Bayesian hierarchical approach to estimate insulin sensitivity by minimal model

We adopted Bayesian analysis in combination with hierarchical (population) modelling to estimate simultaneously population and individual insulin sensitivity (S^I) and glucose effectiveness (S^G) with the minimal model of glucose kinetics using data collected during insulin-modified intravenous glucose tolerance test (IVGTT) and made comparison with the standard non-linear regression analysis. After fasting overnight, subjects with newly presenting Type II diabetes according to World Health Organization criteria (n=65; 53 males, 12 females; age, 54±9 years; body mass index, 30.4±5.2 kg/m²; means±S.D.) underwent IVGTT consisting of a 0.3 g of glucose bolus/kg of body weight given at time zero for 2 min, followed by 0.05 unit of insulin/kg of body weight at 20 min. Bayesian inference was carried out using vague prior distributions and log-normal distributions to guarantee non-negativity and, thus, physiological plausibility of model parameters and associated credible intervals. Bayesian analysis gave estimates of S^I in all subjects. Non-linear regression analysis failed in four cases, where Bayesian analysis-derived S^I was located in the lower quartile and was estimated with lower precision. The population means of S^I and S^G provided by Bayesian analysis and non-linear regression were identical, but the interquartile range given by Bayesian analysis was tighter by approx. 20% for S^I and by approx. 15% for S^G. Individual insulin sensitivities estimated by the two methods were highly correlated (r^S=0.98; P<0.001). However, the correlation in the lower 20% centile of the insulin-sensitivity range was significantly lower than the correlation in the upper 80% centile (r^S=0.71 compared with r^S=0.99; P<0.001). We conclude that the Bayesian hierarchical analysis is an appealing method to estimate S^I and S^G, as it avoids parameter estimation failures, and should be considered when investigating insulin-resistant subjects.