In settings where interference between units is possible, we define the prevalance of indirect effects to be the number of units who are affected by the treatment of others. This quantity does not fully identify an indirect effect, but may be used to show whether such effects are widely prevalent. Given a randomized experiment with binary-valued outcomes, methods are presented for conservative point estimation and one-sided interval estimation. No assumptions beyond randomization of treatment are required, allowing for usage in settings where models or assumptions on interference might be questionable. To show asymptotic coverage of our intervals in settings not covered by existing results, we provide a central limit theorem that combines local dependence and sampling without replacement. Consistency and minimax properties of the point estimator are shown as well. The approach is demonstrated on an experiment in which students were treated for a highly transmissible parasitic infection, for which we find that a significant fraction of students were affected by the treatment of schools other than their own.

翻译：在单元间可能存在相互干扰的情形下，我们将间接效应的普遍性定义为受他人处理影响的单元数量。该指标虽不能完全识别间接效应，但可用于显示此类效应是否广泛存在。针对二元结果变量的随机实验，本文提出了保守点估计与单侧区间估计方法。该方法仅需处理随机化假设，无需依赖其他假设，因此可用于干扰模型或假设可能存疑的场景。为证明现有结论未覆盖情形下区间的渐近覆盖性，我们提出了一个结合局部依赖与无放回抽样的中心极限定理。同时证明了点估计量的相合性与极小极大性质。该方法在一项针对高度传染性寄生虫感染的学生实验中得到验证，我们发现显著比例的学生受到非本校处理的影响。