Optimal experimental design strategies for detecting hormesis

Hormesis is a widely observed phenomenon in many branches of life sciences, ranging from toxicology studies to agronomy, with obvious public health and risk assessment implications. We address optimal experimental design strategies for determining the presence of hormesis in a controlled environment using the recently proposed Hunt-Bowman model. We propose alternative models that have an implicit hormetic threshold, discuss their advantages over current models, and construct and study properties of optimal designs for (i) estimating model parameters, (ii) estimating the threshold dose, and (iii) testing for the presence of hormesis. We also determine maximin optimal designs that maximize the minimum of the design efficiencies when we have multiple design criteria or there is model uncertainty where we have a few plausible models of interest. We apply these optimal design strategies to a teratology study and show that the proposed designs outperform the implemented design by a wide margin for many situations.