Combining evidence on air pollution and daily mortality from the 20 largest US cities: a hierarchical modelling strategy
Reports over the last decade of association between levels of particles in outdoor air and daily mortality counts have raised concern that air pollution shortens life, even at concentrations within current regulatory limits. Criticisms of these reports have focused on the statistical techniques that are used to estimate the pollution–mortality relationship and the inconsistency in findings between cities. We have developed analytical methods that address these concerns and combine evidence from multiple locations to gain a unified analysis of the data. The paper presents log-linear regression analyses of daily time series data from the largest 20 US cities and introduces hierarchical regression models for combining estimates of the pollution–mortality relationship across cities. We illustrate this method by focusing on mortality effects of PM10 (particulate matter less than 10 m in aerodynamic diameter) and by performing univariate and bivariate analyses with PM10 and ozone (O3) level. In the first stage of the hierarchical model, we estimate the relative mortality rate associated with PM10 for each of the 20 cities by using semiparametric log-linear models. The second stage of the model describes between-city variation in the true relative rates as a function of selected city-specific covariates. We also fit two variations of a spatial model with the goal of exploring the spatial correlation of the pollutant-specific coefficients among cities. Finally, to explore the results of considering the two pollutants jointly, we fit and compare univariate and bivariate models. All posterior distributions from the second stage are estimated by using Markov chain Monte Carlo techniques. In univariate analyses using concurrent day pollution values to predict mortality, we find that an increase of 10 g m-3 in PM10 on average in the USA is associated with a 0.48% increase in mortality (95% interval: 0.05, 0.92). With adjustment for the O3 level the PM10-coefficient is slightly higher. The results are largely insensitive to the specific choice of vague but proper prior distribution. The models and estimation methods are general and can be used for any number of locations and pollutant measurements and have potential applications to other environmental agents.