ABSTRACT

This research entails, the differential incidence of Type 2 Diabetes Mellitus between male and female using Beta-Binomial and Negative Binomial models. From the previous works done we discovered that Type 2 Diabetes Mellitus incidence is at increase level in the Region and Localities across the country.In view of this we intend to study gender sensitivity to Type 2 Diabetes Mellitus. Secondary data for a period of 10 years were collected from medical records of General Hospital, Ifaki-Ekiti. Beta-Binomial and Negative Binomial models were used to fit the Type 2 Diabetes mellitus between male and female patients and to estimate the parameter of both model on type 2 diabetes mellitus between male and female patients.The two models were compared in term of goodness of fit and best fit using AIC with appropriate confidence interval obtained for the two fitted models . The study revealed that Beta-Binomial out performed Negative Binomial model in fitting the incidence of Type 2 Diabetes mellitus. Therefore, the result shows that Beta-Binomial is a good compound distribution to fit a model on type 2 diabetes mellitus.

TABLE OF CONTENTS

over Page………………………………………………………………………..…………..i
Title Page………………………………………………………………………….…………ii
Declaration …………………………………………………………………………………………………………………. iii
Certification ……………………………………………………………………………………………………………….. iv
Dedication ………………………………………………………………………………………………………………….. iv
Acknowledgements ……………………………………………………………………………………………………… v
Abstract ……………………………………………………………………………………………………………………… vi
List of Figures……………………………………………………………………………………………………………… x
List of Tables ……………………………………………………………………………………………………………… xi
List of Appendices …………………………………………………………………………………………………….. xii
CHAPTER ONE ………………………………………………………………………………………………………… 1
INTRODUCTION ……………………………………………………………………………………………………… 1
1.1Background to the Study …………………………………………………………………………………………. 1
1.2 Statement of the problem ……………………………………………………………………………………… 2
1.3 Aim and Objectives of the Study …………………………………………………………………………….. 3
1.4 Justification of the Study ………………………………………………………………………………………… 3
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CHAPTER TWO ………………………………………………………………………………………………………. 5
LITERATURE REVIEW ………………………………………………………………………………………….. 5
2.1 Review of Related Literature ………………………………………………………………………………….. 5
2.2 Types / Classification of Diabetes Mellitus ……………………………………………………………. 12
2.3 PREDIABETES …………………………………………………………………………………………………… 14
2.4 Limitation of Negative Binomial Distribution…………………………………………15
CHAPTER THREE …………………………………………………………………………………………………. 16
RESEARCH METHODOLOGY …………………………………………………………………………….. 16
3.1 Introduction …………………………………………………………………………………………………………. 16
3.2 Method of Data Collection ……………………………………………………………………………….. 16
3.3 Beta-Binomial ……………………………………………………………………………………………………… 16
3.4 Credible interval ………………………………………………………………………………………………. 17
3.5 Derivation of Beta-Binomial Distribution ………………………………………………………….. 18
3.6 Negative Binomial ……………………………………………………………………………………………….. 20
3.7 Derivation of Mean and Variance of Negative Binomial Distribution. …………………….. 21
CHAPTER FOUR ……………………………………………………………………………………………………. 23
RESULTS AND DISCUSSION ………………………………………………………………………………. 23
CHAPTER FIVE ……………………………………………………………………………………………………… 28
SUMMARY, CONCLUSION AND RECOMMENDATION …………………………………… 28
5.1 Summary ……………………………………………………………………………………………………………… 28
5.2 Conclusion ………………………………………………………………………………………………………… 28
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5.3 Recommendation ……………………………………………………………………………………………….. 28
5.4 Contribution to knowledge ………………………………………………………………………………….. 29
5.5 Area of Further Research ……………………………………………………………………………………. 29
References…………………………………………………………………………………………………………………. 30
Appendices ……………………………………………………………………………………………………………….. 32

