Modeling pharmacokinetic data using heavy-tailed multivariate distributions

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.