An evaluation of population D-optimal designs via pharmacokinetic simulations

One goal of large scale clinical trials is to determine how a drug is processed by, and cleared from, the human body [i.e., its pharmacokinetic (PK) properties] and how these PK properties differ between individuals in a population (i.e., its population PK properties). Due to the high cost of these studies and the limited amount of data (e.g., blood samples) available from each study subject, it would be useful to know how many measurements are needed and when those measurements should be taken to accurately quantify population PK model parameters means and variances. Previous studies have looked at optimal design strategies of population PK experiments by developing an optimal design for an individual study (i.e., no interindividual variability was considered in the design), and then applying that design to each individual in a population study (where interindividual variability is present). A more algorithmically and informationally intensive approach is to develop a population optimal design, which inherently includes the assessment of interindividual variability. We present a simulation-based evaluation of these two design methods based on nonlinear Gaussian population PK models. Specifically, we compute standard individual and population D-optimal designs and compare population PK model parameter estimates based on simulated optimal design measurements. Our results show that population and standard D-optimal designs are not significantly different when both designs have the same number of samples per individual. However, population optimal designs allow for sampling schedules where the number of samples per individual is less than the number of model parameters, the theoretical limit allowed in standard optimal design. These designs with a low number of samples per individual are shown to be nearly as robust in parameter estimation as standard D-optimal designs. In the limit of just one sample per individual, however, population D-optimal designs are shown to be inadequate.