Application of Multivariate and Bivariate Normal Distributions to Estimate Duration of Diabetes

Abstract

Diabetic nephropathy (DN) is one of the major complications of type 2 diabetes. Studies have shown that duration of diabetes and serum creatinine (SrCr) is significant predictors for determining the renal health status of a patient. In this study we have estimated the duration of diabetes of a patient on the basis of their latest renal health status. For this we have developed the joint distribution of three correlated random variables namely duration of diabetes, Serum Creatinine (SrCr) and fasting blood glucose (FBG) to estimate the duration of disease of type 2 diabetic nephropathy patients. This is done by considering two datasets; the first one gives the complete information (from the time of diagnosis till termination of study) and the other gives the latest information (latest 19 months) about the renal health status of a patient. We have used the complete information from the first data to estimate the duration of disease for the DN patients belonging to second dataset. Multivariate analysis is applied for estimating these disease durations by firstly selecting the appropriate distributions for the above three random variables. Then we have checked the normal approximation for each distribution and finally we have checked multivariate normality by applying Mardia test. The distributions of three correlated random variable were found to be approximately normal and they were also found to be jointly normal, therefore three dimensional multivariate normal (MVN) distributions is considered to be an appropriate distribution for duration of diabetes, SrCr and FBG. Conditional expectation under MVN is applied to estimate the duration of diabetes for given values of SrCr and FBG. We have also applied bivariate normal (BVN) distribution as the special case of MVN distribution and estimated the durations of diabetes on the basis of SrCr only. Further we have compared the estimated durations from both MVN and BVN distributions graphically. This estimation procedure will help medical fraternity to guide those patients who have incomplete record history, about their approximate duration of disease. Also it will help in monitoring and evaluating the severity of DN complication.