Optimal designs for population pharmacokinetic studies of a drug with large assay variability for patients with restrictive sampling schedules

Objective: This work aimed to determine an optimal design for patients with restrictive sampling schedules who received a drug* that displays huge assay variability, is rapidly absorbed and has a very short elimination half-life.

Methods: Rich data from 20 patients were modelled in R (using nlme) to determine the structural pharmacokinetic (PK) model, PK parameters, inter-patient and residual variability.  The following variations of the one-compartment model were considered: Bateman, Dost (assumes absorption and elimination rates are equal)1, zero-order input, Weibull input and n-transit compartment input.  For a candidate model, an optimal design was then developed in POPT2 for a study with 40 patients where four blood samples per patient were allowed (over three sampling frames), with a minimum of 15 minutes between samples.  These constraints were identified from a survey of 16 experts who conduct PK studies of this drug in the field.  The optimal sampling times from these models were compared, along with the expected standard errors (SEs) from the designs.  To evaluate each model’s optimal design, data were selected at the optimal sampling times from the rich data (or closest to), and also from another rich dataset of 19 patients.  The corresponding model was then fitted to this new dataset of 39 patients each with four sampling times, and results were compared with expected results from POPT.

Results: The rich data exhibited large inter-patient variability in the absorption phase and substantial residual variability.  For some patients the absorption phase was longer or equal to the elimination phase.  The Bateman model converged, but appeared unstable (imprecise and highly variable BSVs).  The Dost model converged quickly and provided a reasonable fit.  The other models either failed to converge (Weibull and n-transit compartment input) or provided a poor fit (zero-order input).  The resulting optimal sampling times from the Bateman and Dost models were fairly similar, but expected SEs for Bateman were larger than Dost.  During evaluation, the Bateman model failed to converge; while the Dost model converged and provided a reasonable fit.

Conclusion: Given the nature of this drug the Bateman model is problematic. The Dost model adequately fitted the rich data and the reduced dataset with four blood samples at sampling times determined using optimal design methodology.

*Concealed on request of the owner of the data


1. F. H. Dost. Grundlagen der Pharmakokinetik, 2. Gufl., G. Thieme, Stuttgart 1968, pp. 38–47.

2. Duffull SB, POPT. Installation and user guide. Ver 3.0 (2006) www.winpopt.com