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Disentangling spatial interference and spatial confounding biases in causal inference

Isqeel Ogunsola, Olatunji Johnson

TL;DR

This paper tackles biases in causal inference arising from spatial interference and spatial confounding by framing the problem through a DAG perspective and deriving analytical bias expressions under general distributions, notably Poisson. It shows that the magnitude and direction of bias depend on the treatment/interference structure, weight matrices, and exposure distributions, and it distinguishes direct from indirect spatial confounding, revealing that they are not interchangeable. Through extensive simulations and a real-data application, the authors demonstrate when interference and confounding bias estimators and their corrections are most impactful, and they propose a simple bias-adjustment procedure. The work advances spatial causal inference by providing bias decompositions for complex settings, clarifying conceptual ambiguities, and outlining a path toward joint adjustment for interference and both direct and mediated confounding in future parametric frameworks.

Abstract

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.

Disentangling spatial interference and spatial confounding biases in causal inference

TL;DR

This paper tackles biases in causal inference arising from spatial interference and spatial confounding by framing the problem through a DAG perspective and deriving analytical bias expressions under general distributions, notably Poisson. It shows that the magnitude and direction of bias depend on the treatment/interference structure, weight matrices, and exposure distributions, and it distinguishes direct from indirect spatial confounding, revealing that they are not interchangeable. Through extensive simulations and a real-data application, the authors demonstrate when interference and confounding bias estimators and their corrections are most impactful, and they propose a simple bias-adjustment procedure. The work advances spatial causal inference by providing bias decompositions for complex settings, clarifying conceptual ambiguities, and outlining a path toward joint adjustment for interference and both direct and mediated confounding in future parametric frameworks.

Abstract

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.
Paper Structure (32 sections, 4 theorems, 44 equations, 10 figures, 13 tables)

This paper contains 32 sections, 4 theorems, 44 equations, 10 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Spatial interference
  3. Spatial confounding
  4. Clarity on spatial confounding from Directed Acyclic Graph (DAG) perspective.
  5. Causal effect identification assumptions
  6. Analytical framework
  7. Bias derivation
  8. Quantifying bias due to spatial interference
  9. Choosing the weight matrix, Psi
  10. Direct spatial confounding and Bias with Poisson distributed treatment and confounder
  11. Quantifying bias due to direct and indirect spatial confounding.
  12. Bias in the presence of spatial interference and spatial confounding (direct and indirect)
  13. Simulation study
  14. Evaluation metrics
  15. Bias induced by spatial interference
  16. ...and 17 more sections

Key Result

Proposition 1

Given a model of the form in Equation equation 2 and assuming only $\beta_a$ is unknown, the bias due to spatial interference in non-spatial and spatial settings are given respectively as $Bias\left(\hat{\beta_a^{*}}|A\right)= \beta_{\tilde{a}}\frac{A^T \Psi A}{\left(A^{T} A\right)}$ and $Bias\left

Figures (10)

  • Figure 1: Spatial confounding
  • Figure 2: Direct Spatial Confounding
  • Figure 3: Indirect Spatial Confounding
  • Figure 4: Box plots showing the bias for discrete and continuous treatment with k-NN and distance based weights in non spatial setting
  • Figure 5: Box plots showing the bias for discrete and continuous treatment with k-NN and distance based weights in spatial setting
  • ...and 5 more figures

Theorems & Definitions (8)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof