Optimal Designs for the Two-Dimensional Interference Model

• 成果类型: Article
• 署名作者: Hedayat, A. S.; Xu, Heng; Zheng, Wei
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Nektar Therapeutics; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1654877
• 发表日期: 2020
• 页码: 1812-1821
• 关键词: neighbor-balanced designs; universally optimal designs; optimal crossover designs; locally optimal designs; nonlinear models; block-designs

摘要

Recently, there have been some major advances in the theory of optimal designs for interference models when the block is arranged in one-dimensional layout. Relatively speaking, the study for two-dimensional interference model is quite limited partly due to technical difficulties. This article tries to fill this gap. Specifically, we set the tone by characterizing all possible universally optimal designs simultaneously through one linear equations system (LES) with respect to the proportions of block arrays. However, such a LES is not readily solvable due to the extremely large number of block arrays. This computational issue could be resolved by identifying a small subset of block arrays with the theoretical guarantee that any optimal design is supported by this subset. The nature of two-dimensional layout of the block has made this task very technically challenging, and we have theoretically derived such subset for any size of the treatment array and any number of treatments under comparison. This facilitates the development of the algorithm for deriving either approximate or exact designs. for this article are available online.