A spectral adjustment for spatial confounding

TL;DR

This paper introduces a spectral domain approach to adjust for spatial confounding, enabling estimation of causal effects under specific coherence conditions between treatment and unmeasured confounders.

Contribution

It develops a spectral framework for spatial confounding adjustment, proposing methods from parametric to semi-parametric, applicable to various spatial data types.

Findings

Spectral conditions ensure causal effect estimability.

Global-scale confounding dissipates at local scales.

Proposed methods improve confounder adjustment in spatial data.

Abstract

Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. In this paper, we derive necessary conditions on the coherence between the treatment variable of interest and the unmeasured confounder that ensure the causal effect of the treatment is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. The key assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the treatment variable to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matern coherence function to more robust semi-parametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets