Efficient and Robust Block Designs for Order-of-Addition Experiments
Chang-Yun Lin
TL;DR
This paper tackles the need for efficient block designs in Order-of-Addition experiments when unit heterogeneity exists. It develops an indicator-function framework tailored to position-based OofA models and introduces a word length pattern criterion to guide robust block designs, complemented by construction algorithms that stack orthogonal Latin squares and orthogonal arrays. Through correlation analyses and simulation studies, the authors demonstrate that the proposed block OofA designs achieve substantial block-size reductions while maintaining power and controlling type I error at practical levels, and they validate the approach with a five-drug experiment showing correct identification of active position effects under batch variation. The work offers a practical, scalable methodology for designing block OofA experiments in complex settings and provides a foundation for extending these techniques to other domains where the order of component addition is critical.
Abstract
Designs for Order-of-Addition (OofA) experiments have received growing attention due to their impact on responses based on the sequence of component addition. In certain cases, these experiments involve heterogeneous groups of units, which necessitates the use of blocking to manage variation effects. Despite this, the exploration of block OofA designs remains limited in the literature. As experiments become increasingly complex, addressing this gap is essential to ensure that the designs accurately reflect the effects of the addition sequence and effectively handle the associated variability. Motivated by this, this paper seeks to address the gap by expanding the indicator function framework for block OofA designs. We propose the use of the word length pattern as a criterion for selecting robust block OofA designs. To improve search efficiency and reduce computational demands, we develop algorithms that employ orthogonal Latin squares for design construction and selection, minimizing the need for exhaustive searches. Our analysis, supported by correlation plots, reveals that the algorithms effectively manage confounding and aliasing between effects. Additionally, simulation studies indicate that designs based on our proposed criterion and algorithms achieve power and type I error rates comparable to those of full block OofA designs. This approach offers a practical and efficient method for constructing block OofA designs and may provide valuable insights for future research and applications.