Optimal designs for comparing curves.
Optimal designs for comparing curves.
复制标题
比较曲线的最佳设计。
DOI：
10.1214/15-aos1399
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发表时间：
2016-06
影响因子：
4.5
通讯作者：
Schorning K
中科院分区：
文献类型：
--
作者：
Dette H;Schorning K
我们考虑了两条回归曲线的比较的最优设计问题，该问题用于建立两组剂量反应关系之间的相似性。一对最优设计使两个回归函数之间的差置信带的宽度最小化。针对这一非标准设计问题，发展了最优设计理论(等价性定理、效率界)，并对一些常用的剂量响应模型进行了显式优化设计。结果在几个建立剂量反应关系模型的例子中得到了说明。证明了回归曲线比较的最优设计对不是单个模型的最优设计对。特别是，用本文提出的最优设计代替常用的“非最优”设计，使信任带的宽度减少了50%以上。
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%.