Optimal Experimental Design Strategies for Detecting Hormesis

Abstract

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, 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.

A web-based tool for designing experimental studies to detect hormesis and estimate the threshold dose

“…For instance, when there is only interest in one model, the user selects the model from the given list, the dose space and the nominal values of the parameters for the model. The app also evaluates the efficiency of any generated design relative to one of the predefined designs that include the design for the WET test, the design for the toxicity study of the chemical diethylhexl phthalate (DEHP), a carcinogen, on mice given by Dette et al (2011) or any desired design that the user inputs in the corresponding box.…”

“…The app facilitates comparison of the efficiencies of various optimal designs for the two models discussed in our paper and those studied in Dette et al (2011).The tab “Models to compare” allows the user to modify the predefined comparison (Figure 2 bottom). For particular cases, the user has to select the design interval meaningfully, choose the two models among the five available models, and carefully modify the nominal values for the model parameters.…”

“…The errors in both models are assumed to be normally and independently distributed each with mean 0 and constant variance. These assumptions are the same as those used in Dette et al . (2011) for designing studies to detect existence of hormesis.…”

“…One of their findings was that increasing the number of low-level doses improves the power for detecting hormetic effect and that current designs do not seem adequate to detect existence of hormesis. The work by Dette et al (2011) appears to be the first technical piece of work to set up formal hypotheses to detect hormesis and estimate threshold level and construct different types of optimal designs for various purposes in such studies. In particular, a hypothesis to formally test whether hormesis exists using a model based approach is formulated in Dette et al (2011).…”

“…A second goal is to create a set of user-friendly codes that is freely accessible to all and allows researchers to find tailor-made optimal designs for their problems, compare competing designs and evaluate robustness properties of a selected design. In particular, the online tool allows us to readily compare efficiencies of different designs across models, including the different models proposed for studying hormesis in Dette et al (2011). We expect that having an online tool is likely going to be more effective than providing computer programs to researchers in biomedicine in terms of encouraging them to explore important design issues.…”