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1.  Estimating causal effects of air quality regulations using principal stratification for spatially correlated multivariate intermediate outcomes 
Biostatistics (Oxford, England)  2012;13(2):289-302.
Methods for causal inference regarding health effects of air quality regulations are met with unique challenges because (1) changes in air quality are intermediates on the causal pathway between regulation and health, (2) regulations typically affect multiple pollutants on the causal pathway towards health, and (3) regulating a given location can affect pollution at other locations, that is, there is interference between observations. We propose a principal stratification method designed to examine causal effects of a regulation on health that are and are not associated with causal effects of the regulation on air quality. A novel feature of our approach is the accommodation of a continuously scaled multivariate intermediate response vector representing multiple pollutants. Furthermore, we use a spatial hierarchical model for potential pollution concentrations and ultimately use estimates from this model to assess validity of assumptions regarding interference. We apply our method to estimate causal effects of the 1990 Clean Air Act Amendments among approximately 7 million Medicare enrollees living within 6 miles of a pollution monitor.
doi:10.1093/biostatistics/kxr052
PMCID: PMC3297824  PMID: 22267524
Air pollution; Bayesian statistics; Causal inference; Principal stratification; Spatial data
2.  Estimating the acute health effects of coarse particulate matter accounting for exposure measurement error 
Biostatistics (Oxford, England)  2011;12(4):637-652.
In air pollution epidemiology, there is a growing interest in estimating the health effects of coarse particulate matter (PM) with aerodynamic diameter between 2.5 and 10 μm. Coarse PM concentrations can exhibit considerable spatial heterogeneity because the particles travel shorter distances and do not remain suspended in the atmosphere for an extended period of time. In this paper, we develop a modeling approach for estimating the short-term effects of air pollution in time series analysis when the ambient concentrations vary spatially within the study region. Specifically, our approach quantifies the error in the exposure variable by characterizing, on any given day, the disagreement in ambient concentrations measured across monitoring stations. This is accomplished by viewing monitor-level measurements as error-prone repeated measurements of the unobserved population average exposure. Inference is carried out in a Bayesian framework to fully account for uncertainty in the estimation of model parameters. Finally, by using different exposure indicators, we investigate the sensitivity of the association between coarse PM and daily hospital admissions based on a recent national multisite time series analysis. Among Medicare enrollees from 59 US counties between the period 1999 and 2005, we find a consistent positive association between coarse PM and same-day admission for cardiovascular diseases.
doi:10.1093/biostatistics/kxr002
PMCID: PMC3202305  PMID: 21297159
Air pollution; Coarse particulate matter; Exposure measurement error; Multisite time series analysis
3.  On quantifying the magnitude of confounding 
Biostatistics (Oxford, England)  2010;11(3):572-582.
When estimating the association between an exposure and outcome, a simple approach to quantifying the amount of confounding by a factor, Z, is to compare estimates of the exposure–outcome association with and without adjustment for Z. This approach is widely believed to be problematic due to the nonlinearity of some exposure-effect measures. When the expected value of the outcome is modeled as a nonlinear function of the exposure, the adjusted and unadjusted exposure effects can differ even in the absence of confounding (Greenland , Robins, and Pearl, 1999); we call this the nonlinearity effect. In this paper, we propose a corrected measure of confounding that does not include the nonlinearity effect. The performances of the simple and corrected estimates of confounding are assessed in simulations and illustrated using a study of risk factors for low birth–weight infants. We conclude that the simple estimate of confounding is adequate or even preferred in settings where the nonlinearity effect is very small. In settings with a sizable nonlinearity effect, the corrected estimate of confounding has improved performance.
doi:10.1093/biostatistics/kxq007
PMCID: PMC2883302  PMID: 20203259
Collapsibility; Confounding; Odds ratio

Results 1-3 (3)