BAYESIAN NONPARAMETRIC POPULATION-MODELS - FORMULATION AND COMPARISONWITH LIKELIHOOD APPROACHES

Population approaches to modeling pharmacokinetic and/or pharmacodynam ic data attempt to separate the variability in observed data into with in- and between-individual components. This is most naturally achieved via a multistage model. At the first stage of the model the data of a particular individual is modeled with each individual having his own set of parameters. At the second stage these individual parameters are assumed to have arisen from some unknown population distribution,whic h Ice shall denote F. The importance of the choice of second stage dis tribution has led to a number of flexible approaches to the modeling o f F. A nonparametric maximum likelihood estimate of F was suggested by Mallet whereas Davidian and Gallant proposed a semiparametric maximum likelihood approach where the maximum likelihood estimate is obtained over a smooth class of distributions. Previous Bayesian work has conc entrated largely on F being assigned to a parametric family, typically the normal ol Student's t. We describe a Bayesian nonparametric appro ach using the Dirichlet process. We use Markov chain Monte Carlo simul ation to implement the procedure. We discuss each procedure and compar e our approach with those of Mallet and Davidian and Gallant, using si mulated data for a pharmacodynamic dose-response model.