On the combination of c- and D-optimal designs: General approaches and applications in dose-response studies

Dose-response modeling in areas such as toxicology is often conducted using a parametric approach. While estimation of parameters is usually one of the goals, often the main aim of the study is the estimation of quantities derived from the parameters, such as the ED50 dose. From the view of statistical optimal design theory such an objective corresponds to a c-optimal design criterion. Unfortunately, c-optimal designs often create practical problems, and furthermore commonly do not allow actual estimation of the parameters. It is therefore useful to consider alternative designs which show good c-performance, while still being applicable in practice and allowing reasonably good general parameter estimation. In effect, using optimal design terminology this means that a reasonable performance regarding the D-criterion is expected as well. In this article, we propose several approaches to the task of combining c- and D-efficient designs, such as using mixed information functions or setting minimum requirements regarding either c- or D-efficiency, and show how to algorithmically determine optimal designs in each case. We apply all approaches to a standard situation from toxicology, and obtain a much better balance between c- and D-performance. Next, we investigate how to adapt the designs to different parameter values. Finally, we show that the methodology used here is not just limited to the combination of c- and D-designs, but can also be used to handle more general constraint situations such as limits on the cost of an experiment.