Regularized principal spline functions to mitigate spatial confounding.

Area of Science:

• Spatial statistics
• Biostatistics
• Epidemiology

Background:

• Unmeasured confounding in spatial designs distorts inferential results.
• Spatial confounding arises when unobserved variables influence both exposure and outcome.
• Existing models may fail to adequately address this bias, leading to inaccurate conclusions.

Purpose of the Study:

• To propose a novel Bayesian semi-parametric regression model to adjust for unmeasured confounding in spatial designs.
• To investigate the relationship between confounding bias in non-spatial and semi-parametric models.
• To evaluate the effectiveness of the proposed method in reducing confounding bias.

Main Methods:

• Developed a Bayesian semi-parametric regression model incorporating a principal spline basis function matrix.
• Utilized spike-and-slab priors for basis expansion coefficients to enable variable selection.
• Conducted an extensive simulation study to compare the proposed method with existing approaches.

Main Results:

• The proposed Bayesian semi-parametric approach significantly reduces confounding bias compared to competing methods.
• The method demonstrates robustness against bias amplification.
• The reduction in bias is contingent upon spatial structures, basis expansion type, and regularization.

Conclusions:

• The novel Bayesian semi-parametric model offers a superior solution for addressing unmeasured confounding in spatial data.
• The findings highlight the importance of considering spatial structures and employing appropriate modeling techniques.
• The proposed method provides a more reliable approach for estimating exposure effects in the presence of unmeasured spatial confounders.