A key methodological challenge in observational studies with interference between units is twofold: (1) each unit's outcome may depend on many others' treatments, and (2) treatment assignments may exhibit complex dependencies across units. We develop a general statistical framework for constructing robust causal effect estimators to address these challenges. We first show that, without restricting the patterns of interference, the standard inverse probability weighting (IPW) estimator is the only uniformly unbiased estimator when the propensity score is known. In contrast, no estimator has such a property if the propensity score is unknown. We then introduce a \emph{low-rank structure} of potential outcomes as a broad class of structural assumptions about interference. This framework encompasses common assumptions such as anonymous, nearest-neighbor, and additive interference, while flexibly allowing for more complex study-specific interference assumptions. Under this low-rank assumption, we show how to construct an unbiased weighting estimator for a large class of causal estimands. The proposed weighting estimator does not require knowledge of true propensity scores and is therefore robust to unknown treatment assignment dependencies that often exist in observational studies. If the true propensity score is known, we can obtain an unbiased estimator that is more efficient than the IPW estimator by leveraging a low-rank structure. We establish the finite sample and asymptotic properties of the proposed weighting estimator, develop a data-driven procedure to select among candidate low-rank structures, and validate our approach through simulation and empirical studies.

翻译：在存在单元间干扰的观察性研究中，关键的方法学挑战具有双重性：(1) 每个单元的结果可能依赖于其他许多单元的处理；(2) 处理分配可能在单元间表现出复杂的依赖性。为应对这些挑战，我们开发了一个构建稳健因果效应估计器的通用统计框架。我们首先证明，在不限制干扰模式的情况下，当倾向得分已知时，标准的逆概率加权（IPW）估计器是唯一的一致无偏估计器。相反，若倾向得分未知，则不存在具有此类性质的估计器。随后，我们引入潜在结果的低秩结构作为关于干扰的一类广泛的结构性假设。该框架涵盖了匿名干扰、最近邻干扰和加性干扰等常见假设，同时灵活地允许更复杂的、特定于研究的干扰假设。在此低秩假设下，我们展示了如何为一大类因果估计量构建无偏的加权估计器。所提出的加权估计器无需已知真实倾向得分，因此对观察性研究中常存在的未知处理分配依赖性具有稳健性。若真实倾向得分已知，我们可通过利用低秩结构获得比IPW估计器更高效的无偏估计器。我们建立了所提加权估计器的有限样本与渐近性质，开发了一种数据驱动程序以在候选低秩结构中进行选择，并通过仿真与实证研究验证了我们的方法。