Modeling Overdispersed Dengue Data via Poisson Inverse Gaussian Regression Model: A Case Study in the City of Campo Grande, MS, Brazil.

Dengue fever is a tropical disease transmitted mainly by the female mosquito that affects millions of people every year. As there is still no safe and effective vaccine, currently the best way to prevent the disease is to control the proliferation of the transmitting mosquito. Since the proliferation and life cycle of the mosquito depend on environmental variables such as temperature and water availability, among others, statistical models are needed to understand the existing relationships between environmental variables and the recorded number of dengue cases and predict the number of cases for some future time interval. This prediction is of paramount importance for the establishment of control policies. In general, dengue-fever datasets contain the number of cases recorded periodically (in days, weeks, months or years). Since many dengue-fever datasets tend to be of the overdispersed, long-tail type, some common models like the Poisson regression model or negative binomial regression model are not adequate to model it. For this reason, in this paper we propose modeling a dengue-fever dataset by using a Poisson-inverse-Gaussian regression model. The main advantage of this model is that it adequately models overdispersed long-tailed data because it has a wider skewness range than the negative binomial distribution. We illustrate the application of this model in a real dataset and compare its performance to that of a negative binomial regression model.