Considerable recent work has focused on methods for analyzing experiments which exhibit treatment interference -- that is, when the treatment status of one unit may affect the response of another unit. Such settings are common in experiments on social networks. We consider a model of treatment interference -- the K-nearest neighbors interference model (KNNIM) -- for which the response of one unit depends not only on the treatment status given to that unit, but also the treatment status of its $K$ ``closest'' neighbors. We derive causal estimands under KNNIM in a way that allows us to identify how each of the $K$-nearest neighbors contributes to the indirect effect of treatment. We propose unbiased estimators for these estimands and derive conservative variance estimates for these unbiased estimators. We then consider extensions of these estimators under an assumption of no weak interaction between direct and indirect effects. We perform a simulation study to determine the efficacy of these estimators under different treatment interference scenarios. We apply our methodology to an experiment designed to assess the impact of a conflict-reducing program in middle schools in New Jersey, and we give evidence that the effect of treatment propagates primarily through a unit's closest connection.

翻译：近年来，大量研究关注于分析存在处理干扰的实验方法——即一个单元的处理状态可能影响另一个单元的响应。此类情形在社会网络实验中十分常见。我们考虑一种处理干扰模型——K近邻干扰模型（KNNIM），其中单个单元的响应不仅取决于该单元自身的处理状态，还取决于其K个"最近"邻居的处理状态。我们通过KNNIM推导出因果估计量，从而能够识别每个K近邻如何对处理的间接效应产生贡献。我们为这些估计量提出无偏估计，并推导出这些无偏估计的保守方差估计。随后，我们考虑在直接效应与间接效应之间无弱交互作用的假设下对这些估计量进行扩展。我们通过模拟研究检验这些估计量在不同处理干扰场景下的有效性。我们将该方法应用于一项评估新泽西州中学冲突减少项目影响的实验，并提供证据表明处理效应主要通过单元的最紧密联系进行传播。