Comparison of two design optimality criteria applied to a nonlinear model

Area of Science:

• * Pharmacometrics and Pharmacokinetics
• * Chemical Kinetics
• * Statistical Modeling

Background:

• * Nonlinear mathematical models are common in chemical kinetic and pharmacokinetic studies.
• * Parameter estimation in nonlinear models can be challenging due to parameter curvature.
• * D-optimality, effective for linear models, is less suitable for nonlinear models with significant curvature.

Purpose of the Study:

• * To compare D-optimality and Q-optimality criteria for nonlinear model parameter estimation.
• * To evaluate the performance of these criteria under varying degrees of parameter curvature.
• * To determine the number of observations needed to mitigate curvature effects using a parameter-effect curvature measure.

Main Methods:

• * Comparison of D-optimality (linear approximation) and Q-optimality (quadratic approximation) for minimizing confidence ellipsoid volume.
• * Calculation of relative design efficiencies for both optimality criteria.
• * Utilizing a parameter-effect curvature measure to quantify and reduce curvature effects.

Main Results:

• * Calculated designs derived from D-optimality and Q-optimality criteria show significant differences.
• * Q-optimum designs demonstrate superior statistical properties as model parameter curvature increases.
• * The study provides graphical and tabular data illustrating these findings.

Conclusions:

• * Q-optimality is a more effective criterion than D-optimality for parameter estimation in nonlinear models, particularly those with high curvature.
• * The choice of optimality criterion significantly impacts design efficiency in nonlinear modeling.
• * The parameter-effect curvature measure aids in optimizing experimental design for improved parameter estimation accuracy.