论文标题
优化干扰下的随机和确定性饱和设计
Optimizing Randomized and Deterministic Saturation Designs under Interference
论文作者
论文摘要
随机饱和设计是一系列设计，它们可能随机地分配了与每个人群的每个群集的比例不同。结果，他们概括了众所周知的（分层）完全随机的设计和基于群集的随机设计，这些设计被包括在特殊情况下。我们表明，在稳定的单位治疗值假设下，基于群集或分层的完全随机设计实际上是随机饱和设计中均值估计器的偏置和方差的最佳选择。但是，当存在干扰时不再是这种情况。我们提供了干扰线性模型下差异估计器的偏差和方差的封闭形式，并研究了每个目标的优化。除了随机饱和设计外，我们还提出了一种确定性饱和设计，其中固定而不是随机的簇的处理比例，以便在正确的模型规范下进一步改善估计量。通过模拟，我们说明了将随机饱和设计优化到图和潜在结果结构的优点，并展示了由精心选择的确定性饱和设计所产生的其他改进。
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.
