Model choice in time series studies of air pollution and health

Multi-city time series studies of particulate matter (PM) and mortality and morbidity have provided evidence that daily variation in air pollution levels is associated with daily variation in mortality counts. These findings served as key epidemiological evidence for the recent review of the United States National Ambient Air Quality

Standards (NAAQS) for PM. As a result, methodological issues concerning time series analysis of the relation between air pollution and health have attracted the attention of the scientific community and critics have raised concerns about the adequacy of current model formulations. Time series data on pollution and mortality are generally analyzed using log-linear, Poisson regression models for overdispersed counts with the daily number of deaths as outcome, the (possibly lagged) daily level of pollution as a linear predictor, and

smooth functions of weather variables and calendar time used to adjust for time-varying confounders. Investigators around the world have used different approaches to adjust for confounding, making it difficult to compare results across studies. To date, the statistical properties of

these different approaches have not been comprehensively compared. We quantify and characterize model uncertainty in adjusting for seasonal and long-term trends via simulation and by applying various modelling

approaches to the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) database. The database is comprised of daily time series of several pollutants, weather variables, and mortality counts covering the period 1987--2000 for the largest 100 cities in the

United States. We find that the bias in the estimates generally decreases with more aggressive smoothing and that model selection methods which optimize prediction may not be suitable for obtaining an estimate with small bias.