标题： 多响应实验在线性和稀疏性约束下的最优精确设计 显示英文标题

标题： Optimal Exact Designs of Multiresponse Experiments under Linear and Sparsity Constraints

摘要： 我们提出一种计算方法，在有限的设计空间上构建精确设计，这些设计在标准线性和特定的“稀疏性”约束组合下，对于多响应回归实验是最佳的。 线性约束处理例如多种资源消耗的限制和最优设计增强的问题，而稀疏性约束控制设计所使用的不同试验条件的集合。 关键思想是构建一个人工的最优设计问题，该问题可以使用任何现有的数学规划技术来解决纯线性约束下的单变量响应最优设计问题。 然后，该人工问题的解可以直接转换为具有组合线性和稀疏性约束的主多变量响应设置的最优设计。 我们通过具有安全、疗效和成本约束的剂量反应实验来展示该方法的实用性和灵活性，其中成本也取决于所使用不同剂量的数量。 显示英文摘要

摘要： We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear constraints address, for example, limits on multiple resource consumption and the problem of optimal design augmentation, while the sparsity constraints control the set of distinct trial conditions utilized by the design. The key idea is to construct an artificial optimal design problem that can be solved using any existing mathematical programming technique for univariate-response optimal designs under pure linear constraints. The solution to this artificial problem can then be directly converted into an optimal design for the primary multivariate-response setting with combined linear and sparsity constraints. We demonstrate the utility and flexibility of the approach through dose-response experiments with constraints on safety, efficacy, and cost, where cost also depends on the number of distinct doses used.