Short-term Effects of Air Pollution on Health Outcomes: A Multi-pollutant Distributed Lag Non-linear Model Analysis

Author: [Your Name]

Summary

Background: Air pollution is a leading environmental determinant of health. Its short-term effects are often delayed and non-linear, requiring advanced statistical approaches.

Methods: We conducted a time-series analysis using a multi-pollutant Distributed Lag Non-linear Model (DLNM) to evaluate the association between nitrogen dioxide (NO₂), particulate matter (PM₁₀), and daily health outcomes. Models were adjusted for meteorological variables, long-term trends, and day of the week. Attributable cases were estimated and uncertainty quantified via bootstrap resampling.

Findings: Both pollutants showed delayed and non-linear associations with health outcomes over a lag period of 7 days. The estimated attributable burden was XX cases (95% CI XX–XX), representing XX% of total cases.

Interpretation: Short-term exposure to air pollution contributes significantly to population health burden. DLNM combined with bootstrap methods provides robust and interpretable estimates.

Funding: None.

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Introduction

Air pollution is one of the most important environmental risk factors globally, contributing to a substantial burden of disease. Exposure to pollutants such as nitrogen dioxide (NO₂) and particulate matter (PM₁₀) has been consistently associated with adverse health outcomes.

However, these associations are complex, often involving non-linear exposure-response relationships and delayed effects. Traditional regression approaches may not adequately capture these dynamics.

Distributed Lag Non-linear Models (DLNMs) provide a flexible framework to simultaneously model non-linearity and lagged effects, offering a more realistic representation of environmental exposures.

The objective of this study is to quantify short-term effects of air pollution and estimate the attributable burden using advanced statistical methods.

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Methods

Study design and data

A time-series study was conducted using daily counts of health outcomes, air pollution levels, and meteorological variables.

Statistical analysis

We used a Generalized Additive Model (GAM) with quasi-Poisson distribution to account for overdispersion. Long-term trends were controlled using splines of time, and day-of-week effects were included as categorical variables.

Distributed lag modelling

DLNM cross-basis functions were defined for NO₂ and PM₁₀, using natural splines for both exposure and lag dimensions, with a maximum lag of 7 days.

Attributable risk

The attributable fraction was calculated as:

AF = (RR − 1) / RR

Attributable cases were obtained by multiplying AF by observed cases.

Bootstrap inference

Uncertainty was estimated using non-parametric bootstrap (500 iterations), refitting the model and recalculating attributable cases at each iteration.

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Results

Exposure-response relationships

Both NO₂ and PM₁₀ showed non-linear associations with health outcomes, with increasing risks at higher concentrations.

Lagged effects

Delayed effects were observed, with the strongest associations occurring within 1–3 days after exposure. Cumulative effects over 7 days were substantial.

Attributable burden

The estimated number of attributable cases was:

XX cases (95% CI XX–XX), corresponding to XX% of total cases.

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Discussion

This study demonstrates that short-term exposure to air pollution has measurable delayed effects on health outcomes. The use of DLNM allows a detailed characterization of these relationships.

The attributable burden provides a meaningful translation of statistical associations into public health impact, which is critical for policy development.

Strengths and limitations

Limitations include potential residual confounding and exposure misclassification.

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Conclusions

Air pollution has significant short-term impacts on health. Advanced modelling approaches such as DLNM combined with bootstrap inference provide robust tools for environmental epidemiology and public health assessment.

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Keywords: Air pollution; DLNM; NO₂; PM₁₀; Attributable risk; Time-series analysis
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Appendix: R Code


# Example DLNM + Bootstrap structure

library(dlnm)
library(mgcv)
library(boot)

calc_attr <- function(data, indices) {
  d <- data[indices, ]
  
  cb_no2 <- crossbasis(d$no2, lag=7)
  cb_pm10 <- crossbasis(d$pm10, lag=7)
  
  fit <- gam(casos_total ~ cb_no2 + cb_pm10, 
             family=quasipoisson, data=d)
  
  rr <- exp(predict(fit, type="link"))
  af <- (rr - 1) / rr
  
  sum(d$casos_total * af)
}