An investigation of distributed lag models in the context of air pollution and mortality time series analysis

In particulate air pollution mortality time series studies, the particulate air pollution exposure measure used is typically the current day's or the previous day's air pollution concentration or a multi-day moving average air pollution concentration. Distributed lag models (DLMs) that allow for differential air pollution effects that are spread over multiple days are seen as an improvement over using a single- or multi-day moving average air pollution exposure measure. However, at the current time, the statistical properties of DLMs as a measure of air pollution exposure have not been investigated. In this paper, a simulation study is used to investigate the performance of DLMs as a measure of air pollution exposure in comparison with single- and multi-day moving average air pollution exposure measures under various forms for the true effect of air pollution on mortality. The simulation study shows that DLMs offer a more robust measure of the effect of air pollution on mortality and avoid the potential for a large negative bias compared with single- or multi-day moving average air pollution exposure measures. This is important information. In many U.S. cities, particulate air pollution concentrations are observed only once every six days, meaning it is often only possible to use single-day particulate air pollution exposure measures. The results from this paper will help quantify the magnitude of the negative bias that can result from using single-day exposure measures. The implications of this work for future air pollution mortality time series studies are discussed. The data used in this paper are concurrent daily time series of mortality, weather, and particulate air pollution from Cook County, IL, for the period 1987-1994.