A Bayesian hierarchical approach for relating PM(2.5) exposure to cardiovascular mortality in North Carolina

Abstract

Considerable attention has been given to the relationship between levels of fine particulate matter (particulate matter < or = 2.5 microm in aerodynamic diameter; PM(2.5) in the atmosphere and health effects in human populations. Since the U.S. Environmental Protection Agency began widespread monitoring of PM(2.5) levels in 1999, the epidemiologic community has performed numerous observational studies modeling mortality and morbidity responses to PM(2.5) levels using Poisson generalized additive models (GAMs). Although these models are useful for relating ambient PM(2.5) levels to mortality, they cannot directly measure the strength of the effect of exposure to PM(2.5) on mortality. In order to assess this effect, we propose a three-stage Bayesian hierarchical model as an alternative to the classical Poisson GAM. Fitting our model to data collected in seven North Carolina counties from 1999 through 2001, we found that an increase in PM(2.5) exposure is linked to increased risk of cardiovascular mortality in the same day and next 2 days. Specifically, a 10- microg/m3 increase in average PM(2.5) exposure is associated with a 2.5% increase in the relative risk of current-day cardiovascular mortality, a 4.0% increase in the relative risk of cardiovascular mortality the next day, and an 11.4% increase in the relative risk of cardiovascular mortality 2 days later. Because of the small sample size of our study, only the third effect was found to have > 95% posterior probability of being > 0. In addition, we compared the results obtained from our model to those obtained by applying frequentist (or classical, repeated sampling-based) and Bayesian versions of the classical Poisson GAM to our study population.

Figure 1. Joint distribution of ambient PM_2.5 level and log relative risk on the same day (A), the next day (B), 2 days later (C), and 3 days later (D), with lines summarizing the direction of association (described in ”Results”). Darker areas represent regions of higher probability. The exponential of the slope of the line in each panel represents the proportion change in relative risk per unit change in ambient level.

Figure 2. Posterior means for relative risk of mortality in Alamance County over the period studied. Vertical bars indicate 1 January for each year in the analysis.