Optimal experimental designs for dose–response studies with continuous endpoints

In most areas of clinical and preclinical research, the required sample size determines the costs and effort for any project, and thus, optimizing sample size is of primary importance. An experimental design of dose–response studies is determined by the number and choice of dose levels as well as the allocation of sample size to each level. The experimental design of toxicological studies tends to be motivated by convention. Statistical optimal design theory, however, allows the setting of experimental conditions (dose levels, measurement times, etc.) in a way which minimizes the number of required measurements and subjects to obtain the desired precision of the results. While the general theory is well established, the mathematical complexity of the problem so far prevents widespread use of these techniques in practical studies. The paper explains the concepts of statistical optimal design theory with a minimum of mathematical terminology and uses these concepts to generate concrete usable D-optimal experimental designs for dose–response studies on the basis of three common dose–response functions in toxicology: log-logistic, log-normal and Weibull functions with four parameters each. The resulting designs usually require control plus only three dose levels and are quite intuitively plausible. The optimal designs are compared to traditional designs such as the typical setup of cytotoxicity studies for 96-well plates. As the optimal design depends on prior estimates of the dose–response function parameters, it is shown what loss of efficiency occurs if the parameters for design determination are misspecified, and how Bayes optimal designs can improve the situation.