Combining Evidence on Air Pollution and Daily Mortality from the 20 Largest US Cities: A Hierarchical Modelling Strategy

Abstract

Summary. 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 ®ndings between cities. We have developed analytical methods that address these concerns and combine evidence from multiple locations to gain a uni®ed 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 PM 10 (particulate matter less than 10 m in aerodynamic diameter) and by performing univariate and bivariate analyses with PM 10 and ozone (O 3 ) level. In the ®rst stage of the hierarchical model, we estimate the relative mortality rate associated with PM 10 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-speci®c covariates. We also ®t two variations of a spatial model with the goal of exploring the spatial correlation of the pollutant-speci®c coef®cients among cities. Finally, to explore the results of considering the two pollutants jointly, we ®t 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 ®nd that an increase of 10 g m À3 in PM 10 on average in the USA is associated with a 0.48% increase in mortality (95% interval: 0.05, 0.92). With adjustment for the O 3 level the PM 10 -coef®cient is slightly higher. The results are largely insensitive to the speci®c 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.

A longitudinal study of mortality and air pollution for São Paulo, Brazil

“…Both humidity and up to lag 3 of temperature are significant. Our main conclusion is in agreement with other recent findings that there is an association between air pollution and mortality (Saez et al, 1999;Dominici et al, 2000 ). The results are also in agreement with a previous study of air pollution and mortality for people over 65 years old in São Paulo based on data collected shortly before ours ( Saldiva et al, 1995 ).…”

“…There are also many studies with endpoint mortality ( Dockery et al, 1993;Bachárová et al, 1996;Dab et al, 1996;Katsouyanni et al, 1996;Sunyer et al, 1996;Vigotti et al, 1996;Wojtniak and Piekarsky, 1996;Zmirou et al, 1996 ), and a consensus now seems to be emerging that there is an association between air pollution and mortality (Saez et al, 1999;Dominici et al, 2000 ).…”

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

“…In this paper we extend previous modelling approaches developed in NMMAPS for P M 10 (Dominici et al, 2000) to take into account the following characteristics of the summer ozone data (from June 1 st to September 30 th ). Unlike P M 10 , summer ozone levels are measured daily, thus allowing estimation of health effects associated with exposure to ozone in the past few days instead of health effects associated with a one day impulse in air pollution concentrations.…”

Bayesian statistics in medicine: a 25 year review

“…Another meeting on disease clusters and ecological studies included various Bayesian developments [264][265][266]. A read paper showed a very detailed examination of projections of the AIDS epidemic [267], and another used hierarchical modelling to combine evidence on air pollution and daily mortality in the 20 largest U.S. cities [268]. In the burgeoning area of molecular population genetics, another read paper compared algorithms based on importance sampling and Markov chain Monte Carlo in making inference [269].…”