Many public health interventions are conducted in settings where individuals are connected to one another and the intervention assigned to randomly selected individuals may spill over to other individuals they are connected to. In these spillover settings, the effects of such interventions can be quantified in several ways. The average individual effect measures the intervention effect among those directly treated, while the spillover effect measures the effect among those connected to those directly treated. In addition, the overall effect measures the average intervention effect across the study population, over those directly treated along with those to whom the intervention spills over but who are not directly treated. Here, we develop methods for study design with the aim of estimating individual, spillover, and overall effects. In particular, we consider an egocentric network-based randomized design in which a set of index participants is recruited from the population and randomly assigned to treatment, while data are also collected from their untreated network members. We use the potential outcomes framework to define two clustered regression modeling approaches and clarify the underlying assumptions required to identify and estimate causal effects. We then develop sample size formulas for detecting individual, spillover, and overall effects. We investigate the roles of the intra-class correlation coefficient and the probability of treatment allocation on the required number of egocentric networks with a fixed number of network members for each egocentric network and vice-versa.

翻译：许多公共卫生干预措施是在个体相互关联的环境中实施的，被随机分配到干预组的个体可能对其关联的其他个体产生溢出效应。在存在溢出效应的背景下，此类干预措施的效果可通过多种方式量化。平均个体效应衡量直接接受干预者的干预效果，而溢出效应则衡量与直接接受干预者相关联个体的效果。此外，总体效应衡量整个研究人群中（包括直接接受干预者及未直接接受干预但受到干预溢出影响的个体）的平均干预效果。本文旨在开发研究方法，以估计个体效应、溢出效应及总体效应。具体而言，我们考虑一种基于自我中心网络的随机化设计：从人群中招募一组索引参与者并随机分配干预，同时收集其未接受干预的网络成员数据。我们利用潜在结果框架定义两种聚类回归建模方法，并阐明识别与估计因果效应所需的基本假设。随后，我们推导出用于检测个体效应、溢出效应及总体效应的样本量计算公式。我们系统分析了组内相关系数、治疗分配概率对所需自我中心网络数量的影响（当每个自我中心网络的成员数固定时），反之亦然。