The New England Journal of Statistics in Data Science

Designing longitudinal studies is generally a very challenging problem because of the complex optimization problems. We show the popular nature-inspired metaheuristic algorithm, Particle Swarm Optimization (PSO), can find different types of optimal exact designs for longitudinal studies with different correlation structures for different types of models. In particular, we demonstrate PSO-generated D-optimal longitudinal studies for the widely used Michaelis-Menten model with various correlation structures agree with the reported analytically derived locally D-optimal designs in the literature when there are only 2 observations per subject, and their numerical D-optimal designs when there are 3 and 4 observations per subject. We further show the usefulness of PSO by applying it to generate new locally D-optimal designs to estimate model parameters when there are 5 or more observations per subject. Additionally, we find various optimal longitudinal designs for a growth curve model commonly used in animal studies and for a nonlinear HIV dynamic model for studying T-cells in AIDS subjects. In particular, c-optimal exact designs for estimating one or more functions of model parameters (c-optimality) were found, along with other types of multiple objectives optimal designs.