SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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CALIFORNIA Discussion on Spatial Epidemiology:Discussion on Spatial Epidemiology:with focus on Chronic Effects of Air with focus on Chronic Effects of Air

Pollution Pollution

Kiros Berhane, Ph.D.

(with Duncan Thomas, Jim Gauderman and the CHS Team)

Department of Preventive MedicineKeck School of Medicine

University of Southern CaliforniaLos Angeles, CA, USA

(e-mail: kiros@usc.edu)

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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• Long Term Cohort Studies– The Children’s Health Study– The multi-Level modeling Paradigm

• Spatio-temporal Issues

• Integrated modeling

• Discussion points

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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BackgroundBackground• Designed to take advantage of existing air

monitoring data to choose optimal sites

• Exploits temporal, spatial, and individual comparisons

• Extensive exposure and health assessment to support all three levels of comparison

• Study Goal: To assess whether air pollution (regional and/or local) is associated with chronic health effects in children?

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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LLLL

LLLL

LLLL

LMLH

HMLM

HHHH

HHHH

LHMH

HHHL HMHL

MMMM

MLLL

O3, PM10, NO2, H+: L = low M = Medium H = High

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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– Level I: Between times (k) within subjects (i )

ycik = aci + bci tcik + zcik + (xcik–xci)1 + ecik

– Level II: Between subjects within community (c)

bci = Bc + zci + (xci – Xc)2 + eci

– Level III: Between communities

Bc = 0 + Zc + Xc 3 + ec

Fitted simultaneously as a mixed effects model

Linear Multi-level ModelLinear Multi-level Model

Spatio-temporal effects could be assessed at any of the levels Berhane et al, Berhane et al, Statist Sci Statist Sci 2004; 19: 414-4402004; 19: 414-440

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Accounting for Intra-Accounting for Intra-Community Variation Community Variation

Goals:• To build a model for personal exposure

combining spatio-temporal model for ambient concentrations with time-activity data from questionnaires and measurements

• To optimize the design of time/activity sampling

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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WW

YY

ZZ

XX

Traffic, Traffic, Land UseLand Use

Local ExposureLocal ExposureMeasurementsMeasurements

HealthHealthOutcomeOutcome

True True ExposureExposure

LLLocationsLocations

PPRegionalRegional

BackgroundBackground

Molitor et al, Molitor et al, AJEAJE 2506;164:69-76 (nonspatial) 2506;164:69-76 (nonspatial)Molitor et al, Molitor et al, EHPEHP 2507:1147-53 (spatial) 2507:1147-53 (spatial)

Bayesian Spatial Bayesian Spatial Measurement Error ModelMeasurement Error Model

Subsample Subsample S | Y, L, WS | Y, L, W

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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Spatial Regression ModelSpatial Regression Model• Exposure model

E(Xi) = WiW = land use covariates, dispersion model predictions

cov(Xi,Xj) = 2Iij + 2 exp(– Dij)

MESA Air spatio-temporal model:

x(s,t) = X0(s) + k Xk(s) Tk(t)

• Measurement model E(Zi) = Xi

• Disease model g[E(Yi)] = Xi

• Multivariate exposure model (“co-kriging”)

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ASSIGNMENT OF LOCAL ASSIGNMENT OF LOCAL EXPOSURESEXPOSURES

• For all homes in cohort, we can assign an estimated exposure based on fitted parameters

• Systematic component depends on community ambient level and traffic density

• Random component is weighted mean of measurements at other homes, using estimated covariance matrix

E(xci) = Zci´ ji (xcj Zci´) Ccij / Ccii

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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Spatial Model: for Full CohortSpatial Model: for Full Cohort• Fit subsample data, regressing measurements Z on

predictors WE(Zi) = Wi cov(Zi,Zj) = 2Iij + 2 exp(–Dij)

• Impute exposures X to all subjects based on W and mean of residuals for neighbors

Xi = Zi + iNj (Zj – Xj) wij

• Fit full cohort, regressing health outcomes Y on imputed X, weighted by uncertainties of imputations

E(Yi) = Xi var(Yi) = 2 + 2 var(Xi)

Thomas, LDA 2007; 13: 565-81

^

^

^ ^

^ ^

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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Multivariate CAR ModelMultivariate CAR Model

• Structured covariance matrix with submatrices for each pollutant (p,q) and their correlations

cov(Xpi,Xqj) = pq exp(pq Dij)

• Hope is to incorporate atmospheric chemistry and dispersion theory in means and covariance models

• We have currently spatial measurements on samples of homes for NO2 and O3, but not the same homes

• Plans to measure NO2, NO, and O3 in a larger sample of homes

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Sampling StrategiesSampling Strategies• Case-control: choose S to be set of asthma cases and their

town-matched controls

• Surrogate diversity: choose S that maximizes the variance of traffic density

• Spatial diversity: choose S that maximizes the geographic spread of measurements

– Maximize total distance from all other points

– Maximize minimum distance from nearest point

– Maximize the informativeness of sample for predicting non-sample points

• Hybrid: First measure cases and controls; then add additional subjects that would be most informative for refining E(X |Z,P,W )

Thomas, LDA 2007; 13: 565-81

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Additional SubstudiesAdditional Substudies• Personal exposure measurements• Biomarkers of latent disease processes• Time-activity data– Have “usual” times and subjective activity levels in

various locations (home, school, playgrounds, in transit, etc.)

– Plan to obtain GPS measurements of actual time-resolved locations on a subsample for short periods

– Also plan to obtain step-counts and/or accelerometry on a subsample for short periods

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Further Extensions of the Integrated Further Extensions of the Integrated Research programResearch program

SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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CALIFORNIA Discussion PointsDiscussion Points• Issues with exposure modeling for Intra-community

variation– Measurement error?– Implications of using snapshots in space/time to assess long term

exposure? – Implications of sampling strategies?

• Differences in spatio-temporal resolution of data: Outcome vs. Exposure– Implications for health effects analysis?

• Integrated Modeling approaches vs. Compartmentalized modeling– Which way to go?

• Issues in Chronic vs. Acute effects analysis– Are they really different?

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SAMSI Workshop: September 15, 2009SAMSI Workshop: September 15, 2009

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THANK YOU!THANK YOU!

Contact me atkiros@usc.edu