Modelling Overdispersion in Disease Count Data: A Statistical Application to Cholera Outbreak Records in Borno State

Count data on disease outbreak cases frequently exhibit overdispersion, where variance exceeds the mean, rendering Poisson-based models statistically inappropriate and requiring negative binomial or zero-inflated regression alternatives that are rarely applied in Nigerian epidemiological practice. This study models overdispersion in cholera outbreak count data from Borno State, North East Nigeria, comparing Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial regression specifications. Weekly cholera case counts disaggregated by LGA from 2017 to 2022 were obtained from the Borno State Ministry of Health and the Nigeria Centre for Disease Control. Overdispersion was formally tested by Cameron-Trivedi auxiliary regression. Model comparison used Akaike and Bayesian information criteria. Vuong tests discriminated between standard and zero-inflated models. The Cameron-Trivedi test confirmed severe overdispersion (coefficient = 2.84, p < 0.001). The zero-inflated negative binomial model provided the best statistical fit (AIC = 4,218 vs Poisson AIC = 8,941). The zero-inflation component showed that 38 percent of zero case weeks reflected structural absence of cholera risk, distinct from sampling zeros. LGA population density (IRR = 1.42), displacement camp proximity (IRR = 2.3), and rainfall lagged by two weeks (IRR = 1.18) were significant case count predictors. The study demonstrates the statistical importance of correct count model specification in Nigerian outbreak analysis and recommends zero-inflated negative binomial as the default for weekly outbreak surveillance count data. Keywords: overdispersion, negative binomial regression, cholera, Borno State, count data modelling