D-optimal Designs for Complex Nonlinear Models in Chemical Kinetics, PK/PD, and Environmental Science

The D-optimal design for complex nonlinear models was investigated. D-optimality criterion maximized the determinant of the information matrix and provided answers to practical questions about how the data should be collected for precise estimation of unknown parameters in nonlinear models.;The nonlinear chemical kinetics model, compartment models, Klimpel's flotation recovery model, and rational models were discussed. A method was developed to obtain the lower bound of the maximal numbers of D-optimal design points for each model by the Tchebycheff system to facility the computational search for the optimal designs in practice.;For the chemical kinetics model, conditions when the D-optimal design was the saturated design were established for both bounded and unbounded design space, For compartment models, it was also proved that boundary points are always optimal design points. The mathematical expression between the model parameter and the other design point for the saturated design of Klimpel's flotation recovery model was also derived. Simulations were performed for each model to investigate D-efficiency when the parameter misspecification happened. Results showed that the D-efficiency highly depended on the interval in which the unknown parameters were evaluated and the magnitude of deviation of the nominal values from the true parameter values.