ZERO-INFLATED COUNT MODELS WITH APPLICATION TO ANNUAL TRENDS IN THE INCIDENCE OF SELECTED INFECTIOUS DISEASE AMONG UNDER-5 CHILDREN IN OYO STATE, NIGERIA

Abstract

Cases of infectious diseases reported monthly to health facility are usually presented as count data potentially with excess zeros. Poisson and negative binomial regression have been used for modeling count data but do not take into account the presence of excess zeros and the problem of over-dispersion. Hence, this study was designed to model the annual trends in the incidence of infectious diseases among under-5 children using the better of two statistical models - zero inflated negative binomial (ZINB) and zero inflated Poisson regression (ZIP) - to determine the effects of month, year and geographical location on the occurrence of malaria, pneumonia, diarrhoea and measles among under-5 children. A longitudinal surveillance data of under-5 children was obtained from the Integrated Diseases Surveillance and Response (IDSR) of Oyo State Ministry of Health from 2010 to 2014.The number of cases of malaria, pneumonia, diarrhea and measles per local government area were outcome variables and explanatory variables were month of reporting. year of reporting and the LGAs. 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 based on the values of Vuong z-statistic, AIC and BIC selection criteria. The ZINB regression model was used to determine the effects of month, year of reporting and LGA on the occurrence of infectious diseases, incidence rate ratios and 95% Cl were recorded. The Analyses were conducted using SPSS version 20, Microsoft Excel and R statistical package. The incidence of malaria cases decreased slightly from, 35.81 per 1000 in 2011 to 35.64 per 1000 in 2013.The highest incidence rate of pneumonia was in 2012 (7 per 1000). The incidence rate for diarrhoea was (20.36 per 1000) in 2010. The incidence of measles was static at (1.01 per 1000) from 2011 to 2013. The Vuong z-statistic of the ZlNB models were -17.079, 7.952. - 12.372 and -3.656, the BIC corrected were -17.079. -7.952, -12.372 and -3.577 and BIC corrected were -17.079, -7.952, -12.372 and -3.355 for malaria, pneumonia, diarrhea and measles respectively. ZINB model showed V < -1.96 on the three tests criteria for the four infectious diseases, thus indicating that ZINB had the best fit. The risk of malaria was highest in 2014 by 258.9% (IRR = 3.589, 95% CI: 3.045, 4.232). The risk of pneumonia was lowest in 2014 by 82.7% (IRR= 0.173, 95% CI: 0.092, 0.324). Risk of diarrhoea was lowest in 2011 by 22.7% (IRR = 0.773, 95% Cl: 0.688, 0.867). Risk of measles was lowest in 2012 by 90.4% (IRR= 0.096. 95% CI: 0.043, 0.217). There was a general decline in the incidence of malaria and diarrhea, a modest increase in measles incidence and an initial rise with subsequent decline in pneumonia incidence. The year of reporting was a predictor of the occurrence of these infectious diseases. The study suggests ZINB as the best model for researchers dealing with count data having excess zeros and over-dispersion.