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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
Pub. online: 10 August 2023      Type: Methodology Article      Open accessOpen Access
Area: Biomedical Research
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.

References

[1] 
AbdelAziz, A. M., Alarabi, L., Basalamah, S. and Hendawi, A. (2021). A multi-objective optimization method for hospital admission problem – a case study on COVID-19 patients. Algorithms 14(2) 38. https://doi.org/10.3390/a14020038.
[2] 
Bonyadi, M. R. and Michalewicz, Z. (2014). A locally convergent rotationally invariant particle swarm optimization algorithm. Swarm Intelligence 8(3) 159–198.
[3] 
Boon, J. E. (2007). Generating exact D-optimal designs for polynomial models. Spring Simulation Multiconference 2 121–126.
[4] 
Butler, G. and Wolkowicz, G. (1985). A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM Journal on Applied Mathematics 45(1) 138–151. https://doi.org/10.1137/0145006. MR0775486
[5] 
Cheng, R. and Jin, Y. (2015). A competitive swarm optimizer for large scale optimization. IEEE Transactions on Cybernetics 45(2) 191–204.
[6] 
Cook, R. D. and Nachtsheim, C. J. (1980). A comparison of algorithms for constructing exact D-optimal designs. Technometrics 22(3) 315–324. https://doi.org/10.2307/1267577. MR0653111
[7] 
Dette, H. and Kunert, J. (2014). Optimal designs for the Michaelis-Menten model with correlated observations. Statistics: A Journal of Theoretical and Applied Statistics 48(6) 1254–1267. https://doi.org/10.1080/02331888.2013.839680. MR3269733
[8] 
Eberhart, R. and Kennedy, J. (1995). A new optimizer using particle swarm theory. In Micro Machine and Human Science, 1995. MHS’95., Proceedings of the Sixth International Symposium on 39–43. IEEE.
[9] 
Falco, I. D., Cioppa, A. D., Scafuri, U. and Tarantino, E. (2020). Coronavirus COVID-19 spreading in Italy: optimizing an epidemiological model with dynamic social distancing through Differential Evolution. arXiv preprint arXiv:2004.00553v3.
[10] 
Fedorov, V. (1972). Theory of optimal design. Academic, New York. MR0403103
[11] 
Gomes, D. C. D. S. and Serra, G. L. D. O. (2021). Machine learning model for computational tracking forecasting the COVID-19 dynamic propagation. IEEE Journal of Biomedical and Health Informatics 25(3) 515–622.
[12] 
Haines, L. M. (1987). The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models. Technometrics 29 439–447. MR2637962
[13] 
Han, C., Chaloner, K. and Perelson, A. S. (2002). Bayesian analysis of a population HIV dynamic model. In Case Studies in Bayesian Statistics, editors: Constantine Gatsonis, Robert E. Kass, Alicia Carriquiry, Andrew Gelman, David Higdon, Donna K. Pauler and Isabella Verdinelli, Lecture Notes in Statistics: Vol. VI, 223–337. Springer. https://doi.org/10.1007/978-1-4612-2078-7_10. MR1959658
[14] 
He, S., Peng, Y. and Sun, K. (2020). SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dynamics 101 10, 100071107102005743.
[15] 
Hosseini, E., Ghafoor, K. Z., Sadiq, A. S., Guizani, M. and Emrouznejad, A. (2020). COVID-19 optimizer algorithm, modeling and controlling of coronavirus distribution process. IEEE Journal of Biomedical and Health Informatics 24(10) 2765–2775.
[16] 
Lai, T. L., Choi, K. P., Tong, T. X. and Wong, W. K. (2021). A statistical approach to adaptive parameter tuning in nature-inspired optimization and optimal sequential design of dose-finding Trials. Statistica Sinica. In press. https://doi.org/10.5705/ss.20. MR4338089
[17] 
Lopez, S., France, J., Gerrits, W., Dhanoa, M., Humphries, D. and Dijkstra, J. (2000). A generalized Michaelis-Menten equation for the analysis of growth. Journal of Animal Science 78(7) 1816–1828.
[18] 
Makade, R. G., Chakrabarti, S. and Jamil, B. (2020). Real time estimation and prediction of the mortality caused due to COVID-19 using particle swarm optimization and finding the most influential parameter. Infectious Disease Modelling 5 772–782.
[19] 
Maloney, J. and Heidel, J. (2003). An analysis of a fractal kinetics curve of savageau. Anziam Journal 45 261–269. https://doi.org/10.1017/S1446181100013316. MR2017748
