Fitting multiple regression models to lipid levels in Type II diabetic males

Abstract

The main objective of this thesis is to study the relationship between Fasting Blood Glucose and the predictors Age, Weight, LDL, HDL and Triglycerides in 44 diabetic males. Diabetes Mellitus is a condition caused by deficiency of insulin which results in the elevation of sugar or glucose in the blood. Fasting Blood Glucose readings are taken from a fasting glucose test performed on a blood sample taken when the patient has been fasting (except for water intake) for at least 8 hours. Cholesterol is a waxy, fat-like compound used in the structure of cell membranes, synthesis of bile acids and synthesis of steroid hormones. LDL is known as the 'bad cholesterol' and is the major cholesterol carrier in the blood. HDL is known as the 'good cholesterol'. It carries cholesterol in the blood from other parts of the body back to the liver, which leads to its removal from the body. Triglycerides is the chemical form in which most fat exists in food as well as in the body. Even though only a small portion of our Triglycerides is found in the blood, high blood triglycerides levels are associated with heart disease and are often accompanied by other factors such as low HDL or a tendency towards diabetes. Type II diabetes mellitus is associated with obesity and widespread abnormalities in the blood. In fact, high triglycerides, high LDL cholesterol (bad) and low HDL cholesterol (good) are often seen in diabetic patients. Since the response and predictor variables of the data being considered in this study are all covariates, then a multiple regression model is the best contender to model the data. Abstract Multiple regression can be applied to lipid levels in diabetic males, since it will help determine what variables contribute to the explanation of the response variable and to what degree. Thus, it can also check the relationships between the response variable and the predictors. A suitable fitted least squares regression equation for the full model is found to be: FBG = -11.881+0.07202Age + 0.157Weight + 1.581LDL-1.035HDL + 0.877Triglycerides The regression equation verifies the fact that FBG levels increase as Age, Weight, LDL and Triglycerides increase. It can also be noted that the coefficient of HDL is negative showing that a decrease in FBG levels results if HDL increases. Since the predictors Age and HDL resulted to be insignificant in the presence of the other variables, then, by means of Sequential variable selection the following parsimonious model has been obtained: FBG = -13.315 + 0.176Weight + 2.171LDL + 1.129Triglycerides The above equation shows that the risk factors for FBG levels in a diabetic male are mainly Weight, LDL and Triglycerides. Weight has been found to be the most correlated with FBG, so the males who are more likely to develop this form of diabetes, are those who have excess weight. Since extreme cases can seriously bias the results by 'pulling' or 'pushing' the regression line in a particular direction, then, a detailed study of residuals is also presented. The analysis of residuals and influence diagnostics will serve as indicators of any outliers or influential points.