Power estimation using simulations for air pollution time-series studies

Abstract

BackgroundEstimation 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.MethodsPower 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.ResultsIn 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.ConclusionsThese 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.

Joint Effects of Ambient Air Pollutants on Pediatric Asthma Emergency Department Visits in Atlanta, 1998–2004

“…35 Our study used a long time series (6 years) with fairly high daily event counts, leading to ample power. 36 This may allow for a higher degree of collinearity with less adverse impact on model performance than would be the case for a study with a shorter time series or lower average daily counts. Effect estimate variances in our models did not appear severely inflated, providing some reassurance that concurvity was not excessive in relation to our study size.…”

“…28 This can lead to better power for detection of effects of some pollutants, or pollutant combinations, than others. 36 …”

Global Association of Air Pollution and Cardiorespiratory Diseases: A Systematic Review, Meta-Analysis, and Investigation of Modifier Variables

“…47,48 We have considered only single pollutants, which does not take into consideration potential additive effects of multiple pollutants. 49 Although mortality is often used as surrogate for incidence, we must be cautious about using mortality, especially for cardiorespiratory disease, as it may not be well-reported on death certificates. We observed significant heterogeneity in our analyses.…”

Sample size issues in time series regressions of counts on environmental exposures

“…The only published method we have found addressing these questions specifically for time series regression of counts focused on power estimation and used simulations [7]. There have in addition been long-published methods for sample size determination and power estimation more generally in generalised linear models [8][9][10], with some focused on Poisson regression [11].…”

“…At least two computer packages have implemented some of these: G*Power, which is free [12], and NCSS:PASS, which is commercially available [13]. However, it has been noted that application to the count time series context was not straightforward [7]. Calculations need to be tailored to the specifics of each study, and the algorithmic nature of the approaches does not facilitate insight into primary determinants of precision and power in typical time series regression contexts.…”