A Component-Position Model, Analysis and Design for Order-of-Addition Experiments

An order-of-addition experiment is a kind of experiment in which the response is affected by the addition order of materials or components. In many situations, performing the full design with all possible permutations of components is unaffordable, especially when the number of components is larger than four. We introduce a component-position model for analyzing data from such experiments and study associated problems. We further propose a new type of design, called component orthogonal array, as a fraction of the full design for order-of-addition experiments. It is shown that component orthogonal arrays have the same D-efficiency as the full design under our proposed model. Component orthogonal arrays also perform well under the existing pairwise ordering model. Two drug combination experiments are used to show the effectiveness of the proposed model and designs. Supplementary materials for this paper are available online.

添加顺序实验（order-of-addition experiment）是一类响应结果受材料或组分的添加顺序影响的实验。在多数场景中，若对组分的所有可能排列实施全设计，往往成本高昂，尤其当组分数目超过4时。本文提出一种用于分析此类实验数据的组分-位置模型（component-position model），并对相关问题展开研究。进一步，本文提出一种新型实验设计——组分正交阵列（component orthogonal array），作为添加顺序实验全设计的分式设计。研究表明，在本文提出的模型框架下，组分正交阵列与全设计具备相同的D效率（D-efficiency）。此外，组分正交阵列在现有成对顺序模型下亦表现优异。本文通过两个药物组合实验验证了所提模型与设计的有效性。本文的补充材料可在线获取。