NONMEM improves group parameter estimation for the minimal model of glucose kinetics

The minimal model of glucose kinetics interprets blood glucose and insulin concentrations after an interprets blood glucose and insulin concentrations after an intravenous glucose tolerance test (IVGTT) and provides parameters describing tissue insulin sensitivity and glucose-dependent tissue glucose disposal. In the standard application, the model is fitted to each experimental subject's points by nonlinear least squares, with suitable weighing. The variability of parameter estimates may, however, represent a problem, making the model in practice unidentifiable on a group of experimental subjects undergoing some treatment of interest. To obviate this problem, a specific modification to the original protocol has been introduced: administering tolbutamide 20 min after the glucose bolus has been shown to improve parameter stability. With this modification, however, the converse model of pancreatic secretion can no more be fitted on the collected series of concentrations. The application of the nonlinear mixed effects model (NONMEM) loss function allows estimation of parameter population means, variances, and covariances to be made on all sampled subjects simultaneously. Although this procedure does not allow an individual subject's parameters to be estimated, the variability of the group parameter estimates is greatly reduced compared with the standard method. In the present work, 20 healthy volunteers have been studied with an IVGTT, and group parameters have been computed in both standard and NONMEM ways: asymptotic parameter coefficients of variation with NONMEM were at least twenty times smaller than the corresponding sample parameter coefficients of variation obtained with the classical method.