Finding optimal designs for estimating hormesis effect sizes

Abstract

There is increasing interest in hormesis as the phenomenon gains growing recognition in toxicology, public health and medicine. This paper is the first to focus on constructing model-based optimal designs for estimating the expected amount of hormesis using measures based on the area-under-the-curve (AUC). These measures can be used regardless of the choice of dose–response model. We first review optimal design techniques and propose new designs for estimating the degree or amount of hormesis with maximum precision at minimal cost when the sample size is large or small. We use a variety of state-of-the-art algorithms , including nature-inspired metaheuristic algorithms to search for the optimal designs. While the latter are not new, they are very flexible, fast and do not need technical assumptions for them to work well. Consequently, they are general purpose optimization algorithms and can be used to optimize any one or more objective functions for different models. When the experiment has two or more objectives, possibly with unequal interest, we find Pareto-optimal designs that balance the tradeoffs among the objectives. Experimental data are used to motivate and illustrate our approaches.