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 polluti on 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 inconsis tency in findings between cities. We have developed analytical methods that address these concerns and combine evidence from multiple locations to gai n 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 introd uces hierarchical regression models for combining estimates of the pollutio n-mortality relationship across cities. We illustrate this method by focusi ng on mortality effects of PM10 (particulate matter less than 10 mum in aer odynamic diameter) and by performing univariate and bivariate analyses with PM10 and ozone (O-3) level. In the first stage of the hierarchical model, we estimate the relative mortality rate associated with PM10 for each of th e 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 o f a spatial model with the goal of exploring the spatial correlation of the pollutant-specific coefficients among cities. Finally, to explore the resu lts of considering the two pollutants jointly, we fit and compare univariat e and bivariate models. Ail posterior distributions from the second stage a re estimated by using Markov chain Monte Carlo techniques. In univariate an alyses using concurrent day pollution Values to predict mortality, we find that an increase of 10 mug m(-3) in PM10 on average in the USA is associate d with a 0.48% increase in mortality (95% interval: 0.05, 0.92). With adjus tment for the O-3 level the PM10-coefficient is slightly higher. The result s 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.