Bayesian identification of a population compartmental model of C-peptide kinetics

When models are used to measure or predict physiological variables and parameters in a given individual, the experiments needed are often complex and costly. A valuable solution for improving their cost effectiveness is represented by population models. A widely used population model in insulin secretion studies is the one proposed by Van Cauter et al. (Diabetes 41:368-377, 1992), which determines the parameters of the two compartment model of C-peptide kinetics in a given individual from the knowledge of his/her age, sex, body surface area, and health condition (i.e., normal, obese, diabetic). This population model was identified from the data of a large training set (more than 200 subjects) via a deterministic approach. This approach, while sound in terms of providing a point estimate of C-peptide kinetic parameters in a given individual, does not provide a measure of their precision. In this paper, by employing the same training set of Van Cauter et al., we show that the identification of the population model into a Bayesian framework (by using Markov chain Monte Carlo) allows, at the individual level, the estimation of point values of the C-peptide kinetic parameters together with their precision. A successful application of the methodology is illustrated in the estimation of C-peptide kinetic parameters of seven subjects (not belonging to the training set used for the identification of the population model) for which reference values were available thanks to an independent identification experiment.