Designs for testing lack of fit for a nonlinear dose-response curve model

We would like to estimate the parameters of a dose-response function with the greatest precision as possible. For a two-parameter model, this is equivalent to minimizing the area of the confidence ellipsoid, i.e., a D-optimal design. Previous work on this particular model has included minimal designs. These designs are unable to determine lack of fit. We introduce a distinct dose level to the design to be able to estimate the lack of fit. The minimal and new designs will be compared, and the sample size needed to achieve adequate power for the lack-of-fit test will be derived.