Biostatistics CoreSoutheastern Center for Air Pollution

and Epidemiology (SCAPE)

RD83479901

Lance Waller

Personnel

• Lance Waller• W. Dana Flanders (Epidemiologic methods)• Mitchel Klein (Epidemiologic methods)• Howard Chang (Spatiotemporal statistics)

• Thanks to:– Katie Gass (Doctoral Student, C&RT)– John Pearce (Post-doc, self-organizing maps)

• Welcome to:– Jenna Krall (Post-doc, spatiotemporal statistics)

Overall goals

• Biostatistical support within each project– Design and analysis plan– Analysis and interpretation

• Methodological development motivated by and applied to project data– Areas of particular interest:

• Spatiotemporal statistics• Epidemiologic analysis• Linking exposure(s) to outcome(s)

Embedded in Projects• Project 1: Instrumentation for Comprehensive Air Quality

– General discussions of quantifying measurement error• Project 2: Commuter Study

– Design and analysis plan– Data analysis and interpretation (Flanders)

• Project 3: Pediatric Birth Cohort– Plan for assessing confounding– Bayesian ensemble estimates for source apportionment (Chang)– Fused CMAQ exposure (Chang)

• Project 4: Multi-city time series– Model development to address within and between city variation– Source apportionment and epidemiologic associations (Krall)

Methodological contributions• Confounder identification/causal inference (Flanders and Klein)• Geographically weighted regression (Waller)• Spatiotemporal statistics (Chang)• Classification and regression trees (Gass, Klein, Flanders, Chang)• Self-organizing map classification (Pearce, Waller)• Measurement error (Chang)• Climate change projections (Chang)• Ensemble estimation (Chang)• Spatiotemporal zero-inflated models (Chang)• Estimating joint effects (Klein)• Fused exposure estimates (Chang)

Recent publications (to appear)• Gass KM, Balachandran S, Chang HH, Russell AG, Strickland MJ.

Ensemble-based source apportionment of fine particulate matter and emergency department visits for pediatric asthma. American Journal of Epidemiology, accepted.

• Reich BJ, Chang HH, Foley K. A spectral method for spatial downscaling. Biometrics, in press.

• Winquist A, Schauer JJ, Turner J, Klein M, Sarnat SE. Impact of ambient fine particulate matter carbon measurement methods on observed associations with acute cardiorespiratory morbidity. Journal of Exposure Science and Environmental Epidemiology, accepted.

• Chang HH, Hao H, Sarnat SE. A statistical modeling framework for projecting future ambient ozone and its health impact due to climate change. Atmospheric Environment 89:290-297, 2014.

More publications• Darrow LA, Klein M, Flanders WD, Mulholland JA, Tolbert PE, Strickland MJ. Air

pollution and acute respiratory infections among children 0-4 years: an 18-year time-series study. American Journal of Epidemiology 180:968-77, 2014.

• Dionisio KL, Baxter LK, Chang HH. An empirical assessment of exposure measurement error and effect attenuation in bipollutant epidemiologic models. Environmental Health Perspectives 122(11):1216-24, 2014.

• Gass K, Klein M, Chang HH, Flanders WD, Strickland MJ. Classification and regression trees for epidemiologic research. Environmental Health 13:17, 2014.

• Hu X, Waller LA, Lyapustin A, Wang Y, Al-Hamdan MZ, Crosson WL, Estes MG, Estes SM, Quattrochi DA, Puttaswamy SJ, Liu Y. Estimating ground-level PM2.5 concentrations in the Southeastern United States using MAIAC AOD retrievals and a two-stage model. Remote Sensing of Environment 140:220-232, 2014.

• Hu X, Waller LA, Lyapustin A, Wang Y, Liu Y. 2014. 10-Year Spatial and Temporal Trends of PM2.5 Concentrations in the Southeastern U.S. Estimated Using High-Resolution Satellite Data. Atmospheric Chemistry and Physics 14:6301-6314.

More publications• Neelon B, Chang HH, Ling Q, Hastings SN. Flexible space-time hurdle models for

zero-inflated count data: exploring spatiotemporal trends in emergency department visits. Statistical Methods and Medical Research, 2014, DOI: 10.1177/0962280214527079.

• Pearce JL, Waller LA, Chang HH, Klein M, Mulholland JA, Sarnat JS, Sarnat SE, Strickland MJ, Tolbert PE. Using self-organizing maps to develop ambient air quality classifications for use in multipollutant health studies: a time-series example. Environmental Health 13:56, 2014.

• Russell A, Holmes H, Frieberg M, Ivey S, Hu Y, Balachandran S, Mulholland J, Tolbert P, Sarnat J, Sarnat S, Strickland M, Chang H, Liu Y. Use of Air Quality Modeling Results in Health Effects Research. In Air Pollution Modeling and Its Application XXIII (D. Steyn and R. Mathur eds.) 2014.

