This work is concerned with the efficient design of biological experiments to quantify the dose-response relationship of a substance, which is one of the most fundamental steps in risk assessment. To obtain such relationships, biological experiments need to be performed at different dose levels to observe the corresponding bioactivity responses of animals. Because of costs, ethics, or other limitations, sample sizes are usually restricted and efficient use of resources is critical. Thus, the design of experiments, i.e., the selection of experimental doses and the allocation of animals, plays an important role in the estimation of dose-response relationships. Efficient design for dose-response modeling is challenging due to the special features of toxicity data, i.e., the possibly nonlinear nature of dose-response curves and the typical variance heterogeneity (non-constant variance) involved. In this work, an experimental design procedure particularly suitable to toxicity data collection is developed to guide the dose selection and animal allocation in experiments. The design procedure is built in a two-stage Bayesian paradigm, which provides a statistically valid mechanism to utilize prior information for the design of future experiments. Most appropriate dose-response and variance models are identified to describe the toxicity data. Bootstrapping, a computationally intensive resampling method as opposed to conventional statistical inference methods, are used to derive important information from the preliminary data required by the subsequent experimental design. To achieve practically useful designs, multiple design criteria are considered simultaneously, and multi-objective metaheuristics are adapted to search for a set of Pareto optimum designs, which allow for the evaluation of various tradeoffs in practical experimental settings. The efficiency of the proposed design methods over conventional designs is demonstrated through extensive simulation experiments as well as the toxicology study of a series of engineering nanomaterials.
The Toxicologist. Society of Toxicology 50th Annual Meeting and ToxExpo, March 6-10, 2011, Washington, DC