A Randomized Exchange Algorithm for Optimal Design of Multi-Response Experiments

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 matrix polynomial. 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 to bivariate dose-response Emax models for clinical trials, both without and with the inclusion of covariates.

💡 Research Summary

The paper addresses the problem of computing optimal approximate designs for multi‑response regression models, a topic that has received relatively little attention compared with the single‑response case. Building on the randomized exchange algorithm (REX) introduced by Harman et al. (2020) for single‑response models, the authors propose mREX (multi‑response RE X), a generalized algorithm that works for any differentiable Kiefer Φₚ‑optimality criterion (p ∈