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Confounding in statistical epidemiology represents a pivotal challenge, referring to the distortion in the perceived relationship between an exposure and an outcome due to the presence of a third variable, known as a confounder. This variable is associated with both the exposure and the outcome but is not a direct link in their causal chain. Its presence can lead to erroneous interpretations of the exposure's effect, either exaggerating or underestimating the true association. This...
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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Consistency of common spatial estimators under spatial confounding.

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  • 1Department of Biostatistics, Johns Hopkins University, 605 N Wolfe Street, Baltimore, Maryland 21215, U.S.A.

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Summary
This summary is machine-generated.

Spatial confounding can bias regression results. This study shows generalized least squares (GLS) estimators are consistent under spatial confounding, even with complex error structures, provided exposure has nonspatial variation.

Keywords:
Causal inferenceGaussian processGeneralized least squaresSpatial confoundingSpatial statistics

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Area of Science:

  • Spatial statistics
  • Geostatistics
  • Econometrics

Background:

  • Spatial confounding, an unmeasured variable influencing exposure and outcome, poses challenges for regression analysis.
  • Traditional spatial regression estimators may exhibit asymptotic bias under spatial confounding.

Purpose of the Study:

  • To evaluate the asymptotic performance of spatial regression estimators under spatial confounding.
  • To establish conditions for consistent estimation of linear exposure effects in the presence of spatial confounding.

Main Methods:

  • Asymptotic analysis of ordinary least squares (OLS) and restricted spatial regression estimators.
  • Proof of infill consistency for generalized least squares (GLS) with Matérn or squared exponential kernels.
  • Theoretical analysis of spatial estimators under fixed function and random function confounding.

Main Results:

  • OLS and restricted spatial regression estimators are asymptotically biased under spatial confounding.
  • GLS estimators demonstrate infill consistency under spatial confounding with mild assumptions.
  • Spatial estimators (GLS, Gaussian process, spline) are consistent under both fixed and random function confounding.

Conclusions:

  • Contrary to some literature, traditional spatial estimators can consistently estimate linear exposure effects under spatial confounding if exposure has nonspatial variation.
  • The findings provide theoretical support for using GLS and related models in spatial regression with confounding.