Summary:

We construct ${\mu }_p$-optimal approximate designs for comparing population curves in hierarchical models with group-specific treatment. Equivalence theorems are given to confirm ${\mu }_p$-optimality of designs and the optimal allocation of sample size in each group. An illustrative application to find ${\mu }_1$ and ${\mu }_{\infty }$-optimal designs is presented for the random slope models with two-treatment group assignments.

中文翻译：

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分层模型中比较人口曲线的优化设计

概括：

我们构建 ${\mu }_{磷}$- 用于比较分层模型中群体曲线与组特定治疗的最佳近似设计。给出等价定理来证实${\mu }_{磷}$- 设计的最优性和每组样本量的最佳分配。一个说明性的应用程序来查找${\mu }_1$ 和 ${\mu }_{\infty }$- 为具有两个治疗组分配的随机斜率模型提供了最佳设计。