标题： 最优设计用于具有疗效与毒性结果的活性控制剂量寻找试验 显示英文标题

标题： Optimal designs for active controlled dose finding trials with efficacy-toxicity outcomes

摘要： 针对疗效和毒性结局的非线性回归模型在剂量寻找试验中（例如制药药物开发）越来越被使用。然而，关于相关活性对照试验的实验设计研究仍然很少。 本文我们推导了在活性对照临床剂量寻找试验中估计疗效和毒性的最优设计，当双变量连续结局由至多二次多项式、Michaelis-Menten 模型、Emax 模型或其组合建模时。我们确定了最优设计所需的不同剂量水平数量的上限，并提供了设计空间边界点包含在最优设计中的条件。 我们还给出了最小支持的$D$-最优设计的解析描述，并表明它们不依赖于双变量结局之间的相关性。 我们通过数值例子说明所提出的方法，并展示了$D$-最优设计在最近文献中考虑的一项试验中的优势。 显示英文摘要

摘要： Nonlinear regression models addressing both efficacy and toxicity outcomes are increasingly used in dose-finding trials, such as in pharmaceutical drug development. However, research on related experimental design problems for corresponding active controlled trials is still scarce. In this paper we derive optimal designs to estimate efficacy and toxicity in an active controlled clinical dose finding trial when the bivariate continuous outcomes are modeled either by polynomials up to degree 2, the Michaelis- Menten model, the Emax model, or a combination thereof. We determine upper bounds on the number of different doses levels required for the optimal design and provide conditions under which the boundary points of the design space are included in the optimal design. We also provide an analytical description of the minimally supported $D$-optimal designs and show that they do not depend on the correlation between the bivariate outcomes. We illustrate the proposed methods with numerical examples and demonstrate the advantages of the $D$-optimal design for a trial, which has recently been considered in the literature.