OPTIMAL DESIGNS FOR COMPARING CURVES

• 成果类型: Article
• 署名作者: Dette, Holger; Schorning, Kirsten
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1399
• 发表日期: 2016
• 页码: 1103-1130
• 关键词: weighted polynomial regression; models; CONVERGENCE; EQUIVALENCE; EFFICIENCY

摘要

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non-standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular, it is shown that the use of the optimal designs proposed in this paper instead of commonly used non-optimal designs yields a reduction of the width of the confidence band by more than 50%.