Optimal designs for estimating critical effective dose under model uncertainty in a dose response study

Toxicologists have been increasingly using a class of models to describe a continuous response in the last few years. This class consists of nested nonlinear models and is used for estimating various parameters in the models or some meaningful function of the model parameters. Our work here is first to address design issues for this popular class of models among toxicologists. Specifically we construct a variety of optimal designs under model uncertainty and study their properties for estimating the critical effective dose (CED), which is model dependent. Two types of optimal designs are proposed: one type maximizes the minimum of efficiencies for estimating the CED regardless which member in the class of models is the appropriate model, and (ii) maximin compound optimal design that simultaneously selects the most appropriate model and provides the best estimate for CED at the same time. We compare relative efficiencies of these optimal designs and commonly used designs for estimating CED. To facilitate use of these designs, we have constructed a website that practitioners can generate tailor-made designs for their settings