Optimality and efficiency of two-treatment repeated measurement designs
两处理重复测量设计的最优性与效率AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究两处理交叉实验的最优设计，未涉及所列面板数据估计或因果识别方法。
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两处理重复测量设计的最优性与效率
- 研究问题
- 在不同协方差结构下，如何分配受试者到两处理交叉序列以获得最优重复测量设计，并计算非最优设计的效率？
- 方法与思路
- 作者将已有一般最优性结果专门化到两处理情形，以线性方程确定序列分配比例，并给出处理效应信息矩阵。
- 材料陈述的贡献
- 摘要称导出部分设计必须对偶平衡的条件，确认三四期设计最优性，构造五六期新设计，并给出特定设计的效率公式。
- 阅读关注点
- 应核对处理效应模型、最优性准则、对偶与平衡的定义，以及任意协方差和自回归协方差下结论的适用范围。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；未给出模型细节和分配公式，重复测量设计本身不能等同于面板识别方法。
原文摘要
For an arbitrary covariance matrix and any number of treatments and periods, necessary and sufficient conditions for the optimality of a repeated measurements, i.e. crossover or changeover, design were given in the, as yet, unpublished report by H. B. Kushner ‘Optimal repeated measurements designs: the linear optimality equations’ (Kushner, report). Here we specialise the results to the two-treatment case. We give linear equations whose solutions are the proportions of subjects allocated to each treatment sequence in the most general optimal design. The treatment effects information matrix of an optimal design is also presented. The results are applied to several situations. For arbitrary covariance matrices, we show that designs consisting of at most two treatment sequences and their duals must necessarily be dual balanced to be optimal. For autoregressive covariance matrices, we confirm that designs of Matthews (1987) for three and four periods are optimal and we derive new optimal designs for five and six periods. Some optimality results of Laska & Meisner (1985) are extended. A simple formula for the efficiency of a dual balanced nonoptimal design is provided and used to compute the exact efficiencies of some of Kunert's (1991) designs.