Title: Comparison of methods for D-optimal design for nonlinear mixed effects models
Authors: Ketil Tvermosegaard - London School of Hygiene and Tropical Medicine (United Kingdom) [presenting]
John Whittaker - GlaxoSmithKline (United Kingdom)
David Woods - University of Southampton (United Kingdom)
Abstract: Methods to find D-optimal designs for nonlinear mixed effects (NLME) models typically rely on an approximation of the Fisher information matrix (FIM) as a proxy for the variance of the maximum likelihood estimator (MLE). In the classic approach, the model is linearised around the expected value of the random effect and the FIM of this linearised model is used to approximate the true FIM. In a more recent approach, the FIM of the linearised model is viewed as a function of the point around which we linearise and then integrated with respect to the distribution of the random effect. Both these FIM approximations are implemented in generalised R-code and applied to industrially relevant examples drawn from the literature. Clear qualitative differences are established. Resulting designs often differ in terms of location of design points and replication structure. To enable a quantitative comparison of resulting designs, a third, recently proposed, FIM approximation is implemented to act as a gold standard (because it avoids linearisation and theoretically allows for arbitrarily high precision). It is used to compute relative efficiencies of designs. The results indicate that the added integration step most likely does not add to the quality of the resulting designs.