Bayesian hierarchical distributed lag models for summer ozone exposure and cardio-respiratory mortality

Abstract

In this article we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 large U.S. cities included in the National Morbidity, Mortality and Air Pollution Study (NMMAPS) for the summers of 1987-1994. In the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP mortality associated with short-term exposure to summer ozone. In the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by taking into account the variability within and across cities. We perform the calculations with respect to several random effects distributions (normal, t-student, and mixture of normal), thus relaxing the common assumption of a two-stage normal-normal hierarchical model. We assess the sensitivity of the results to: (i) lag structure for ozone exposure; (ii) degree of adjustment for long-term trends; (iii) inclusion of other pollutants in the model; (iv) heat waves; (v) random effects distributions; and (vi) prior hyperparameters. On average across cities, we found that a 10ppb increase in summer ozone level over the previous week is associated with a 1.25 per cent increase in CVDRESP mortality (95 per cent posterior regions: 0.47, 2.03). The relative rate estimates are also positive and statistically significant at lags 0, 1 and 2. We found that associations between summer ozone and CVDRESP mortality are sensitive to the confounding adjustment for PM₁₀, but are robust to: (i) the adjustment for long-term trends, other gaseous pollutants (NO₂, SO₂ and CO); (ii) the distributional assumptions at the second stage of the hierarchical model; and (iii) the prior distributions on all unknown parameters. Bayesian hierarchical distributed lag models and their application to the NMMAPS data allow us to estimate of an acute health effect associated with exposure to ambient air pollution in the last few days on average across several locations. The application of these methods and the systematic assessment of the sensitivity of findings to model assumptions provide important epidemiological evidence for future air quality regulations.

Keywords: Bayesian hierarchical model; cardiovascular and respiratory mortality; distributed lag model; ozone.

Figure 1

Box-plots of summer ozone levels for 19 large U.S. cities in NMMAPS for the period 1987–1994

Figure 2

Box-plots of log(daily CVDRESP death count) for 19 large U.S. cities in NMMAPS in summer months of 1987–1994

Figure 3

City-specific relative rates estimates (percent increases in CVDRESP mortality associated with 10ppb increase in ozone) and their 95 per cent confidence intervals, with overall ozone effect and its 95 per cent posterior regions at the end. These effects are estimated by use of a distributed lag model for one week and at lags 0, 1 and 2 days

Figure 4

(a) Posterior distribution of average relative rate (μ) and (b) of the heterogeneity parameter (τ) obtained by combining city-specific relative rates estimates under a distributed lag model and single-lag models

Figure 5

City-specific ozone relative rates estimates at lag 2 adjusted by another pollutant (PM₁₀, NO₂, SO₂ or CO), plotted against ozone relative rates estimates at lag 2. The cross is plotted corresponding to the two overall relative rates (adjusted versus unadjusted) and their 95 per cent posterior regions

Figure 6

Sensitivity analysis of the city-specific effects at lag 2 with respect to the degrees of freedom in the smooth functions of time. The number of degrees of freedom vary from 4 to 16 with increasing step = 2. Each polygon captures the change in the city-specific relative rates estimates with their corresponding 95 per cent confidence intervals. The last polygon captures the change of overall ozone effect estimates with its 95 per cent posterior regions