A STUDY OF AN EFFICIENCY OF HANDLING OVERDISPERSION USING POISSON REGRESSION AND ZERO INFLATED POISSON REGRESSION: A THALASEMIA CASE STUDY

Abstract

Thalassemia is a blood related illness though descendant. Increasing number of patients suffering from thalassemia, especially among children has been reported year by year and has been identified ahead of other hereditary diseases in many parts of the world especially in Malaysia. Therefore, the increasing numbers of this illness annually, attracts the interest among the researchers to put an extra effort in order to overcome this illness. Other than that, most patients were also exposed other chronic diseases such as hemorrhagic illness, health problems, heart failure, influenza, anemia, pneumonia, acute bronchitis, asthma, acute tonsillitis, jaundice and tuberculosis. Data from patients especially among children has been successfully collected and it has been manifested in the form of statistic for analysis. The collected data then has been categorized according to certain scales appropriate to the analysis conducted. Due to the existence of many zero values in the data, the data is said to be suffering from over dispersion. This problem can be overcome by means of a zero-inflated Poisson regression model to reduce the value of zero. These models involved in this research are the Poisson regression model and the zero-inflated Poisson regression model. These methods are widely used to analyze count data. Actually these models are part of class of models in generalized linear models (GLM). One requirement of the Poisson distribution model is that the mean is equal to the variance. While the zero-inflated Poisson regression model applied when the mean is smaller than the variance. The results showed that, the percentage of male patients is slightly higher than the female patients and patients consist of Malays (91.0%), Chinese (6.1%), Indians (0.4%) and other races (2.4%). Apart from the research done, it showed that the thalassemia patients have a significant relation to the predictor variables such as health problems 1.0768 (p=0.0001), heart failure 0.9911(p=0.0001), influenza 0.5576 (p=0.0012), anemia 0.3868 (p=0.0001), pneumonia 0.6962 (p=0.0001), acute bronchitis 0.7090 (p=0.0001), asthma 0.8172 (p=0.0001), acute tonsillitis 0.5715 (p=0.0002), jaundice 1.7287 (p=0.0001) and tuberculosis 1.0139 (p=0.0002). However, for variable of hemorrhagic illness was found that the value of p is greater than the significant level and in conclusion, this variable is not significant to the case studies conducted. Based on the selection of the best model, the value of p for Vuong test is positive and statistically significant (p less than 0.0001, n=930). Thus, the final result from the analysis showed the zero-inflated Poisson regression model is more suitable in order to analyze the data of thalasemia patients among children. This is because, Poisson regression model is most appropriate for data that has no overdispersion while zero-inflated Poisson regression model is most appropriate for data that has overdispersion. This research can be used as the strategy of a better health management especially in patient management, to cut down the number of thalassemia patients among children.