Carlo Zaccardi | Searcharxiv

arXiv2026

On the PM2.5 -- Mortality Association: A Bayesian Model for Spatio-Temporal Confounding

In epidemiological studies of air pollution and public health, estimating the health impact of exposure to air pollution may be hindered by the unknown functional form of the exposure-outcome association and by unmeasured confounding factors that are linked to both exposure and outcome. These challenges are especially relevant in spatio-temporal analyses, where their joint exploration remains limited. To study the effects of fine particulate matter on mortality among elderly people in Italy, we propose a Bayesian spatial dynamic generalized linear model that captures the non-linear exposure-outcome association and decomposes the exposure effect across fine and coarse spatio-temporal scales of variation. Together, these features allow reducing the spatio-temporal confounding bias and recovering the shape of the association, as demonstrated through simulation studies. The real-data analysis reveals a clear temporal pattern in the exposure effect, with peaks during summer months. We argue that this finding may be due to interactions of particulate matter with air temperature and unmeasured confounders.

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arXiv2025

Regularized Principal Spline Functions to Mitigate Spatial Confounding

This paper proposes a new approach to address the problem of unmeasured confounding in spatial designs. Spatial confounding occurs when some confounding variables are unobserved and not included in the model, leading to distorted inferential results about the effect of an exposure on an outcome. We show the relationship existing between the confounding bias of a non-spatial model and that of a semi-parametric model that includes a basis matrix to represent the unmeasured confounder conditional on the exposure. This relationship holds for any basis expansion, however it is shown that using the semi-parametric approach guarantees a reduction in the confounding bias only under certain circumstances, which are related to the spatial structures of the exposure and the unmeasured confounder, the type of basis expansion utilized, and the regularization mechanism. To adjust for spatial confounding, and therefore try to recover the effect of interest, we propose a Bayesian semi-parametric regression model, where an expansion matrix of principal spline basis functions is used to approximate the unobserved factor, and spike-and-slab priors are imposed on the respective expansion coefficients in order to select the most important bases. From the results of an extensive simulation study, we conclude that our proposal is able to reduce the confounding bias more than competing approaches, and it also seems more robust to bias amplification.

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