Moderation effects and elasticities in compositional regression with a total. Application to Bayesian spatiotemporal modelling of all-cause mortality from environmental stressors

TL;DR

This paper extends compositional regression models to include total and moderation effects, applying a Bayesian spatiotemporal approach to analyze environmental stressors' impact on mortality, revealing complex interactions between temperature, pollution, and health outcomes.

Contribution

It introduces a novel extension of compositional regression models to incorporate total and moderation effects within a Bayesian framework, with practical application to environmental health data.

Findings

Extreme temperatures increase mortality risk after four days.

Total air pollution, especially NO2, elevates mortality risk regardless of temperature.

Particulate matter increases mortality only during extreme heat days.

Abstract

Compositional regression models with a real-valued response variable can generally be specified as log-contrast models subject to a zero-sum constraint on the model coefficients. This formulation emphasises the relative information conveyed in the composition, while the overall total is regarded irrelevant. In this work, such a setting is extended to account not only for total effects, formally defined in a so-called T-space, but also for moderation or interaction effects. This is applied in the context of complex spatiotemporal data modelling, through an adaptation of the integrated nested Laplace approximation (INLA) method within a Bayesian estimation framework. Particular emphasis is placed on the interpretation of model coefficients and results, both on the original scale of the response variable and in terms of elasticities. The methodology is demonstrated through a detailed case study investigating the relationship between all-cause mortality and the interaction between extreme temperatures, air pollution composition, and total air pollution in Catalonia, Spain, during the summer of 2022. The results indicate that extreme temperatures are associated with an increased risk of mortality four days after exposure. Additionally, exposure to total air pollution, especially to NO2, is linked to elevated mortality risk regardless of temperature. In contrast, particulate matter is associated to increased mortality only when exposure occurs on days of extreme heat.