Computational Methods for D-optimal Design in Nonlinear Mixed Effects Models

This thesis aims to make a first step towards a foundation for a different, more practical approach to employing the principles of optimal experimental design in nonlinear mixed effects models. As an alternative to approaches which aim to mathematically account for parameter uncertainty and misspecification, it is proposed that the “space of possible parameter guesses” is investigated more directly, by visualising the resulting optimal designs and their relative performance. To provide some justification for the computational choices made in the packages, the thesis provides a comparison of two linearisation-based approaches to approximating the Fisher information matrix (First Order and Integrated First Order), a necessary step in computing D-optimality objective functions. This comparison is performed by utilising an approximation (Monte Carlo / Adaptive Gaussian Quadrature) which is not based on linearisation and which theoretically allows arbitrarily low error but at a high computational cost. It is concluded that the computationally cheaper First Order approximation is likely to be superior in all cases. A number of models taken from the applied and theoretical literature are introduced. Through these examples, it is shown how one can use the R-packages developed for this thesis (doptim and randon) to check robustness of proposed designs against parameter misspecification, in terms of information lost. A gentle introduction to using the packages is also provided, and it is demonstrated how to find D-, Dsand DA-optimal designs for nonlinear mixed effects models and, because the objective functions are made available to the user, how custom objective functions such as compound objective functions can also be generated and optimised