Population pharmacokinetic measures, their estimation and selection of sampling times

In pharmacokinetic (PK) studies, including bioavailability assessment, various population PK measures, such as area under the curve (AUC), maximal concentration (C(max)) and time to maximal concentration (T(max)) are estimated. In this paper we compare a model-based approach, where parameters of a compartmental model are estimated and the explicit formulae for PK measures are used, and a model-independent approach, where numerical integration algorithms are used for AUC and sample estimates for C(max) and T(max). Since regulatory agencies usually require the model-independent estimation of PK measures, we focus on the empirical approach while using the model-based approach and corresponding measures as a benchmark. We show how to "split" a single sampling grid into two or more subsets, which substantially reduces the number of samples taken for each patient, but often has little effect on the precision of estimation of PK measures in terms of mean squared error (MSE). We give explicit formulae for the MSE of the empirical estimator of AUC for a simple example and discuss how costs may be taken into account.