Bayesian Nonparametric Population Models: Formulation and Comparison with Likelihood Approaches

Abstract

Population approaches to modeling pharmacokinetic and or pharmacodynamic data attempt to separate the variability in observed data into within- 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 which we shall denote F. The importance of the choice of second stage distribution has led to a number of flexible approaches to the modeling of 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 concentrated largely on F being assigned to a parametric family, typically the normal or Student's t. We describe a Bayesian nonparametric approach using the Dirichlet process. We use Markov chain Monte Carlo simulation to implement the procedure. We discuss each procedure and compare our approach with those of Mallet and Davidian and Gallant, using simulated data for a pharmacodynamic dose-response model.