Associated factor of mortality rate amongst patients with AIDS and HIV-TB co-infections using zero inflated negative binomial method - Abdullah, Mohd Asrul Affendi (2014)
Many data sets are characterized as count data with a preponderance of zeros. Data in the form of counts and proportions arise in many fields such as studies in medicine, public health, toxicology, epidemiology, sociology, psychology, engineering, agriculture and soon. When the dependent variable is a nonnegative count variable, a Poisson regression model is commonly used to explain the relationship between the outcome variable and a set of explanatory variables. However, if extra-zero Poisson counts are observed, it has been suggested that a zero-inflated Poisson regression model is more appropriate than the classical Poisson regression model. One frequently encountered problem in these data is that simple models such as the Poisson and the Binomial models failed to explain the variation that exists. Often, data exhibit extra-dispersion (over or under dispersion). Another complication in data in the form of counts and proportions is that they are sometimes too sparse, that is smaller values have greater tendency to occur. In the Poisson case counts that occur are generally small and in the binomial case the binomial denominators are often small. Therefore, valid procedures are needed to detect departures from the simple models. Hence, when a lot of extra zero exists, zero inflated Negative Binomial has been suggested when overdispersion is present. It is more appropriate than the classical Negative Binomial regression model. Hence, this thesis follows the general objective, that is to compare Zero-Inflated Negative Binomial and Negative Binomial in identifying associated factors. The specific objective is to fit a Zero-Inflated Negative Binomial death rate regression model for mortality rate among AIDS/HIV co-infection patients and to compare Zero-Inflated Negative Binomial death rate regression with Negative Binomial death rate, which is the best model when a data existing zeroes values. It follows by to determine overdispersion in the model. Lastly, to investigate the potential confounding factors affecting mortality rate among disease mapping coinfection patients among HIV-TB and AIDS. In this thesis, mortality rate is a subject of interest as dependent variable according to age categories by years. The data are analyzed from AIDS patients and HIV-TB mortality cases for comparing between Negative Binomial mortality and Zero Inflated Negative Binomial Mortality (ZINBM) which is better. Beyond this substantive concern, the choice should be based on the model providing the closest fit between the observed and predicted values. Unfortunately, the literature presents anomalous findings in terms of model superiority. In addition, the Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) values were used to compare the fit between models. The results suggested that the literature are not entirely anomalous. However, the accuracy of the findings depended on the proportion of zeros and the distribution for the non zeros. ZINBDR tend to be the superior model, than the negative binomial model. The findings suggested there should be consideration of the proportion of zeroes and the distribution for the nonzero when selecting a model to accommodate zero-inflated data.