The $D_{MP}$-criterion is proposed to generate optimal designs for the logistic regression model with reduced separation probabilities. This compound criterion has two components: (a) the $D$-efficiency of the candidate design and (b) a penalty term that captures the average distance of the candidate design's support points from the region of maximum prediction variance (MPV). A $D_{MP}$-optimal design maximizes the $D_{MP}$-criterion. The aim is to obtain compromise experimental designs with high $D$-efficiencies that are more robust to separation than a $D$-optimal design of equal size. This paper presents the $D_{MP}$-criterion and demonstrates examples of its potential use as a means of mitigating separation in the design phase of a binary response experiment. For the examples presented, the local $D_{MP}$-optimal designs offer a 20-30% reduction in separation probability over the local $D$-optimal designs while maintaining $D$-efficiencies over 93%. A robust design methodology is also demonstrated, where a robust $D_{MP}$-optimal design is compared to a Bayesian $D$-optimal design and shown to have comparable $D$-efficiencies across a range of randomly drawn parameter values while offering a mean reduction in separation probability of 23.9%.

中文翻译：

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逻辑回归模型的 D 有效和分离稳健设计的复合最优性标准

这 $D_{米磷}$-criterion 被提议为逻辑回归模型生成优化设计并降低分离概率。该复合标准有两个组成部分：(a)$D$- 候选设计的效率和 (b) 一个惩罚项，它捕获候选设计的支持点与最大预测方差 (MPV) 区域的平均距离。一种$D_{米磷}$- 优化设计最大化 $D_{米磷}$-标准。目的是获得具有高$D$- 比分离更稳健的效率 $D$- 相同尺寸的最佳设计。本文介绍了$D_{米磷}$-标准并展示了其作为一种在二元响应实验设计阶段减轻分离的潜在用途的示例。对于提供的示例，本地$D_{米磷}$- 最佳设计比局部设计降低了 20-30% 的分离概率 $D$- 优化设计，同时保持 $D$- 效率超过 93%。还展示了稳健的设计方法，其中稳健的$D_{米磷}$- 最优设计与贝叶斯相比 $D$- 最佳设计并显示具有可比性 $D$- 一系列随机抽取的参数值的效率，同时平均降低了 23.9% 的分离概率。