Resampling methods in sparse sampling situations in preclinical pharmacokinetic studies

Toxicokinetic studies often require destructive sampling and the determination of drug concentrations in the various organs. Classically, the corresponding information is summarized in one mean concentration-time profile, which is regarded as representative for the animal population. On the basis of a mean profile, only estimates of the secondary pharmacokinetic parameters (for example AUC, t(1/2)) but no variability measures may be obtained. In this paper two resampling techniques are contrasted to Bailer's approach. The results obtained show that the resampling techniques can be considered a reliable alternative to Bailer's approach for the estimation of the standard error of the AUCl(o)(tk) in the case of normally distributed concentration data. They can be extended to the estimation of a variety of other secondary pharmacokinetic parameters and their respective standard deviations. One disadvantage with Bailer's method is its restriction to linear functions of the concentrations. On the other hand, using the population approach, prior knowledge of the underlying pharmacokinetic model is necessary. The resampling techniques discussed here, the "pseudoprofile-based bootstrap" (PpbB) and the "pooled data bootstrap" (PDB), are noncompartmental approaches. They are applicable under nonnormal data constellations and permit the estimation of the usual secondary pharmacokinetic parameters along with their standard deviations, standard errors, and other statistical measures. To assess the accuracy, precision, and robustness of the resampling estimators, theoretical data from three different pharmacokinetic models with different add-on errors (up to 100% variability) were analyzed. Even for the data sets with high variability, the parameters calculated with resampling techniques differ not more than 10% from the true values. Thus, in the case of data that are not normally distributed or when additional secondary pharmacokinetic parameters and their variability are to be estimated, the resampling methods are powerful tools in the safety assessment in preclinical pharmacokinetics and in toxicokinetics where generally sparse data situations are given.