A study of the association between daily mortality and ambient air pollutant concentrations in Pittsburgh, Pennsylvania.

We have studied the possible association of daily mortality with ambient pollutant concentrations (PM10, CO, O3, SO2, NO2, and fine [PM2.5] and coarse PM) and weather variables (temperature and dew point) in the Pittsburgh, PA, area for two age groups--less than 75, and 75 and over--for the 3-year period of 1989-1991. Correlation functions among pollutant concentrations show important seasonal dependence, and this fact necessitates the use of seasonal models to better identify the link between ambient pollutant concentrations and daily mortality. An analysis of the seasonal model results for the younger-age group reveals significant multicollinearity problems among the highly correlated concentrations of PM10, CO, and NO2 (and O3 in spring and summer), and calls into question the rather consistent results of the single- and multi-pollutant non-seasonal models that show a significant positive association between PM10 and daily mortality. For the older-age group, dew point consistently shows a significant association with daily mortality in all models. Collinearity problems appear in the multi-pollutant seasonal and non-seasonal models such that a significant, positive PM10 coefficient is accompanied by a significant, negative coefficient of another ambient pollutant, and the identity of this other pollutant changes with season. The PM2.5 data set is half that of PM10. Identical-model runs for both data sets reveal instability in the pollutant coefficients, especially for the younger age group. The concern for the instability of the pollutant coefficients due to a small signal-to-noise ratio makes it impossible to ascertain credibly the relative associations of the fine- and coarse-particle modes with daily mortality. In this connection, we call for caution in the interpretation of model results for causal inference when the models use fully or partially estimated PM values to fill large data gaps.

A simulation study of confounding in generalized linear models for air pollution epidemiology.

Confounding between the model covariates and causal variables (which may or may not be included as model covariates) is a well-known problem in regression models used in air pollution epidemiology. This problem is usually acknowledged but hardly ever investigated, especially in the context of generalized linear models. Using synthetic data sets, the present study shows how model overfit, underfit, and misfit in the presence of correlated causal variables in a Poisson regression model affect the estimated coefficients of the covariates and their confidence levels. The study also shows how this effect changes with the ranges of the covariates and the sample size. There is qualitative agreement between these study results and the corresponding expressions in the large-sample limit for the ordinary linear models. Confounding of covariates in an overfitted model (with covariates encompassing more than just the causal variables) does not bias the estimated coefficients but reduces their significance. The effect of model underfit (with some causal variables excluded as covariates) or misfit (with covariates encompassing only noncausal variables), on the other hand, leads to not only erroneous estimated coefficients, but a misguided confidence, represented by large t-values, that the estimated coefficients are significant. The results of this study indicate that models which use only one or two air quality variables, such as particulate matter [less than and equal to] 10 microm and sulfur dioxide, are probably unreliable, and that models containing several correlated and toxic or potentially toxic air quality variables should also be investigated in order to minimize the situation of model underfit or misfit.

The need for a more robust ozone air quality standard.

The present National Ambient Air Quality Standard for ozone has many statistical problems, including use of extreme values which have inherent large fluctuations, a compliance test that can gradually lower the target of the design value below the standard level, and inconsistencies between the number-of-exceedances criterion and the design value. The above problems can be avoided or minimized by using a more robust statistic, such as the 95th percentile, and applying a statistical compliance test, without sacrificing the stringency of the standard. Analysis of EPA's ozone data shows that the annual 95th percentiles and their three-year means have less variability than the annual second highest values and the fourth highest values in three years, respectively. At t test for the mean of the annual 95th percentiles is proposed for compliance testing not only to preserve the averaging concept of the present standard, but also to take account of ozone concentration fluctuations in order to increase the stability of the compliance status of a site or a Metropolitan Statistical Area. A procedure is provided to adjust the level of the 95th-percentile standard so that the stringency of the present standard is preserved.