MODELING PHARMACOKINETIC DATA USING HEAVY-TAILED MULTIVARIATE DISTRIBUTIONS

Abstract

Pharmacokinetic studies of drug and metabolite concentrations in the blood are usually conducted as crossover trials, especially in Phases I and II. A longitudinal series of measurements is collected on each subject within each period. Dependence among such observations, within and between periods, will generally be fairly complex, requiring two levels of variance components, for the subjects and for the periods within subjects, and an autocorrelation within periods as well as a time-varying variance. Until now, the standard way in which this has been modeled is using a multivariate normal distribution. Here, we introduce procedures for simultaneously handling these various types of dependence in a wider class of distributions called the multivariate power exponential and Student t families. They can have the heavy tails required for handling the extreme observations that may occur in such contexts. We also consider various forms of serial dependence among the observations and find that they provide more improvement to our models than do the variance components. An integrated Ornstein–Uhlenbeck (IOU) stochastic process fits much better to our data set than the conventional continuous first-order autoregression, CAR(1). We apply these models to a Phase I study of the drug, flosequinan, and its metabolite.

Keywords:

• Autocorrelation
• Crossover trial
• Integrated Ornstein–Uhlenbeck process
• Multivariate elliptical distributions
• Variance components

Acknowledgments

All of the models, except the random coefficients with nlme, were fitted using a specially written Fortran subroutine that constructed the likelihood function; this was dynamically loaded into the R [10] software for optimization. The function, called elliptic, is available in the public R library called growth at www.luc.ac.be/~jlindsey/rcode.html. We thank Robert Gentleman, Ross Ihaka, and the members of R core for developing R, a fast S-Plus clone freely available under the GNU licence and Knoll Pharmaceuticals, Nottingham, for allowing us to use the data.