CHAPTER ONE

INTRODUCTION
1.1.Background to the Study
Diabetes mellitus is a group of diseases caused by high level of blood glucose resulting from insufficient production of insulin and how insulin works. People with diabetes may develop serious complication such as heart disease, stroke, kidney failure, blindness and premature death. The term diabetes mellitus describes a metabolic disorder of multiple aetiology characterized by chronic hyperglycemia with disturbance of carbohydrate, fat and protein metabolism resulting from defecting insulin secretion and insulin action. The incidence(rate) of diabetes mellitus has been a global, regional as well as local public health issue. According to, WHO(2016), an estimated 422 million adults were living with diabetes mellitus in 2014 and IDF(2015), showed that 415 million people were living with diabetes in which Europe accounted for 59.8 million , North America and Caribbean accounted for 44.3 million, Middle East and North Africa accounted for 35.4 million, South East Asia accounted for 78.3 million, Western Pacific accounted for 153.2 million, Africa accounted 14.2 million and South and Central America accounted for 29.6 million people with diabetes in 2015 respectively. It is also globally projected that by 2040, 642 million people will be living with diabetes (IDF,2015). In Nigeria, there were more than 1.56 million cases of diabetes in 2015, between the ages of 20 to 79 years (IDF,2015), More so, WHO,(2016) estimated that 1.7 million Nigerians were living with diabetes.
There are risk factors causing type 2 diabetes mellitus and they include overweight, unhealthy diet, physical inactivity, increasing age, high blood pressure, impaired glucose tolerance and poor nutrition during pregnancy (IDF,2015).The other risk
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factors associated with Type 2 Diabetes Mellitus, is smoking, sedentary lifestyle, obesity, alcohol, consumption, and obstructive sleep, and WHO,(2016), noted that overweight and obesity are the strongest risk factors of type 2 diabetes mellitus. Globally, there are major intervention set to prevent incidence(rate)of Type 2 Diabetes Mellitus. The interventions include dietary intervention or physical activity intervention or both. It is discovered that combining dietary intervention and physical activity intervention is considered to be effective and efficient, According to (ADA,2007), an individual intervention is also effective by changing of lifestyle and avoidance of all the risk factors associated with Type 2 diabetes mellitus. The effect of diabetes mellitus include long-term damage, dysfunction and failure of various organs. It may present with characteristics symptoms such as thirst, polyuria, blurring of vision and weight loss. In most severe forms ketoacidosis or a non-ketotic hyperosmolar(shortage of insulin, in response the body switches to burning fatty acid which produces acidic ketone) may develop, frequent sweating which can lead to coma and in the absence of effective treatment, death may result.
1.2 Statement of the problem
The issue of type 2 diabetes mellitus to every state in the Nation has become problematic or order of the day and demand urgent attention from the government,to solve the incidence of type 2 diabetes while there is growing studies on diabetes.
In a different study, Chukwu,(2014), found out that there is high incidence of diabetes in the rural area than the urban area in Udi local Government Area of Enugu State. Lawrence et al., (2013), use Bayesian small area estimates of diabetes mellitus incidence, they find out that there is high level of diabetes in small countries in U.S.A.
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Ebenezer et al., (2003), studied the incidence (rate) of Type 2 Diabetes Mellitus(when the blood glucose level rise above 7.0mmol/L) in Port-Harcourt. He discovered that diabetes is on high increase in Port-Harcourt. In this research, we want to compare two models to know which distribution will best fit gender sensitivity (prone to disease) to Type 2 Diabetes Mellitus based on Beta-Binomial and Negative Binomial models, we intend to check the blood glucose level of the patients from their medical records. Therefore, in line with the study this research wish to examine Beta-Binomial and Negative Binomial models to determine which model best describe gender sensitivity to type 2 diabetes mellitus.
1.3 Aim and Objectives of the Study
The aim of this research work is to investigate the differential incidence of type 2 diabetes mellitus between male and female patients using Beta-Binomial and Negative Binomial models The specific objectives are to:
i. Estimate the parameter of the two models on Type 2 Diabetes Mellitus between male and female.
ii. Compare between the two models usingAkaike Information Criterion (AIC) to determine the best fitted model; and
iii. Compare the confidence interval between the two fitted models.
1.4 Justification of the Study
The nature of this research will help us to determine which models will best describe the gender sensitivity to type 2 diabetes mellitus out of both beta-binomial and negative binomial distribution, since most of the literature study aggregate incidence to types 2
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diabetes mellitus by using various statistical tools like chi-square, t-test and many more to justify their claims. Therefore, this study differs from most existing literatures on the account that the study will employ Beta-Binomial and Negative Binomial models to carry out comparison in order to estimate the probabilitiesof both models between genders. To compare between the two model their Akaike Information Criterion, and determine the confidence interval in order to show variability between gender sensitivity to diabetes mellitus.

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