Particle Swarm Optimization for Finding Efficient Longitudinal Exact Designs for Nonlinear Models

Chen, Ping-Yang; Chen, Ray-Bing; Wong, Weng Kee

doi:10.51387/23-NEJSDS45

The New England Journal of Statistics in Data Science

Particle Swarm Optimization for Finding Efficient Longitudinal Exact Designs for Nonlinear Models

Volume 1, Issue 3 (2023), pp. 299–313

Ping-Yang Chen Ray-Bing Chen Weng Kee Wong

https://doi.org/10.51387/23-NEJSDS45

Pub. online: 10 August 2023 Type: Biomedical Research

Open Access

Accepted
13 May 2023

Published
10 August 2023

Abstract

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.

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Open access article under the CC BY license.

Keywords

HIV-dynamic model Locally D-optimal design Maximin optimal design Michaelis-Menten model Nature-inspired metaheuristic algorithm

Funding

The research of Wong was partially supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639. Wong is also partially supported by the Yushan Fellow Program by the Ministry of Education (MOE), Taiwan and he is grateful for the additional support and hospitality from The National Cheng Kung University in Tainan, Taiwan. The research of Chen was partially supported by the National Science Council under Grant NSC101-2118-M-006-002-MY2 and the Center for Data Science in the Miin Wu School of Computing at National Cheng Kung University.

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