Comparison of Markov chain Monte Carlo and generalized least square methods on a model of glucose / insulin dynamics with GLP1-DPP4 interaction

Abstract

In this paper, the performances of Markov Chain Monte Carlo (MCMC) method and Generalized Least Square (GLS) method are compared when they are used to estimate the parameters in a nonlinear differential model of glucose/insulin metabolism with GLP1-DPP4 interaction. 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. We show the results from three different runs to obtain parameter estimations by both MCMC and GLS. The true values (TV), point estimates (PM), standard deviation (SD) and 95% credible intervals (CI) of population parameters based on the two methods are presented. Our results suggest that MCMC is better able to estimate the parameters based upon 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 without knowledge of the distribution of the data and when heterogeneity of variance is evident.