Design of cross-over trials for pharmacokinetic studies

We describe a method for constructing D-optimal designs for nonlinear mixed effect models in cross-over pharmacokinetic studies. The method is based on fitting an approximate model using generalised least squares. The design construction is illustrated using an example motivated by a real clinical trial. The example shows that without period effects in the model, the optimal AB/BA design for estimating the treatment difference is independent of subject effects. When period effects are included the optimal design criterion changes significantly with the size of the between-subject variance but the consequences for the choice of optimal sampling times is small. The numerical results are discussed by exploring further the nature of the information matrix under certain conditions. Our results suggest that, under appropriate conditions, some optimality results that apply for linear model repeated measurement designs may also hold in the context of nonlinear mixed effect models.