A randomized exchange algorithm for optimal design of multi-response experiments

Pál Somogyi (), Samuel Rosa () and Radoslav Harman ()
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Pál Somogyi: Comenius University
Samuel Rosa: Comenius University
Radoslav Harman: Comenius University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 6, No 17, 1186 pages

Abstract: Abstract Despite the increasing prevalence of vector observations, computation of optimal experimental design for multi-response models has received limited attention. To address this problem within the framework of approximate designs, we introduce mREX, an algorithm that generalizes the randomized exchange algorithm REX (J Am Stat Assoc 115:529, 2020), originally specialized for single-response models. The mREX algorithm incorporates several improvements: a novel method for computing efficient sparse initial designs, an extension to all differentiable Kiefer’s optimality criteria, and an efficient method for performing optimal exchanges of weights. For the most commonly used D-optimality criterion, we propose a technique for optimal weight exchanges based on the characteristic polynomial of a matrix. The mREX algorithm is applicable to linear, nonlinear, and generalized linear models, and scales well to large problems. It typically converges to optimal designs faster than available alternative methods, although it does not require advanced mathematical programming solvers. We demonstrate the usefulness of mREX on bivariate dose-response Emax models for clinical trials, both without and with the inclusion of covariates.

Keywords: Optimal experimental design; Multi-response models; Convex optimization algorithms; D-optimality; Kiefer’s criteria; Emax models (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-025-01000-7

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