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

TL;DR

This paper tackles the challenge of estimating a non-linear PM2.5–mortality association under unmeasured spatio-temporal confounding. It introduces SDGLMC, a Bayesian spatial dynamic GLM that uses a Taylor-based exposure decomposition to separate large-scale trends from local variation and to model spacetime-varying intercepts and slopes via a state-space formulation. Through simulations and an application to Italian mortality data (2018–2022), the method demonstrates improved control of confounding, recoverable temporal patterns, and interpretable fine-scale associations, including summer peaks and pandemic-era deviations. The approach provides a flexible, data-driven framework for small-area spatio-temporal health analyses of air pollution with potential broader applicability to other exposures and outcomes.

Abstract

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.

Figures (9)

• Figure 1: Long-term averages of SMR (left) and PM2.5 concentrations (right) across HDs from 2018 to 2022. The thicker solid line separates Piemonte (the westernmost region) from Lombardia (the easternmost region).
• Figure 2: Time series of log-transformed daily SMR (orange) and PM2.5 concentrations (black) for Piemonte (top) and Lombardia (bottom), spanning 2018--2022. Vertical dashed lines mark calendar years. orange bands indicate national lockdown periods.
• Figure 3: Simulation Study 1: temporal component of the exposure effect, expressed as percent change in risk associated with a 10-unit increase in the exposure, for each scenario. The red solid line represents the estimate (averaged over 100 replicates) obtained from SDGLMC, and the shaded area indicates the percentiles $2.5$ and $97.5$. The black solid line represents the true temporal component. Null and GLMadj models are not shown because they assume an exposure effect that is constant in time.
• Figure 4: Simulation Study 1: spatial component of the exposure effect, expressed as percent change in risk associated with a 10-unit increase in the exposure. The top panel shows the true spatial component. The remaining panels show the posterior means (averaged over 100 replicates) under each scenario (rows) and model (columns).
• Figure 5: Posterior summary (solid line: mean, shaded area: point-wise limits of 95% posterior credible interval) of the space-averaged local exposure effect, expressed as percent change in mortality risk for a $10\ \mu g/m^3$ increase in PM2.5 concentrations. Vertical dashed lines mark calendar years.

Theorems & Definitions (2)

• Example 3.1
• Example 3.2