Optimal population designs for PK models with serial sampling

In various pharmaceutical applications, repeated measurements are taken from each subject, and model parameters are estimated from the collected data. Examples include dose response modeling and PK/PD studies with serial blood sampling, among others. The quality of the information in an experiment is reflected in the precision of estimates of model parameters, which is traditionally measured by their variance-covariance matrix. In this article, we concentrate on the example of a clinical PK study where multiple blood samples are taken for each enrolled patient, which leads to nonlinear mixed effects regression models with multiple responses. The sampling scheme for each patient is considered a multidimensional point in the space of admissible sampling sequences. We demonstrate how to optimize the precision of parameter estimates by finding the best number and allocation of sampling times. It is shown that a reduced number of samples may be taken without significant loss of precision of parameter estimates. Moreover, our approach allows for taking experimental costs into account, which leads to a more meaningful comparison of sampling schemes and to potential cost savings.