ABSTRACT The balanced allocation of experimental units with regard to various known covariates among several treatment groups, before the physical experiment takes place, is often considered to be the most reasonable allocation scheme in all intervention studies and clinical trials. It is well-known that covariate mean balance over various treatment groups ensures widely used D- and A-optimality. However, it is not well-understood if the reverse proposition holds or not. For continuous covariates, it has been observed previously by the same authors, through a computationally intensive method, that covariate mean balance is nearly achieved for an optimal design. In the present paper, it has been analytically established that, with categorical covariates, the covariate mean balance can be ensured through D- and A-optimality.

中文翻译：

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通过将具有已知分类协变量的实验单元优化分配到两个处理中来确保平衡

摘要 在进行物理实验之前，在多个治疗组之间根据各种已知协变量平衡分配实验单元，通常被认为是所有干预研究和临床试验中最合理的分配方案。众所周知，不同处理组的协变量平均平衡确保了广泛使用的 D 和 A 最优性。然而，相反的命题是否成立尚不清楚。对于连续协变量，同一作者之前已经观察到，通过计算密集型方法，对于优化设计几乎可以实现协变量平均平衡。在本文中，已经通过分析确定，使用分类协变量，可以通过 D 和 A 最优性确保协变量平均平衡。