The hierarchical Bayesian approach to population pharmacokinetic modelling

Compartmental models are widely used to model the profile of drug concentrations versus time from administration in an individual subject. Observed concentrations are then modelled as noisy departures from the underlying profile, the latter characterised for each individual by a small number of 'individual parameters'. When a population of individuals is studied, inter-individual variation is modelled by assuming that the individual profile parameters are drawn from a population distribution, the latter characterised by 'population parameters' describing, in effect, a mean population profile and individual variation around it. From a Bayesian statistical perspective, such models fit exactly into the so-called hierarchical modelling framework, which provides a coherent basis for individual and population inferences and prediction, as well as for decision-making (for example, the design of dosage regimens). This paper outlines the hierarchical model framework and describes how the required computations can be carried out in a straightforward manner by a Markov chain Monte Carlo technique known as Gibbs sampling, even when models involve mean-variance relationships and outliers.