  We consider design issues for toxicology studies when we have a continuous
response and the true mean response is only known to be a member of a class of
nested models. This class of non-linear models was proposed by toxicologists
who were concerned only with estimation problems. We develop robust and
efficient designs for model discrimination and for estimating parameters in the
selected model at the same time. In particular, we propose designs that
maximize the minimum of $D$- or $D_1$-efficiencies over all models in the given
class. We show that our optimal designs are efficient for determining an
appropriate model from the postulated class, quite efficient for estimating
model parameters in the identified model and also robust with respect to model
misspecification. To facilitate the use of optimal design ideas in practice, we
have also constructed a website that freely enables practitioners to generate a
variety of optimal designs for a range of models and also enables them to
evaluate the efficiency of any design.
