Abstract Crossover designs involve two types of treatment effects, a direct effect and a carryover effect, and several optimality results are available for inferring on these two effects separately. However, an aim of a designed experiment is to recommend a single treatment which will be used over longer time periods. When this treatment is used over many periods, the effect on the subject at any time period will be the total of its direct and carryover effects, and so, at the designed experiment stage it is important to study the sum of the direct and carryover effects of the same treatment, that is, the total effect. Not much is known on the optimality of designs for this total effect. In this article we obtain universally optimal designs for total effects under a non-circular model with two periods and correlated errors. We also report some highly efficient designs in this context.

中文翻译：

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用于推断总效应的最佳交叉设计

摘要 交叉设计涉及两种类型的处理效应，直接效应和结转效应，并且有几个最优结果可用于分别推断这两种效应。然而，设计实验的目的是推荐将在更长时间内使用的单一处理。当这种处理在多个时期使用时，在任何时间段对受试者的影响将是其直接和遗留影响的总和，因此，在设计的实验阶段，研究直接和遗留影响的总和很重要相同的治疗，即总效果。对于这种总效应的设计的最优性知之甚少。在本文中，我们在具有两个周期和相关误差的非圆形模型下获得了总效应的普遍最优设计。