Estimating postprandial glucose fluxes using hierarchical Bayes modelling

A new stochastic computational method was developed to estimate the endogenous glucose production, the meal-related glucose appearance rate (Ra meal), and the glucose disposal (Rd) during the meal tolerance test. A prior probability distribution was adopted which assumes smooth glucose fluxes with individualized smoothness level within the context of a Bayes hierarchical model. The new method was contrasted with the maximum likelihood method using data collected in 18 subjects with type 2 diabetes who ingested a mixed meal containing [U-13C]glucose. Primed [6,6-2H2]glucose was infused in a manner that mimicked the expected endogenous glucose production. The mean endogenous glucose production, Ra meal, and Rd calculated by the new method and maximum likelihood method were nearly identical. However, the maximum likelihood gave constant, nonphysiological postprandial endogenous glucose production in two subjects whilst the new method gave plausible estimates of endogenous glucose production in all subjects. Additionally, the two methods were compared using a simulated triple-tracer experiment in 12 virtual subjects. The accuracy of the estimates of the endogenous glucose production and Ra meal profiles was similar [root mean square error (RMSE) 1.0 ± 0.3 vs. 1.4 ± 0.7 μmol/kg/min for EGP and 2.6 ± 1.0 vs. 2.9 ± 0.9 μmol/kg/min for Ra meal; new method vs. maximum likelihood method; P = NS, paired t-test]. The accuracy of Rd estimates was significantly increased by the new method (RMSE 5.3 ± 1.9 vs. 4.2 ± 1.3; new method vs. ML method; P < 0.01, paired t-test). We conclude that the new method increases plausibility of the endogenous glucose production and improves accuracy of glucose disposal compared to the maximum likelihood method.