Two-stage Bayesian factor analysis for air pollution source apportionment and health risk assessment

Abstract

Air pollution, especially particulate matter (PM), presents significant public health challenges and is associated with several Sustainable Development Goals (SDGs), notably SDG 3 (Good Health and Well-being) and SDG 11 (Sustainable Cities and Communities). Effective policy development requires robust statistical approaches to identify pollution sources and quantify their health impacts with appropriate uncertainty. This study develops a novel two-stage Bayesian framework for air pollution source apportionment and health risk assessment, with the aim of quantifying the contribution of distinct particle sources to respiratory health outcomes in children, using particle number size distribution (PNSD) data from London. In the first stage, we construct a Bayesian dynamic factor model with autoregressive components to infer latent pollution sources, incorporating non-negativity constraints and accounting for temporal dependence. In the second stage, we assess the relationship between source-specific exposures and respiratory hospital admissions in children via a Poisson regression model, explicitly propagating uncertainty from the source apportionment stage to the health model. The model identifies four main sources: nucleation, traffic, urban activities, and secondary aerosols. Among these, traffic and secondary sources exhibit the strongest and most consistent associations with increased respiratory hospital admissions. Importantly, models that do not account for uncertainty propagation tend to overestimate health risk associations, underscoring the value of the proposed Bayesian framework. This work illustrates the advantages of integrating Bayesian methods for source apportionment and health effect estimation, with formal uncertainty propagation across model stages. The proposed framework enhances interpretability and supports evidence-based public health and environmental policy. It is readily extensible to other pollutants and settings, contributing to improved air quality management and progress toward global sustainability goals