Nature-inspired Metaheuristics for finding Optimal Designs for the Continuation-Ratio Models

Qiu, Jiaheng; Wong, Weng Kee

doi:10.51387/23-NEJSDS44

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

Jiaheng Qiu Weng Kee Wong

https://doi.org/10.51387/23-NEJSDS44

Pub. online: 7 August 2023 Type: Biomedical Research

Open Access

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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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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