Concentration-dependent cytotoxicity experiments are frequently used in toxicology. Although it has been reported that an adequate choice of concentrations, i.e., the design, substantially improves the quality of the statistical inference, a recent literature review of three major toxicological journals has shown that the corresponding methods are rarely used in toxicological practice.
In this talk, we address the optimal design problem in cytotoxicity experiments both from an applied and a theoretical point of view. On the one hand, we present strategies and concrete examples of how established statistical methodology can be made more accessible to potential users, especially to biologists. On the other hand, we consider a specific biological challenge in cytotoxicity experiments from the statistician’s point of view: identifying alert concentrations where a pre-specified threshold of the response variable is exceeded. We develop a model-based testing procedure for that purpose and address the corresponding optimal design problem. We construct an optimal design criterion to improve the model-based testing procedure concerning its power. Thus, an optimal design minimizes the maximum variance of the alert concentration estimator. Optimal design theory is developed, and the results are illustrated in several examples where the alert concentration is identified under the assumption of different concentration-response relationships. In particular, it is demonstrated within a simulation study that using the optimal design results in more powerful tests for identifying alerts than using other “non-optimal” designs.