Optimal designs for detecting and characterizing hormesis in toxicological tests

Abstract

Toxicological tests are experiments that show the effects of a toxic on organisms, ecosystems, etc. This study focuses on tests in the aquatic environment, in which the test involving Ceriodaphnia Dubia organism stands out. The literature indicates that in two out of every three experiments carried out with this organism, there is hormesis. This study applies optimal experimental design theory to a linear quadratic model with a Poisson distribution for the response, in order to obtain designs that allow efficient detection and characterization of hormesis. To this end, a variety of utility functions are used, including the dose for the zero equivalent point, the area under the curve, the dose at which maximum response is reached or the dose at which there is a given relative inhibition with respect to the control or the maximum. A study of cross efficiencies of the calculated designs shows the importance of correctly defining the goal of the experiment, in order to obtain the most appropriate design.