Bayesian hierarchical approach to estimate insulin sensitivity by minimal model

Abstract

We adopted Bayesian analysis in combination with hierarchical (population) modelling to estimate simultaneously population and individual insulin sensitivity (SI) and glucose effectiveness (SG) 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 SI in all subjects. Non-linear regression analysis failed in four cases, where Bayesian analysis-derived SI was located in the lower quartile and was estimated with lower precision. The population means of SI and SG provided by Bayesian analysis and non-linear regression were identical, but the interquartile range given by Bayesian analysis was tighter by approx. 20% for SI and by approx. 15% for SG. Individual insulin sensitivities estimated by the two methods were highly correlated ( rS=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 ( rS=0.71 compared with rS=0.99; P <0.001). We conclude that the Bayesian hierarchical analysis is an appealing method to estimate SI and SG, as it avoids parameter estimation failures, and should be considered when investigating insulin-resistant subjects.