Optimal Designs for Some Dose-Response Model

In this dissertation, we study the problem of optimal design for nonlinear dose-response model with continuous or binary response. The optimal designs we construct are static (or non-sequential) and approximate designs. Most designs considered are locally optimal in that they depend on the model parameters. We derive the locally optimal designs for different types of dose-response models including least squares regression models with continuous or binary endpoints, and quantile regression models.;First, we assume least squares regression with homoscedasicity in the errors. In Chapter 2, we consider the problem of constructing locally D- and c-optimal designs for a class of dose response models with continuous outcomes. The models belong to exponential class with unknown order of the exponent. It is found that the locally D- and c-optimal designs can be based on minimally supported points under certain situations. In Chapter 3, we consider the problem of seeking locally optimal designs for nonlinear dose response models with binary outcomes. Applying the theory of Chebyshev Systems and other algebraic tool, we show that the locally D-, A-, c-optimal designs for three binary dose response models are minimally supported in finite, compact design intervals.;Second, we assume heteroscedasticity in errors and investigate D-optimal designs for nonlinear quantile regression models in Chapter 4. We construct locally and Bayesian D-optimal design for quantile regression in exponential and log-linear models. The upper bound of the number of support points can be reduced by applying some necessary condition for optimality. Some optimal designs are obtained numerically.;For all designs constructed, we perform efficiency studies to show the benefits of using optimal designs comparing to alternative designs, and evaluate their robustness against parameter misspecification.