Modeling the covariance structure in pharmacokinetic crossover trials

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. However, much of the dependence among such observations, within and between periods, is generally ignored in analyzing this type of data. Usually, only a random coefficient model is fitted for the parameters in the nonlinear mean function, along with allowing the variance to depend on the mean so that it changes over time. Here, we develop models to allow more fully for the structure of the crossover study. We introduce two levels of variance components, for the subjects and for the periods within subjects, and also an autocorrelation within periods. We also retain the time-varying variance, using a separate variance function for this, different from that for the mean. We apply this model to a phase I study of the drug flosequinan and its metabolite. This drug was developed for the treatment of heart failure. Because the metabolite also exhibits an active pharmacologic effect, study of both the parent drug and the metabolite is of interest. We find that the autocorrelation is the element in the covariance structure that most improves the fit of the model but that two levels of variance components can also be necessary.