[20] 
Montepiedra, G., Myers, D. and B., Y. A. (1998). Application of genetic algorithms to the construction of exact D-optimal designs. Journal of Applied Statistics 25 817–826.
[21] 
Pinter, G., Felde, I., Mosavi, A., Ghamisi, P. and Gloaguen, R. (2020). COVID-19 pandemic prediction for hungary; a hybrid machine learning approach. MDPI Mathematics 8 890.
[22] 
Singh, D., Kumar, V., Vaishali and Kaur, M. (2020). Classification of COVID-19 patients from chest CT images using multi-objective Differential Evolution-based convolutional neural networks. European Journal of Clinical Microbiology and Infectious Diseases 39 1379–21389.
[23] 
Sun, J., Feng, B. and Xu, W. (2004). Particle swarm optimization with particles having quantum behavior. In Evolutionary Computation, 2004. CEC2004. Congress on 1, 325–331. IEEE.
[24] 
Sun, J., Xu, W. and Feng, B. (2004). A global search strategy of quantum-behaved particle swarm optimization. In Cybernetics and Intelligent Systems, 2004 IEEE Conference on 1, 111–116. IEEE.
[25] 
Tian, Y., Yang, S. and Zhang, X. (2020). An evolutionary multiobjective optimization based fuzzy method for overlapping community detection. IEEE Transactions on Fuzzy Systems 28(11) 2841–2855.
[26] 
Tian, Y., Zhang, X., Wang, C. and Jin, Y. (2018). An evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Transactions on Evolutionary Computation 24(2) 380–393.
[27] 
Tian, Y., Su, X., Su, Y. and Zhang, X. (2020). EMODMI: a multi-objective optimization based method to identify disease modules. IEEE Transactions on Emerging Topics in Computational Intelligence.
[28] 
Tian, Y., Liu, R., Zhang, X., Ma, H., Tan, K. C. and Jin, Y. (2020). A multi-population evolutionary algorithm for solving large-scale multi-modal multi-objective optimization problems. IEEE Transactions on Evolutionary Computation. MR4361281
[29] 
Tong, T. X., Choi, K. P., Lai, T. L. and Wong, W. K. (2021). Stability Bounds and Almost Sure Convergence of Improved Particle Swarm Optimization Methods. Research in Mathematical Sciences. https://doi.org/10.1007/s40687-020-00241-4. MR4257863
[30] 
van den Bergh, F. and Engelbrecht, A. P. (2002). A new locally convergent particle swarm optimiser. In Systems, Man and Cybernetics, 2002 IEEE International Conference on, 3 6. IEEE.
[31] 
Whitacre, J. M. (2011). Recent trends indicate rapid growth of nature-inspired optimization in academia and industry. Computing 93 121–133. https://doi.org/10.1007/s00607-011-0154-z. MR2860177
[32] 
Whitacre, J. M. (2011). Survival of the flexible: explaining the recent popularity of nature-inspired optimization within a rapidly evolving world. Computing 93 135–146. https://doi.org/10.1007/s00607-011-0156-x. MR2860178
[33] 
Wu, M., Hu, W., Hu, J. and Yen, G. G. (2021). Adaptive multiobjective particle swarm optimization based on evolutionary state estimation. IEEE Transactions on Cybernetics 51(7) 3738–3751.
[34] 
Yang, X. S. (2010). Engineering optimization: an introduction with metaheuristic applications. In Particle Swarm Optimization, John Wiley and Sons.
[35] 
Yeap, B. Y., Catalano, P. J., Ryan, L. M. and Davidian, M. (2003). Robust two-stage approach to repeated measurements analysis of chronic ozone exposure in rats. Journal of Agricultural, Biological, and Environmental Statistics 8(4) 438–454.
[36] 
Yu, R. C. and Rappaport, S. M. (1996). Relation between pulmonary clearance and particle burden: a Michaelis-Menten-like kinetic model. Occupational and Environmental Medicine 53(8) 567–572.
[37] 
Yu, X. Z. and Gu, J. D. (2007). Differences in Michaelis-Menten kinetics for different cultivars of maize during cyanide removal. Ecotoxicology and Environmental Safety 67(2) 254–259.
[38] 
Zhigljavsky, A., Dette, H. and Pepelyshev, A. (2010). A new approach to optimal design for linear models with correlated observations. Journal of the American Statistical Association 105 1093–1103. https://doi.org/10.1198/jasa.2010.tm09467. MR2752605

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© 2023 New England Statistical Society
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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