Comparison of Two Design Optimality Criteria Applied to a Nonlinear Model

Abstract

In chemical kinetic or pharmacokinetic studies, many mathematical models are nonlinear with respect to the model parameters. This may cause serious problems for parameter estimation. A D-optimum design, which is very popular and effective for linear models, is not so good for nonlinear models with strong parameter curvature. In this article, we compare two optimality criteria applied to a nonlinear model. Both of them minimize the volume of the confidence ellipsoid of the parameters: D-optimality uses a linear approximation of the volume, and Q-optimality uses a quadratic approximation. We compute the relative design efficiencies and use a parameter-effect curvature measure to compute the number of observations that reduces the “curvature effect” to a specified level and improves the parameter estimation. The calculated designs differ significantly, and the Q-optimum design shows increasingly better statistical properties as the curvature increases. We present our results both graphically and as tables of numerical values.

Key Words:

• D-optimum design
• Q-optimum design
• Curvature
• Kinetic model
• Reaction order
• Rate constant

Mathematics Subject Classification:

• 62K05
• 62P99

Acknowledgments