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

TL;DR

This paper introduces mREX, a versatile randomized exchange algorithm that efficiently computes optimal designs for multi-response experiments, including complex models like dose-response in clinical trials.

Contribution

The paper presents mREX, an extension of REX, with novel initialization, criteria extension, and exchange methods for multi-response optimal design computation.

Findings

mREX converges faster than existing methods.

Applicable to linear, nonlinear, and generalized linear models.

Demonstrated effectiveness in clinical trial dose-response models.

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 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.