Model robust designs for dose-response models

An optimal experimental design is a structured data collection plan aimed at maximizing the amount of information gathered. Determining an optimal experimental design, however, relies on the assumption that a predetermined model structure, relating the response and covariates, is known a priori. In practical scenarios, such as dose-response modeling, the form of the model representing the "true" relationship is frequently unknown, although there exists a finite set or pool of potential alternative models. Designing experiments based on a single model from this set may lead to inefficiency or inadequacy if the "true" model differs from that assumed when calculating the design. One approach to minimize the impact of the uncertainty in the model on the experimental plan is known as model robust design. In this context, we systematically address the challenge of finding approximate optimal model robust experimental designs. Our focus is on locally optimal designs, so allowing some of the models in the pool to be nonlinear. We present three Semidefinite Programming-based formulations, each aligned with one of the classes of model robustness criteria introduced by Läuter. These formulations exploit the semidefinite representability of the robustness criteria, leading to the representation of the robust problem as a semidefinite program. To ensure comparability of information measures across various models, we employ standardized designs. To illustrate the application of our approach, we consider a dose-response study where, initially, seven models were postulated as potential candidates to describe the dose-response relationship.