MODELLING COUNT DATA WITH EXCESS ZEROS: AN EMPIRICAL APPLICATION TO TYPHOID FEVER CASES IN OYO STATE, NIGERIA

Abstract

The Poisson and negative binomial regression are most popularly used to model count data but with the limitation of not accounting for the excess zeros in the data which may subsequently lead to biased estimates. Hence, this study modeled the occurrence of typhoid fever in Oyo state while accounting for the excess zeros and over-dispersion in the dataset. A longitudinal surveillance data on typhoid fever cases was obtained from the Integrated Disease Surveillance and Response (IDSR) of Oyo state Ministry of health from 2011 to 2014. The number of reported cases of typhoid in the state was the outcome variable while month of reporting, year of reporting, and local government areas (LGA) were the explanatory variables. The presence of over-dispersion in the data was investigated using the mean and variance. Zero-inflated models such as zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-inflated generalized Poisson (ZIGP), and zero-altered Poisson (ZAP or hurdle) were fitted to the data. The Akaike information criteria (AIC) and the -2Logl were used to select the best model among the four. Descriptive statistics, incidence rate ratios, as well as 95% Cl were determined. The total number of typhoid fever cases reported in the state was 2,970 (Mean=3.46, SD=3.89). There was 34.7% increase of typhoid fever incidence between 2011 and 2012 and decline of 89.0% between 2012 and 2014. About 11% of typhoid cases were reported in February and March while the lowest cases of the disease were reported in October (3.4%). The risk of typhoid was highest in Surulere LGA by 30.7% (IRR=4.307. 95% Cl=0.892, 2.028), followed by Oyo west and Oyo East LGA by 89.0% and 56.2% (IRR.=3.890, 95% Cl=0.799, 1.918); (IRR=3.562. 95% Cl=0.743, 1.798) respectively. In addition, the risk of typhoid was lowest in Atisbo LGA by 54.0% (IRR= 1 .540, 9 5% CI= 0.003, 0.861 ). lbarapa East LGA had 61.0% reduced risk of typhoid fever (IRR= 0.39, 95% CI=-1.309, -0.576). The AIC of the models were 51290.47, 30733.61, 51290.47, 51285.73, for the ZIP, ZINB, ZIGP, and ZAP models respectively, thus indicating that ZINB had the least AIC value. The occurrence of typhoid fever was influenced by season (i.e. Month of reporting) and LGA of reporting. The zero inflated negative binomial (ZINB) was found to be the best regression model to estimate the factors that influences the number of typhoid cases in Oyo state in the presence of over-dispersion. The model is recommended for researchers with similar data.