Identifiability of Treatment Effects with Unobserved Spatially Varying Confounders

TL;DR

This paper develops a framework to determine when causal treatment effects can be identified in observational studies with unmeasured spatial confounders, under various spatial models and assumptions.

Contribution

It provides conditions for identifiability of treatment effects in linear models with spatially varying unmeasured confounders, covering common spatial data models.

Findings

Identifiability established for many spatial models under mild conditions.

Highlighting scenarios where identifiability may fail, advising caution in inference.

Framework applicable to both discrete and continuous spatial data.

Abstract

The study of causal effects in the presence of unmeasured spatially varying confounders has garnered increasing attention. However, a general framework for identifiability, which is critical for reliable causal inference from observational data, has yet to be advanced. In this paper, we study a linear model with various parametric model assumptions on the covariance structure between the unmeasured confounder and the exposure of interest. We establish identifiability of the treatment effect for many commonly 20 used spatial models for both discrete and continuous data, under mild conditions on the structure of observation locations and the exposure-confounder association. We also emphasize models or scenarios where identifiability may not hold, under which statistical inference should be conducted with caution.