Sparse-Sampling Optimal Designs in Pharmacokinetics and Toxicokinetics*

The population approach was developed to estimate population characteristics of the pharmacokinetics (PKs) of a drug from a sparse-sampling designed experiment in a set of individuals. This approach can also be used in toxicokinetics to avoid extensive sampling in animals, especially in rodents. As for any estimation procedure, the accuracy of the estimator will rely upon the experimental design performed. In this area, two different design problems may be considered: the population designs, when the population parameters are estimated using a mixed effect model, and the Bayesian design, when individual parameters are estimated using a Bayesian approach. An extension of the D-optimality criteria used in nonlinear regression for these two design problems is proposed. For the population design, the determinant of the Fisher information matrix of the population parameters is evaluated using a first order linearization of the model about the mean. For Bayesian designs, the determinant of the Bayesian information matrix is used. Both methods were applied on a simulated PK experiment with a homoscedastic and a heteroscedastic error model. They were also used to design a toxicokinetic experiment from data from a previous study that were analyzed with NONMEM. In both examples, a one-compartment open model with two PK parameters were used. Several two-point and one-point population and Bayesian designs were evaluated and compared. It was found that most optimal sparse designs involved the D-optimal sampling times. Both the optimal population design and the Bayesian design rely upon the assumed error model. It was shown that the increase in variance when only one point is performed even in twice as many individuals can be important in population designs. For Bayesian designs, an important increase in variance can be observed in the one-point design at nonoptimal times. The proposed approaches were very useful in evaluating and comparing common designs.