Estimating the PM2.5–Mortality Concentration–Response Function in the Rome Longitudinal Study (ROLS): A Methodological Comparison of Linear, Spline, and SCHIF Approaches

Abstract

Introduction

In health impact assessments (HIAs) of air pollution, a crucial issue is the correct specification of the concentration-response function (CRF) between exposure and outcome. Traditional approaches often assume a linear relationship, with the risk of introducing bias when the association is actually non-linear. In this context, Shape Constrained Health Impact Functions (SCHIF) represent a methodological advancement developed specifically for HIA. They allow flexible curves that are consistent with biological plausibility constraints to be modelled, while at the same time they estimate a single effect coefficient, since non-linearity is incorporated into the transformation of exposure in the risk function. SCHIF returns three estimates of the CRF from the optimal model, an ensemble of the best three models, and an ensemble of all estimated models. Simulation studies show that SCHIF better describe the association between PM2.5 and the outcome compared with linear models, but this has not yet been verified using real data.

Objectives

To evaluate, in a real cohort, the methodological robustness of the estimated CRF between chronic exposure to fine particulate matter (PM2.5) and non-accidental mortality obtained with the optimal SCHIF model; to compare the estimates with those obtained from Cox models with exposure specified as a linear term or by natural splines (NS).

Methods

The administrative cohort of residents (30+ years) in Rome on 09/10/2011 (2011 Census) was analysed, with follow-up to 31/12/2019. The following were estimated: (i) a Cox model with a linear term for PM2.5 (L), (ii) a Cox model with NS with 3 knots (S), and (iii) the SCHIF model, adjusted for individual- and area-level variables. The Bayesian Information Criterion (BIC) was used for model selection.

Results

All analytical approaches highlight the presence of a significant effect of PM2.5 exposure on the outcome. In L, the estimated exposure effect is β=0.012 (SE=0.029). However, the comparison with model S is statistically significant, indicating that the association is not adequately described by a linear relationship. In model S, the first spline term is significant (β=0.023; SE=0.009), whereas the additional non-linear terms are not. The optimal SCHIF model identifies a non-linear relationship, with deviation from linearity at the lowest PM2.5 levels, with an estimated coefficient of β(z)=0.140 (SE=0.032)×ω(z|min(z), 0.1)×log(1+z).In the comparison between models, the minimum BIC is observed for the SCHIF model, supporting a better fit to the data.

Conclusions

The SCHIF model shows the best fit and is confirmed as a promising approach for estimating more realistic and robust CRFs, useful in health impact assessments.

Acknowledgments

Project carried out with the technical and financial support of the Ministry of Health - PNC PREV-A-2022-12376.