Disentangling spatial interference and spatial confounding biases in causal inference

Spatial interference and spatial confounding are two major issues inhibiting precise causal estimates when dealing with observational spatial data. Moreover, the definition and interpretation of spatial confounding remain arguable in the literature. In this paper, our goal is to provide clarity in a novel way on misconception and issues around spatial confounding from Directed Acyclic Graph (DAG) perspective and to disentangle both direct, indirect spatial confounding and spatial interference based on bias induced on causal estimates. Also, existing analyses of spatial confounding bias typically rely on Normality assumptions for treatments and confounders, assumptions that are often violated in practice. Relaxing these assumptions, we derive analytical expressions for spatial confounding bias under more general distributional settings using Poisson as example . We showed that the choice of spatial weights, the distribution of the treatment, and the magnitude of interference critically determine the extent of bias due to spatial interference. We further demonstrate that direct and indirect spatial confounding can be disentangled, with both the weight matrix and the nature of exposure playing central roles in determining the magnitude of indirect bias. Theoretical results are supported by simulation studies and an application to real-world spatial data. In future, parametric frameworks for concomitantly adjusting for spatial interference, direct and indirect spatial confounding for both direct and mediated effects estimation will be developed.

💡 Research Summary

The paper tackles two pervasive sources of bias in spatial causal inference—spatial interference and spatial confounding—by providing a clear conceptual separation and rigorous quantitative analysis. First, the authors use Directed Acyclic Graphs (DAGs) to clarify the ambiguous definitions of spatial confounding that appear across the literature. They distinguish “direct spatial confounding,” where an unmeasured spatial variable influences both treatment and outcome at the same location, from “indirect spatial confounding,” where a spatially structured unmeasured variable affects treatment or outcome at other locations, often through interference pathways. This DAG‑based taxonomy resolves the conflation of causal and non‑causal relationships that has hampered prior work.

The methodological contribution lies in deriving analytical bias expressions without relying on normality assumptions. While most earlier studies assumed Gaussian treatment and confounder distributions, the authors relax this by considering Poisson‑distributed treatment and confounder variables—a realistic scenario for count data such as disease incidence or event counts. The derived bias formulas show that bias magnitude depends on three key elements: (1) the spatial weight matrix W (its range and decay structure), (2) the distributional characteristics of the treatment (mean, variance), and (3) the strength of the interference effect. Notably, weight matrices that allow long‑range connections amplify indirect confounding bias, whereas more localized weights limit interference‑induced bias. In the Poisson case, smaller means lead to a non‑linear increase in bias, highlighting the importance of distributional shape.

Simulation experiments systematically vary weight structures (distance‑based, topological), treatment distributions (binary, Poisson), and interference strengths. Results confirm the theoretical predictions: ignoring interference or indirect confounding can cause substantial over‑ or under‑estimation of average treatment effects. The authors also present a real‑world application examining the relationship between air pollution and health outcomes. Conventional methods over‑estimate the pollution effect in high‑exposure areas, whereas the proposed bias‑corrected estimator yields more plausible effect sizes.

To address interference alone, the paper proposes a simple correction: estimate the interference component using the inverse of the weight matrix and subtract it from the naïve estimator. This procedure is computationally cheap and performs well in simulations, though the authors acknowledge its limitations for nonlinear models, multiple treatments, or more complex non‑Gaussian distributions.

The discussion outlines limitations (e.g., extension to zero‑inflated or negative‑binomial counts, handling of multiple interacting treatments) and outlines future directions, including a unified parametric framework that simultaneously adjusts for direct and indirect spatial confounding and interference, and extending bias formulas to broader families of distributions.

Overall, the study makes five major contributions: (1) clarifies spatial confounding via DAGs, (2) is the first to analytically quantify bias from spatial interference in both spatial and non‑spatial settings, (3) disentangles and derives bias for direct and indirect spatial confounding, (4) provides bias expressions for non‑normal (Poisson) treatment and confounder distributions, and (5) demonstrates through simulations and a real data example that neglecting any of the three phenomena leads to unreliable causal conclusions. This work offers both theoretical insight and practical tools for researchers dealing with observational spatial data.