Dual-Orthogonal Arrays for Order-of-Addition Two-Level Factorial Experiments

A new class of orthogonal arrays called dual-orthogonal arrays is proposed in this paper to design order-of-addition two-level factorial experiments in which both component addition orders and component levels can be varied over treatments. Dual-orthogonal arrays can be viewed as an optimal combination of order-of-addition orthogonal arrays and two-level orthogonal arrays. Based on these two different concepts of orthogonality, when a compound model is used to fit the observed data, both pairwise order effects and component main effects can be estimated with optimal efficiency. Under the assumption of normality, these two kinds of parametric effects can also be inferred independently. A three-drug combination study is first used to show that dual-orthogonal arrays can be practical for real-world studies. Both combinatorial and computational methods are then introduced to construct dual-orthogonal arrays. Additionally, a design catalogue is generated for future work.

本文提出了一类名为双正交阵列（dual-orthogonal arrays）的新型正交阵列（orthogonal array），用于设计添加顺序型两水平析因试验（order-of-addition two-level factorial experiments），该类试验中组分的添加顺序与组分水平均可在不同处理间灵活调整。双正交阵列可视为添加顺序型正交阵列（order-of-addition orthogonal arrays）与两水平正交阵列的最优结合体。基于这两种不同的正交性概念，当采用复合模型拟合观测数据时，可同时以最优效率估计两两顺序效应与组分主效应。在正态性假设下，这两类参数效应还可实现独立统计推断。本文首先通过一项三药物组合研究，验证了双正交阵列在实际研究中的实用性。随后本文介绍了组合构造与计算构造两类方法，用于构建双正交阵列。此外，本文还生成了可供后续研究使用的设计目录。