Differential incidence of Type 2 Diabetes Mellitus Using Beta-Binomial and Negative Binomial Models. (Dissertation Sample)

DIFFERENTIAL INCIDENCE OF DIABETES MELLITUS BETWEEN MALE AND FEMALE USING BETA-BINOMIAL AND NEGATIVE BINOMIAL MODELS A CASE STUDY OF GENERAL HOSPITAL IFAKI-EKITI By Matthew AINA P15SCMT8059 DEPARTMENT OF STATISTICS FACULTY OF PHYSICAL SCIENCES AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA FEBRUARY, 2018 DIFFERENTIAL INCIDENCE OF DIABETES MELLITUS BETWEEN MALE AND FEMALE USING BETA-BINOMIAL AND NEGATIVE BINOMIAL MODELS A CASE STUDY OF GENERAL HOSPITAL IFAKI-EKITI BY Matthew AINA P15SCMT8059 A DISSERTATION SUBMITTED TO THE SCHOOL OF POST GRADUATE STUDIES, AHMADU BELLO UNIVERSITY,ZARIA-NIGERIA, IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE DEGREE IN STATISTICS DEPARTMENT OF STATISTICS FACULTY OF PHYSICAL SCIENCES AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA FEBRUARY, 2018 ii Declaration I declare that the work in this dissertation entitled “DIFFERENTIAL INCIDENCE OF DIABETES MELLITUS BETWEEN MALE AND FEMALE USING BETA-BINOMIAL AND NEGATIVE BINOMIAL MODELS” has been performed by me in the Department of Statistics. The information derived from the literature has been acknowledged in the text and a list of references provided. No part of this dissertation was previously presented for another degree or diploma at this or any other institution . Matthew Aina 248285-4445002018030-16510003917950-1651000 Name of Student Signature Date iii Certification This dissertation entitled “DIFFERENTIAL INCIDENCE OF DIABETES MELLITUS BETWEEN MALE AND FEMALE USING BETA-BINOMIAL AND NEGATIVE BINOMIAL MODELS” by Matthew AINA meets the regulations governing the award of the degree of Master of Science of the Ahmadu Bello University, and is approved for its contribution to knowledge and literary presentation. . 27178013862050024853901386205004409440138620500 Chairman Supervisory Committee (Signature) (Date) Dr. T. Dahiru 27178093027500248539093027500440944093027500 Member Supervisory Committee (Signature) (Date) Dr. H. G Dikko 27178011125200024853901112520004409440111252000 Head of Department (Signature) (Date) Dr. H.G Dikko 27178092900500248539092900500440944092900500 Dean, Postgraduate School (Signature) (Date) Prof. S.Z Abubakar iv Dedication This research work is dedicated to God Almighty who has been my sustenance since the start of this programme. v Acknowledgements I show my sincere gratitude to God who has given me the ability to carry out my course work and research successfully. I am sincerely grateful for the intellectual guidance and supervision of my supervisors; Dr T. Dahiru and Dr. H. G Dikko who ensured the successful completion of the work in appropriate time. I must also commend my boss in my place of work Mr. S. A. Phillips for his complete support during the course of my programme. My sincere thanks goes to my beloved wife Mrs. Aina Olubunmi and my children Ayomide Aina, Semilore Aina, and Korede Aina, I pray that the height I cannot attain you will all go beyond it. I also appreciate the invaluable cooperation of my colleagues in this programme I thank you all for your priceless support and in my prayer we shall all achieve our ultimate goals in life. Thank you all. vi Abstract This research entails, the differential incidence of diabetes mellitus between male and female using Beta-Binomial and Negative Binomial models. From the previous researches carried out it was discovered that type 2 Diabetes Mellitus incidence is high in the Region/Localities where people reside. Therefore, this research intends 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. A Beta-Binomial and Negative Binomial models were used to fit the Type 2 Diabetes mellitus between male and female patients and to estimate the probability of both model on type 2 diabetes mellitus between male and female patient .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 and it is recommended that this model can be used to carry out other experimental research. vii Table of Contents Cover Page………………………………………………………………………………..i Title Page…………………………………………………………………………………ii Declarationiii Certificationiv Dedicationv Acknowledgementsvi Abstractvii List of Figuresx List of Tablesxi CHAPTER ONE1 INTRODUCTION1 1.1.Background to the Study1 1.2 Statement of the problem2 The issue of type 2 diabetes mellitus to every state in the Nation has become major problematic or other of the day and demand urgent attention from the government,2 to solve the incidence of type 2 diabetes while there is growing studies on diabetes.2 1.3 Aim and Objectives of the Study3 1.4 Justification of the Study3 LITERATURE REVIEW5 2.1Review of Related Literature5 2.2 Types / Classification of Diabetes Mellitus13 2.3 Prediabetes15 RESEARCH METHODOLOGY16 3.1 Introduction16 3.2Method of Data Collection16 3.3 Beta-Binomial16 3.4 Akaike information criterion17 3.5 Credible interval17 3.5Derivation of Beta Binomial Distribution18 3.6 Negative Binomial20 3.7 Derivation of Mean and Variance of Negative Binomial Distribution.20 viii HYPERLINK \l "page34" CHAPTER FOUR23 CHAPTER FIVE28 SUMMARY, CONCLUSION AND RECOMMENDATION28 5.1 Summary28 5.2Conclusion28 5.3 Recommendation29 5.4 Contribution to knowledge29 5.5 Area of Further Research29 References30 Appendices33 ix List of Figures Figure 4.1:Plot of Beta-Binomial Model on Type 2 Diabetes Mellitus.27 List of Tables Table 4.1: Descriptive Statistics on Diabetes Mellitus between Male and Female.23 Table 4.2: Output of Beta-Binomial Distribution23 x HYPERLINK \l "page34" Table 4.3:Output of Negative Binomial Distribution23 Table 4.4:Output of Negative Binomial Goodness of fit25 Table 4.5:Output of Beta-Binomial Goodness of fit25 xi 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 problem which insulin is produced and how insulin works or both. 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 of diabetes mellitus has been a globally, regionally and locally 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 several 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 1 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 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 America Diabetes Association,(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 state may develop, frequent sweating which can lead to coma and in the absence of effective treatment, death may result. 1.2Statement of the problem The issue of type 2 diabetes mellitus to every state in the Nation has become major problematic or other 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. Ebenezer et al., (2003), studied the incidence rate of diabetes in P...