Zero Inflated Regression Models with Application to Malaria Surveillance Data

Monthly reports of malaria cases are usually presented as count data potentially with excess zeros. The standard Poisson and negative binomial regression used for modeling such data cannot account for excess zeros and over-dispersion. Hence, this study was designed to model the annual trends in the occurrence of malaria among under-5 children using the zero inflated negative binomial (ZINB) and zero inflated Poisson regression (ZIP). The study also determined the effects of month, year and geographical location on the occurrence of malaria. Malaria surveillance data were obtained from the Integrated Disease Surveillance and Response (IDSR) of Oyo State Ministry of Health, Nigeria from 2010 - 2014. Descriptive statistics were conducted to check for the presence of over-dispersion. Model comparisons were performed between ZINB and ZIP and the best model was selected using Vuong z-statistic criteria. Incidence rate ratios and 95% CI were determined. There were slight variations in the incidence of malaria cases; 35.81 per 1000 in 2011, 35.64 per 1000 in 2013 and 35.72 per 1000 in 2014. The highest risk of malaria was in the year 2014 (IRR = 3.59, 95% CI: 3.05, 4.23) and lowest in 2012 (IRR =2.56, 95% CI: 2.31, 2.83). The risk of malaria was highest in October (IRR = 1.47, 95% CI: 1.15, 1.88) and lowest in January (IRR = 0.80, 95% CI: 0.69, 0.94). The highest risk of malaria was reported in Saki West (IRR= 4.77, 95% CI: 3.58, 6.35) and lowest in Ogbomoso South (IRR = 0.73, 95% CI: 0.55, 0.97). The Vuong z-statistic for the ZINB and ZIP models was -17.079 (i.e. V u003c -1.96), indicating that ZINB fits the data better. The zero inflated negative binomial regression is the best model to determine the factors that predict the number of cases of malaria, when there is an indication of over dispersion and excess zeros. Zero inflated negative binomial model is suggested for researchers dealing with similar data.