Confounding and dependence in spatial statistics (joint work with Brian Gilbert, Abhi Datta, and Joan Casey)

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 and 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 using “double machine learning” (DML) methods, in which flexible models are used to regress both the exposure and outcome variables on confounders to arrive at an estimator with favorable robustness properties and convergence rates. These methods are common in iid settings but underdeveloped for settings with dependence; we prove that this approach results in consistent and asymptotically normal estimators under some forms of 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 and apply our methods to a study of the effect of fine particulate matter exposure during pregnancy on birthweight in California.