Optimal test design for binary response data: the example of the fish embryo toxicity test

Abstract

Background: The fish embryo toxicity test (FET) is an established method in toxicology research for quantifying the risk potential of environmental contaminations and other substances. The typical results of the method are the half maximal effective concentration (EC50) or the no observed effect concentration (NOEC). However, from an environmental perspective, it is most important to safely identify the concentration of the substance effect which lies above the effect under control condition (spontaneous effect). The common FET is not optimal to detect ECs for small target effects. This paper shows how to optimize the efficiency and consequently the benefit of the FET for small effects using an adequate experimental design. The approach presented here can be carried over to all test systems generating binary (yes/no) outcomes. Results: The experimental design has three components in this context: determination of spontaneous response, sample size calculation, and dose allocation. A strategy for all three components is proposed from which a design is given including precision requirements and makes the most effective use of the experimental effort. This strategy amounts to expanding the usual FET guidelines of Organisation for Economic Co-operation and Development, German Institute for Standardization, or American Society for Testing and Materials by adding a planning step that adapts the test to the specific user’s need. Conclusions: For the practical calculation of an adapted design, a newly developed software is presented as R package toxtestD. It provides a user-friendly way of developing an optimal experimental design for the FET without in-depth statistical knowledge. The programme is suited for all experimental problems involving a binary outcome and a continuous concentration.