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The New England Journal of Statistics in Data Science


Nature-inspired Metaheuristics for finding Optimal Designs for the Continuation-Ratio Models
Volume 2, Issue 1 (2024), pp. 15–29
Pub. online: 7 August 2023      Type: Methodology Article      Open accessOpen Access
Area: Biomedical Research
Accepted
24 June 2023
Published
7 August 2023

Abstract

The continuation-ratio (CR) model is frequently used in dose response studies to model a three-category outcome as the dose levels vary. Design issues for a CR model defined on an unrestricted dose interval have been discussed for estimating model parameters or a selected function of the model parameters. This paper uses metaheuristics to address design issues for a CR model defined on any compact dose interval when there are one or more objectives in the study and some are more important than others. Specifically, we use an exemplary nature-inspired metaheuristic algorithm called particle swarm optimization (PSO) to find locally optimal designs for estimating a few interesting functions of the model parameters, such as the most effective dose ($MED$), the maximum tolerated dose ($MTD$) and for estimating all parameters in a CR model. We demonstrate that PSO can efficiently find locally multiple-objective optimal designs for a CR model on various dose intervals and a small simulation study shows it tends to outperform the popular deterministic cocktail algorithm (CA) and another competitive metaheuristic algorithm called differential evolutionary (DE). We also discuss hybrid algorithms and their flexible applications to design early Phase 2 trials or tackle biomedical problems, such as different strategies for handling the recent pandemic.

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© 2024 New England Statistical Society
Open access article under the CC BY license.

Keywords
Dose response Models Implicit function theorem Maximin tolerated dose Most effective dose Multiple-objective optimal design

Funding
The research of Wong reported in this publication was partially supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639.

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