Population models are used to describe the dynamics of different subjects belonging to a population and play an important role in drug pharmacokinetics (PK). The identification of such models aims at estimating the typical response of the population together with the individual responses of the subjects starting from from noisy and sparsely sampled data. The typical approach relies on structural parametric models, e.g. compartmental ones. However, in the early phases of a study, a reliable structural model may not be available. In the seminar, a nonparametric identification scheme is presented in which both the average response of the population and the individual ones are modelled as Gaussian stochastic processes. An Empirical Bayes algorithm and an MCMC one for estimating both the typical and the individual curves are worked out. When the curves are modelled as integrated Wiener processes, their estimates turn out to be cubic smoothing splines. The connection with Tychonov regularization and basis function neural networks is also discussed. The identification schemes are tested and compared on simulated data sets as well as on xenobiotics pharmacokinetic data.
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