Nonlinear models are challenging in optimal designs due to their complexity and lack of canonical forms. The complete class strategy provides a unified framework for studying optimal designs for nonlinear models. However, the current strategy does not apply to many models under this framework. In this article, we propose a tool called ancillary functions as an extension to the complete class strategy. We also provide results on minimally supported designs with proper conditions. We demonstrate this tool with two-parameter dose–response models, which include the Beta-Poisson model, the complementary log–log model, and the skewed logit model. The results of this article add to the previous complete class framework and make the minimally supported design available for more nonlinear models that were previously not feasible.

中文翻译：

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具有辅助功能的全类下的优化设计

非线性模型由于其复杂性和缺乏规范形式而在优化设计中具有挑战性。完整的类策略为研究非线性模型的最优设计提供了一个统一的框架。但是，目前的策略不适用于此框架下的许多模型。在本文中，我们提出了一种称为辅助功能的工具，作为对完整类策略的扩展。我们还提供了具有适当条件的最低支持设计的结果。我们用双参数剂量反应模型演示了这个工具，其中包括 Beta-Poisson 模型、互补 log-log 模型和倾斜 logit 模型。本文的结果添加到之前完整的类框架中，并使最小支持的设计可用于以前不可行的更多非线性模型。