Insulin minimal model indexes and secretion: proper handling of uncertainty by a Bayesian approach

The identification of the insulin minimal model (MM) for the estimation of insulin secretion rate (ISR) and physiological indexes (e.g. beta-cell sensitivity) requires the knowledge of C-peptide (CP) kinetics. The four parameters of the two-compartment model of CP kinetics in a given individual can be derived either from an additional bolus experiment or, more frequently, from a population model. However, in both situations, the CP kinetics is uncertain and, in MM identification, it should be treated as such. This paper shows how to handle CP kinetics uncertainty by using a Bayesian methodology. In seven subjects, MM indexes and ISR were estimated together with their confidence intervals, using either the bolus data or the population model to assess CP kinetics. The two main results that arise from the application of the new methodology are: (i) the use of the population model in place of the bolus data to determine CP kinetics does not affect, on average, the point estimates of ISR profile and MM parameters but only the confidence intervals which becomes wider (less than 50%); (ii) in both the bolus and population situation neglecting the uncertainty of CP kinetics, as done in MM literature so far, introduces no bias, on average, on point estimates of MM indexes but only an underestimation of confidence intervals.