In randomized experiments, covariates are often used to reduce variance and improve the precision of treatment effect estimates. However, in many real-world settings, interference between units, where one unit's treatment affects another's outcome, complicates causal inference. This raises a key question: how can covariates be effectively used in the presence of interference? Addressing this challenge is nontrivial, as direct covariate adjustment, such as through regression, can increase variance due to dependencies across units. In this paper, we study covariate adjustment for estimating the total treatment effect under interference. We work under a neighborhood interference model with low-order interactions and build on the estimator of Cortez-Rodriguez et al. (2023). We propose a class of covariate-adjusted estimators and show that, under sparsity conditions on the interference network, they are asymptotically unbiased and achieve a no-harm guarantee: their asymptotic variance is no larger than that of the unadjusted estimator. This parallels the classical result of Lin (2013) under no interference, while allowing for arbitrary dependence in the covariates. We further develop a variance estimator for the proposed procedures and show that it is asymptotically conservative, enabling valid inference in the presence of interference. Compared with existing approaches, the proposed variance estimator is less conservative, leading to tighter confidence intervals in finite samples.

翻译：在随机实验中，协变量常被用于降低方差并提高治疗效应估计的精度。然而，在许多实际场景中，单元之间的干扰（即一个单元的治疗会影响另一单元的结果）使因果推断复杂化。这引出一个关键问题：如何在存在干扰的情况下有效利用协变量？解决这一挑战并非易事，因为直接通过回归等协变量调整可能因单元间的依赖性而增加方差。本文研究了在干扰条件下估计总治疗效应时的协变量调整问题。我们采用具有低阶交互作用的邻域干扰模型，并基于Cortez-Rodriguez等人（2023）的估计器进行拓展。我们提出了一类协变量调整估计器，并证明在干扰网络满足稀疏性条件时，这些估计器渐近无偏且实现"无害保证"：其渐近方差不大于未调整估计器的方差。这一结论与Lin（2013）在无干扰条件下的经典结果相平行，同时允许协变量存在任意依赖性。进一步，我们为所提出的方法开发了方差估计器，并证明其具有渐近保守性，从而在存在干扰时实现有效推断。与现有方法相比，该方差估计器保守性更弱，能够在有限样本下生成更紧致的置信区间。