Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function

We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumptions. An extended model called EMAX is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis-Menten model for a specific choice of parameter settings. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the EMAX model by maximizing a minimum of the D or D, efficiencies taken over a range of values for the nonlinear parameters. In particular, we show that such designs are (a) efficient for estimating parameters in the EMAX model, (b) about 70% efficient for estimating parameters in the Michaelis-Menten model, (c) efficient for testing the Michaelis-Menten model against the EMAX model, and (d) robust with respect to misspecification of the unknown parameters in the nonlinear model.