Two-Stage Experimental Design for Dose-Response Modeling in Toxicology Studies

The efficient design of experiments (i.e., selection of experimental doses and allocation of animals) is important to establishing dose-response relationships in toxicology studies. The proposed procedure for design of experiments is distinct from those in the literature because it is able to adequately accommodate the special features of the dose-response data, which include non-normality, variance heterogeneity, possibly nonlinearity of the dose-response curve, and data scarcity. The design procedure is built in a sequential two-stage paradigm that allows for a learning process. In the first stage, preliminary experiments are performed to gain information regarding the underlying dose-response curve and variance structure. In the second stage, the prior information obtained from the previous stage is utilized to guide the second-stage experiments. An optimization algorithm is developed to search for the design of experiments that will lead to dose-response models of the highest quality. To evaluate model quality (or uncertainty), which is the basis of design optimization, a bootstrapping method is employed; unlike standard statistical methods, bootstrapping is not subject to restrictive assumptions such as normality or large sample sizes. The design procedure in this paper will help to reduce the experimental cost/time in toxicology studies and alleviate the sustainability concerns regarding the tremendous new materials and chemicals.