016 Accepted: 21 September 2016 Published: 10 October 2016

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Abstract

Traditionally, statistical models provide a general basis for analysis of infectious disease count data with its unique characteristics such as low disease counts, underreporting, reporting delays, seasonality, past outbreaks and lack of a number of susceptible. Through this approach, statistical models have provided a popular means of estimating safety performance of various health elements. Predictions relating to infectious disease outbreaks by use of statistical models have been based on Poisson modeling framework and Negative Binomial (NB) modeling framework in the case of overdispersion within the count data. Recent studies have proved that the Poisson- Inverse Gaussian (PIG) model can be used to analyze count data that is highly overdispersed which cannot be effectively analyzed by the traditional Negative Binomial model. A PIG model with fixed/varying dispersion parameters is fitted to two infectious disease datasets and its performance in terms of goodness-of-fit and future outbreak predictions of infectious disease is compared to that of the traditional NB model.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.22
Page(s)	326-333
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), 2016. Published by Science Publishing Group

Keywords

Mixed Models, Poisson-Inverse Gaussian Distribution, Negative Binomial Distribution, Infectious Disease

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APA Style

Vincent Moshi Ouma, Samuel Musili Mwalili, Anthony Wanjoya Kiberia. (2016). Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data. American Journal of Theoretical and Applied Statistics, 5(5), 326-333. https://doi.org/10.11648/j.ajtas.20160505.22

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ACS Style

Vincent Moshi Ouma; Samuel Musili Mwalili; Anthony Wanjoya Kiberia. Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data. Am. J. Theor. Appl. Stat. 2016, 5(5), 326-333. doi: 10.11648/j.ajtas.20160505.22

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AMA Style

Vincent Moshi Ouma, Samuel Musili Mwalili, Anthony Wanjoya Kiberia. Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data. Am J Theor Appl Stat. 2016;5(5):326-333. doi: 10.11648/j.ajtas.20160505.22

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@article{10.11648/j.ajtas.20160505.22,
  author = {Vincent Moshi Ouma and Samuel Musili Mwalili and Anthony Wanjoya Kiberia},
  title = {Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {326-333},
  doi = {10.11648/j.ajtas.20160505.22},
  url = {https://doi.org/10.11648/j.ajtas.20160505.22},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.22},
  abstract = {Traditionally, statistical models provide a general basis for analysis of infectious disease count data with its unique characteristics such as low disease counts, underreporting, reporting delays, seasonality, past outbreaks and lack of a number of susceptible. Through this approach, statistical models have provided a popular means of estimating safety performance of various health elements. Predictions relating to infectious disease outbreaks by use of statistical models have been based on Poisson modeling framework and Negative Binomial (NB) modeling framework in the case of overdispersion within the count data. Recent studies have proved that the Poisson- Inverse Gaussian (PIG) model can be used to analyze count data that is highly overdispersed which cannot be effectively analyzed by the traditional Negative Binomial model. A PIG model with fixed/varying dispersion parameters is fitted to two infectious disease datasets and its performance in terms of goodness-of-fit and future outbreak predictions of infectious disease is compared to that of the traditional NB model.},
 year = {2016}
}

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TY  - JOUR
T1  - Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data
AU  - Vincent Moshi Ouma
AU  - Samuel Musili Mwalili
AU  - Anthony Wanjoya Kiberia
Y1  - 2016/10/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.22
DO  - 10.11648/j.ajtas.20160505.22
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 326
EP  - 333
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.22
AB  - Traditionally, statistical models provide a general basis for analysis of infectious disease count data with its unique characteristics such as low disease counts, underreporting, reporting delays, seasonality, past outbreaks and lack of a number of susceptible. Through this approach, statistical models have provided a popular means of estimating safety performance of various health elements. Predictions relating to infectious disease outbreaks by use of statistical models have been based on Poisson modeling framework and Negative Binomial (NB) modeling framework in the case of overdispersion within the count data. Recent studies have proved that the Poisson- Inverse Gaussian (PIG) model can be used to analyze count data that is highly overdispersed which cannot be effectively analyzed by the traditional Negative Binomial model. A PIG model with fixed/varying dispersion parameters is fitted to two infectious disease datasets and its performance in terms of goodness-of-fit and future outbreak predictions of infectious disease is compared to that of the traditional NB model.
VL  - 5
IS  - 5
ER  -

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Author Information

Vincent Moshi Ouma

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

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

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

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Plain Text BibTeX RIS

APA Style

Vincent Moshi Ouma, Samuel Musili Mwalili, Anthony Wanjoya Kiberia. (2016). Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data. American Journal of Theoretical and Applied Statistics, 5(5), 326-333. https://doi.org/10.11648/j.ajtas.20160505.22

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ACS Style

Vincent Moshi Ouma; Samuel Musili Mwalili; Anthony Wanjoya Kiberia. Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data. Am. J. Theor. Appl. Stat. 2016, 5(5), 326-333. doi: 10.11648/j.ajtas.20160505.22

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AMA Style

Vincent Moshi Ouma, Samuel Musili Mwalili, Anthony Wanjoya Kiberia. Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data. Am J Theor Appl Stat. 2016;5(5):326-333. doi: 10.11648/j.ajtas.20160505.22

Copy | Download

@article{10.11648/j.ajtas.20160505.22,
  author = {Vincent Moshi Ouma and Samuel Musili Mwalili and Anthony Wanjoya Kiberia},
  title = {Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {326-333},
  doi = {10.11648/j.ajtas.20160505.22},
  url = {https://doi.org/10.11648/j.ajtas.20160505.22},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.22},
  abstract = {Traditionally, statistical models provide a general basis for analysis of infectious disease count data with its unique characteristics such as low disease counts, underreporting, reporting delays, seasonality, past outbreaks and lack of a number of susceptible. Through this approach, statistical models have provided a popular means of estimating safety performance of various health elements. Predictions relating to infectious disease outbreaks by use of statistical models have been based on Poisson modeling framework and Negative Binomial (NB) modeling framework in the case of overdispersion within the count data. Recent studies have proved that the Poisson- Inverse Gaussian (PIG) model can be used to analyze count data that is highly overdispersed which cannot be effectively analyzed by the traditional Negative Binomial model. A PIG model with fixed/varying dispersion parameters is fitted to two infectious disease datasets and its performance in terms of goodness-of-fit and future outbreak predictions of infectious disease is compared to that of the traditional NB model.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Poisson Inverse Gaussian (PIG) Model for Infectious Disease Count Data
AU  - Vincent Moshi Ouma
AU  - Samuel Musili Mwalili
AU  - Anthony Wanjoya Kiberia
Y1  - 2016/10/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.22
DO  - 10.11648/j.ajtas.20160505.22
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 326
EP  - 333
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.22
AB  - Traditionally, statistical models provide a general basis for analysis of infectious disease count data with its unique characteristics such as low disease counts, underreporting, reporting delays, seasonality, past outbreaks and lack of a number of susceptible. Through this approach, statistical models have provided a popular means of estimating safety performance of various health elements. Predictions relating to infectious disease outbreaks by use of statistical models have been based on Poisson modeling framework and Negative Binomial (NB) modeling framework in the case of overdispersion within the count data. Recent studies have proved that the Poisson- Inverse Gaussian (PIG) model can be used to analyze count data that is highly overdispersed which cannot be effectively analyzed by the traditional Negative Binomial model. A PIG model with fixed/varying dispersion parameters is fitted to two infectious disease datasets and its performance in terms of goodness-of-fit and future outbreak predictions of infectious disease is compared to that of the traditional NB model.
VL  - 5
IS  - 5
ER  -

Copy | Download