干扰下随机确定性饱和设计的优化
Optimizing Randomized and Deterministic Saturation Designs under Interference
摘要：
随机饱和设计是一个设计族，它随机分配给群体的每个聚类可能不同的治疗比例。因此，他们推广了众所周知的（分层）完全随机化设计和基于簇的随机化设计，这些设计被列为特殊情况。我们发现，在稳定的单位处理值的假设下，无论是基于聚类或分层完全随机化设计实际上是最优的随机饱和设计之间的均值差估计的偏差和方差。然而，当存在干扰时，情况不再如此。我们提供了封闭形式的偏差和方差的差异的均值估计下的线性模型的干扰和调查的优化，这些目标。除了随机饱和设计，我们提出了一个确定性饱和设计，其中集群的治疗比例是固定的，而不是随机的，以进一步提高正确的模型规格下的估计。通过模拟，我们说明了优化随机饱和设计的图形和潜在的结果结构的优点，以及展示精心选择的确定性饱和设计所产生的额外的改进。
英文摘要：
Randomized saturation designs are a family of designs which assign a possibly different treatment proportion to each cluster of a population at random. As a result, they generalize the well-known (stratified) completely randomized designs and the cluster-based randomized designs, which are included as special cases. We show that, under the stable unit treatment value assumption, either the cluster-based or the stratified completely randomized design are in fact optimal for the bias and variance of the difference-in-means estimator among randomized saturation designs. However, this is no longer the case when interference is present. We provide the closed form of the bias and variance of the difference-in-means estimator under a linear model of interference and investigate the optimization of each of these objectives. In addition to the randomized saturation designs, we propose a deterministic saturation design, where the treatment proportion for clusters are fixed, rather than randomized, in order to further improve the estimator under correct model specification. Through simulations, we illustrate the merits of optimizing randomized saturation designs to the graph and potential outcome structure, as well as showcasing the additional improvements yielded by well-chosen deterministic saturation designs.
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