Some statistical issues in modelling pharmacokinetic data

A fundamental assumption underlying pharmacokinetic compartment modelling is that each subject has a different individual curve. To some extent this runs counter to the statistical principle that similar individuals will have similar curves, thus making inferences to a wider population possible. In population pharmacokinetics, the compromise is to use random effects. We recommend that such models also be used in data rich situations instead of independently fitting individual curves. However, the additional information available in such studies shows that random effects are often not sufficient; generally, an autoregressive process is also required. This has the added advantage that it provides a means of tracking each individual, yielding predictions for the next observation. The compartment model curve being fitted may also be distorted in other ways. A widely held assumption is that most, if not all, pharmacokinetic concentration data follow a log-normal distribution. By examples, we show that this is not generally true, with the gamma distribution often being more suitable. When extreme individuals are present, a heavy-tailed distribution, such as the log Cauchy, can often provide more robust results. Finally, other assumptions that can distort the results include a direct dependence of the variance, or other dispersion parameter, on the mean and setting non-detectable values to some arbitrarily small value instead of treating them as censored. By pointing out these problems with standard methods of statistical modelling of pharmacokinetic data, we hope that commercial software will soon make more flexible and suitable models available.