Power estimation using simulations for air pollution time-series studies

Estimation of power to assess associations of interest can be challenging for time-series studies of the acute health effects of air pollution because there are two dimensions of sample size (time-series length and daily outcome counts), and because these studies often use generalized linear models to control for complex patterns of covariation between pollutants and time trends, meteorology and possibly other pollutants. In general, statistical software packages for power estimation rely on simplifying assumptions that may not adequately capture this complexity. Here we examine the impact of various factors affecting power using simulations, with comparison of power estimates obtained from simulations with those obtained using statistical software.

Power was estimated for various analyses within a time-series study of air pollution and emergency department visits using simulations for specified scenarios. Mean daily emergency department visit counts, model parameter value estimates and daily values for air pollution and meteorological variables from actual data (8/1/98 to 7/31/99 in Atlanta) were used to generate simulated daily outcome counts with specified temporal associations with air pollutants and randomly generated error based on a Poisson distribution. Power was estimated by conducting analyses of the association between simulated daily outcome counts and air pollution in 2000 data sets for each scenario. Power estimates from simulations and statistical software (G*Power and PASS) were compared.

In the simulation results, increasing time-series length and average daily outcome counts both increased power to a similar extent. Our results also illustrate the low power that can result from using outcomes with low daily counts or short time series, and the reduction in power that can accompany use of multipollutant models. Power estimates obtained using standard statistical software were very similar to those from the simulations when properly implemented; implementation, however, was not straightforward.

These analyses demonstrate the similar impact on power of increasing time-series length versus increasing daily outcome counts, which has not previously been reported. Implementation of power software for these studies is discussed and guidance is provided.