Recently, addressing spatial confounding has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed definitions do not address the issue of confounding as it is understood in causal inference. We define spatial confounding as the existence of an unmeasured causal confounder with a spatial structure. We present a causal inference framework for nonparametric identification of the causal effect of a continuous exposure on an outcome in the presence of spatial confounding. We propose double machine learning (DML), a procedure in which flexible models are used to regress both the exposure and outcome variables on confounders to arrive at a causal estimator with favorable robustness properties and convergence rates, and we prove that this approach is consistent and asymptotically normal under spatial dependence. As far as we are aware, this is the first approach to spatial confounding that does not rely on restrictive parametric assumptions (such as linearity, effect homogeneity, or Gaussianity) for both identification and estimation. We demonstrate the advantages of the DML approach analytically and in simulations. We apply our methods and reasoning to a study of the effect of fine particulate matter exposure during pregnancy on birthweight in California.

翻译：最近,解决空间混乱已成为空间统计中的一个主要专题,然而,文献提供了相互矛盾的定义,许多拟议定义没有涉及因果推断中理解的混淆问题。我们将空间混淆定义为空间结构存在一种未计量的因果混淆体,我们提出一个因果推断框架,用于在空间混乱的情况下,对持续暴露对结果的因果关系进行非对数识别;我们提议采用双机学习(DML)程序,采用灵活模型,重新推卸对融合者的接触和结果变量,以得出一个具有有利稳健特性和趋同率的因果关系估计器,我们证明这种方法在空间依赖下是一贯和偶然正常的。据我们所知,这是在确定和估计时不依赖限制性的对准假设(如线性、效应同质性或高斯尼)进行空间重叠的第一方法。我们展示了DML方法在分析和模拟中对于孕期的精度影响的好处。我们在加利福尼亚州的实验中运用了比重法和推理研究。我们运用了在妊娠期和模拟中对重度风险的影响。