A Likelihood Approach for Fitting Nonlinear Mixed-Effects Models
to Pharmacokinetic and Pharmacodynamic Data
Douglas Bates
Department of Statistics
University of Wisconsin - Madison
Nonlinear mixed-effects models are widely used in the analysis of
population pharmacokinetic and pharmacodynamic data, providing
valuable information for drug development and for evaluation by
regulatory agencies. Over the years many algorithms for obtaining the
parameter estimates in these models have been developed and
incorporated in various software packages. Estimates from such
algorithms are often compared to assess which are the "better" ways of
determining the estimates. Unfortunately, concentrating on algorithms
and estimates provided by them misses the point. A nonlinear
mixed-effects model is a statistical model and we define the estimates
from such a model as those parameter values that optimize a criterion,
such as the log-likelihood or the posterior density for some prior on
the parameters. If we want to compare algorithms that are intended to
produce maximum likelihood estimates then we should settle on a
reliable way of evaluating the likelihood for a model/data set
combination and compare the likelihoods at the estimates provided by
different algorithms. More importantly we should evaluate the
precision of parameter estimates according to the change in the
likelihood. I'll describe how this can be done. Regretably, doing so
leads to the conclusion that many widely-accepted methods grossly
underestimate the variability in parameter estimates for such models.