Some statistical issues in modelling pharmacokinetic data

Abstract

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.

A simulation‐based confidence band for drug concentrations in blood: an application to a clinical phase I trial

“…Lindsey et al [17,18] have recently pointed out that the log-normal assumption is not necessarily appropriate and other skewed distributions such as Weibull and gamma distributions may be more appropriate. The proposed approach is easily applicable to the cases where other skewed distributions are assumed.…”

Nonlinear mixed effects modelling for estimation of steady state attainment

“…For each subject, the day (t SS ) at which 90% of the estimated subject-specific asymptotic steady state concentration C SS is reached is predicted from the fitted model, using equation (4). This gives a distribution of subject-specific steady state estimates, which can then be utilized to assess the overall occurrence of steady state.…”

Population pharmacokinetics/pharmacodynamics of anesthetics

“…44,45 Pharmacodynamic models are often highly nonlinear, but a mixed-effects approach helps their characterization, 46 and a mixed-effects approach remains useful also with rich data. 47 A model that is constructed based on P values may not be the best description of the data.…”

“…55,56 Furthermore, rich, in particular, PD, data sets may be difficult to model (eg, many sources other than effect-site drug concentration affect EEG surrogate effect parameters), which may lead to correlated residuals and SEs of estimate parameters that may be biased downward. 47 In none of the reviewed PK-PD articles were covariances between first-level random effects reported, whereas their description may be beneficial for the application of population models. The adequacy of the stochastic part of the model may be evaluated using the posterior predictive E385 check, which, in its simplest form, entails comparing the distributions of simulated data from the population model (eg, 95% prediction intervals) with the measured data.…”