Estimation of Population PK Measures: Selection of Sampling Grids
Estimation of Population PK Measures: Selection of Sampling Grids
Valerii Fedorov and Sergei Leonov
Abstract: In clinical pharmacokinetic (PK) studies multiple blood samples are taken for each enrolled patient, and various population PK measures, such as area under the curve (AUC), maximal concentration (Cmax) and time to maximal concentration (Tmax) 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 an empirical, or model-independent, approach, where numerical integration algorithms are used for AUC and sample estimates for Cmax and Tmax. Since regulatory agencies usually require the model-independent estimation of PK measures, we focus on the empirical approach while using the model-based approach 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). For a number of special cases we derive explicit formulae for the MSE of the empirical estimator of AUC. When costs of patient’s enrolment and costs of analyzing samples are introduced, these formulae allow the optimal selection of the number of patients and samples per patient.