• Sarnat JA, Golan R, Greenwald R, Raysoni AU, Kewada P, Winquist A, Sarnat SE, Flanders WD, Mirabelli MC, Zora JE, Bergin MH, Yip F. Exposure to Traffic Pollution, Acute Inflammation and Autonomic Response in a Panel of Car Commuters. Environmental Research 133: 66-76, 2014.

More publications• Sororian S, Holmes H, Friberg M, Ivey C, Hu Y, Mulholland J, Russell

A, Strickland M, Chang H. Temporally and spatially resolved air pollution in Georgia using fused ambient monitoring data and chemical transport model results. In Air Pollution Modeling and Its Application XXIII (D. Steyn and R. Mathur eds.) 2014.

• Strickland MJ, Klein M, Flanders WD, Chang HH, Mulholland JA, Tolbert PE, Darrow LA. Modification of the effect of ambient air pollution on pediatric asthma emergency visits: susceptible subpopulations. Epidemiology 25(6):843-50, 2014.

• Winquist A, Kirrane E, Klein M, Strickland M, Darrow LA, Sarnat SE, Gass K, Mulholland JA, Russell AG, Tolbert PE. Joint effects of ambient air pollutants on pediatric asthma emergency department visits in Atlanta, 1998-2004. Epidemiology 25:666-73, 2014.

Under development

• Review of statistical methods for mixtures• A general definition of causal effects (Flanders

and Klein)• Partial correction for unmeasured

confounders (Flanders)• And many more…

Partial Correction for Unmeasured Confounding

W. Dana Flanders et al

BackgroundPrior Work

In time-series and spatial analyses, previously showed how one can identify confounding and other model miss-specification, e.g.:

BackgroundPrior Work

Method considers time-series model with air pollutants of interest (Xt), confounders (Ct), plus air pollutant some time after the event (Yt), e.g.:

Hypothesized model

Diagnostic model

BackgroundPrior Work

Works because Xt+1 cannot be a cause of or conversely; In fact should be unassociated with after control of and if model correctly specified. (DAG) Model to be evaluated (correctly specified?)

Diagnostic model

Ut

Ct

Xt Yt Xt+1

Causal Diagram, Example.

Xt+1 associated with Yt conditional on Xt and Ct.

Yt = outcome, day t; Ct = covariate, day t;Xt = air pollutant, day t; Xt+1= air pollutant, day t+1; Ut = covariate, day t;

Ut

Ct

Xt Yt Xt+1

Causal Diagram, Example.

Xt+1 independent of Yt conditional on Xt and Ct if no confounding.

Yt = outcome, day t; Ct = covariate, day t;Xt = air pollutant, day t; Xt+1= air pollutant, day t+1; Ut = covariate, day t;

BackgroundPrior Work

• Xt+1 occurs after the onset of disease (a ‘future variable’)

• Xt+1 can be viewed as a negative control exposure (Lipsitch et al Epidemiol 2010)

• Relies on a central tenet of causality:

A cause must precede its effect

• If a future variable is associated with past disease, after accounting for the relevant past exposures, this must reflect a spurious association

BackgroundProxy for a confounder

“Often, when a confounder cannot be adequately measured, it is better to adjust for a surrogate confounder than to use the crude odds ratio (1).”

Hernán et al. Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects Epidemiology. AJE 2002; 155: 176f.(1) Greenland S and Neutra R. Control of confounding in assessment of medical technology. IJE 1980; 9: 361f.

Propose a method to partially reduce confounding

• Build on prior work, using Xt+1

• Xt+1 can be viewed as a surrogate or proxy for an unavailable confounder (Xt+1)... often better to adjust for it.

Key Assumptions

for some continuous function g(.) of ,

• correlation of and with unmeasured confounder both + or both -

#alternatively:

Claim

With these assumptions, the GMM-estimator of obtained by fitting:

is asymptotically less biased than obtained by fitting:

Claim

in sense that *where |*| > |.

Proof for linear model; by analogy for log-linear.

Simulationsbased on real data

Introduce confounding by fitting model without: Temperature lag0, lag1-3

Model cor(xt,xt+1) cor(xt,ut) cor(xt+1,ut)

a) Drop T lag0 0.91 0.62 0.63b) Drop all T 0.91 0.62+ 0.63

Simulationsbased on real data

Introduce “confounding” by fitting model without: TmaxC-terms, or also Tmin-terms

Crude Correct partial corrected a) 0.0096 0.0233 0.0224b) 0.0011 0.0236 0.0112

Crude model omits TempertureCorrect model includes Temperature lag0, lag1, lag2Partial Corrected model: omits Temperature, but includes Xt+1

Preliminary Conclusions

• Theory indicates less bias in linear case by including X, when confounding present (assumptions).

• Simulations suggest same for log-link.• Mean squared error also often reduced• No bias if include Future Indicator in absence

of confounding, but can increase MSE

Preliminary Conclusions

• If ME not negligible, can increase bias & MSE

• Sensitivity analysis

Questions?