Statistical Evaluation of a Glucose / Insulin Nonlinear Differential Equation Model with Classical and Bayesian Procedures

摘要

In this paper, the Markov Chain Monte Carlo (MCMC) method and Generalized Least Square (GLS) method are used to estimate the parameters in a glucose/insulin nonlinear differential model with GLP1-DPP4 interaction, describing the glucose-insulin metabolism. The model is used to generate the data that consists of the time-concentration measurements of plasma glucose and of insulin, which are important in Diabetes Mellitus (DM) treatment. Details on our application of MCMC and GLS to estimate parameters in the model are given in this paper. Our results suggest that MCMC is better able to estimate the parameters based on smaller bias and standard deviation. Although MCMC requires more calculation time than GLS, it offers a more appropriate method, in our opinion, for nonlinear model parameter estimations with no knowledge of the distribution of the data and when heterogeneity of variance is evident.