Optimal experimental designs for big and small experiments in toxicology with applications to studying hormesis via metaheuristics

There are theoretical methods for constructing model-based optimal designs for a given design criterion when the sample size is large. Some of these methods may work for certain models or design criteria and some may find the optimal designs only under a restrictive setting. When the sample size is small, the theory-based methods may become invalid and the optimal designs may also not be implementable. Our first goal is to introduce nature-inspired metaheuristics to efficiently find all types of model-based optimal designs. These metaheuristic algorithms, widely used in engineering, computer science, and artificial intelligence, are generally fast and free of stringent assumptions. For our second goal, we introduce an efficient rounding method to produce an implementable, exact design for small-sized experiments based on large-sample optimal designs. To provide toxicologists with easy access to a variety of model-based optimal designs for both large and small experiments, our third goal is to develop a web-based app. This app will generate different types of model-based optimal designs, allow comparisons, and evaluate the efficiency of any design. As an application, we focus on hormesis and find model-based designs for detecting the presence of hormesis, estimating model parameters and estimating the threshold dose. The methodology is not restricted to studying hormesis only and is broadly applicable for designing other studies in toxicology and beyond.