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

Vincent Moshi Ouma

doi: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.

Highlights

An everlasting fight for humans to cab the virulent of various viruses has been ongoing since time in memorial
The goodness-of-fit test was based on the values of the global deviance, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)
Models with varying dispersion parameters provided better statistical fit for the two datasets as compared to the models with fixed dispersion parameters. This is evidence that the Inverse Gaussian part of the Poisson Inverse Gaussian (PIG) model is more flexible than the Gamma distribution in Negative Binomial (NB) model in handling overdispersed datasets that are common for infectious diseases

Summary

Introduction

An everlasting fight for humans to cab the virulent of various viruses has been ongoing since time in memorial This has been done by use of statistical models. A few studies suggest the PIG model as an alternative to the NB model for modeling count data especially those with longer tails and larger kurtosis [11] [19]. Further extensions of these in recent past have led to the development of mixed models that have the capabilities of handling effectively count data with unique characteristics common to infectious diseases [21]

Objectives

Methods

Results

Conclusion