1. SAMSI Workshop: September 15, 2009 Discussion on Spatial Epidemiology: with focus on Chronic Effects of Air Pollution Discussion on Spatial Epidemiology: with focus on Chronic Effects of Air Pollution Kiros Berhane, Ph.D. (with Duncan Thomas, Jim Gauderman and the CHS Team) Department of Preventive Medicine Keck School of Medicine University of Southern California Los Angeles, CA, USA (e-mail: kiros@usc.edu)

2. SAMSI Workshop: September 15, 2009 Outline Long Term Cohort Studies –The Childrens Health Study –The multi-Level modeling Paradigm Spatio-temporal Issues Integrated modeling Discussion points

3. SAMSI Workshop: September 15, 2009 Childrens Health Study Background 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?

4. SAMSI Workshop: September 15, 2009 LLLL LMLHLMLH HMLMHMLM HHHH LHMHLHMH HHHL HMHLHMHL MMMM MLLL O 3, PM 10, NO 2, H + : L = low M = Medium H = High

5. SAMSI Workshop: September 15, 2009 –Level I: Between times (k) within subjects (i ) y cik = a ci + b ci t cik + z cik + (x cik –x ci ) 1 + e cik –Level II: Between subjects within community (c) b ci = B c + z ci + (x ci – X c ) 2 + e ci –Level III: Between communities B c = 0 + Z c + X c 3 + e c Fitted simultaneously as a mixed effects model Linear Multi-level Model Spatio-temporal effects could be assessed at any of the levels Berhane et al, Statist Sci 2004; 19: 414-440

6. SAMSI Workshop: September 15, 2009 Framework for Spatial Data Consider –individual data on outcomes (Y i ), covariates (Z i ), and locations (P i ) –ecologic data on communities (W c ) We wish to choose a sample S of individuals on whom to measure true exposure (X i ) We develop an exposure model to predict E(X i |Z i,P i,W c ) for subjects not in S We want a hierarchical spatial measurement error model for analysis of Y i | X i,Z i,P i,W c

7. SAMSI Workshop: September 15, 2009 Modeling Approaches Hierarchical random effects model for outcome i = E(Y i ) = A C i + Z i 1 + i 2 + s(P i ) E(A c ) = W c i = E(X i | Z i,P i,W C i ; ) cov(Y i,Y j )| C i =C i = 2 + 2 exp( ||P i P j ||) cov(A c,A d ) = 2 + 2 exp( ||P c P c ||) Likelihood for sampled data L (a,b) = i S Pr(Y,X |Z,S) x i S Pr(Y |Z,S)

8. SAMSI Workshop: September 15, 2009 Accounting for Intra- 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

9. SAMSI Workshop: September 15, 2009 W Y Z X Traffic, Land Use Local Exposure Measurements HealthOutcome TrueExposure L Locations P RegionalBackground Molitor et al, AJE 2506;164:69-76 (nonspatial) Molitor et al, EHP 2507:1147-53 (spatial) Bayesian Spatial Measurement Error Model Subsample S | Y, L, W

10. SAMSI Workshop: September 15, 2009 Spatial Regression Model Exposure model E(X i ) = W i W = land use covariates, dispersion model predictions cov(X i,X j ) = 2 I ij + 2 exp(– D ij ) MESA Air spatio-temporal model: x(s,t) = X 0 (s) + k X k (s) T k (t) Measurement modelE(Z i ) = X i Disease model g[E(Y i )] = X i Multivariate exposure model (co-kriging)

11. SAMSI Workshop: September 15, 2009 ASSIGNMENT OF LOCAL EXPOSURES 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(x ci ) = Z ci ´ j i (x cj Z ci ´ ) C cij / C cii

12. SAMSI Workshop: September 15, 2009 Spatial Model: for Full Cohort Fit subsample data, regressing measurements Z on predictors W E(Z i ) = W i cov(Z i,Z j ) = 2 I ij + 2 exp(– D ij ) Impute exposures X to all subjects based on W and mean of residuals for neighbors X i = Z i + i N j (Z j – X j ) w ij Fit full cohort, regressing health outcomes Y on imputed X, weighted by uncertainties of imputations E(Y i ) = X i var(Y i ) = 2 + 2 var(X i ) Thomas, LDA 2007; 13: 565-81 ^ ^ ^ ^ ^ ^

13. SAMSI Workshop: September 15, 2009 Multivariate CAR Model Structured covariance matrix with submatrices for each pollutant (p,q) and their correlations cov(X pi,X qj ) = pq exp( pq D ij ) Hope is to incorporate atmospheric chemistry and dispersion theory in means and covariance models We have currently spatial measurements on samples of homes for NO 2 and O 3, but not the same homes Plans to measure NO 2, NO, and O 3 in a larger sample of homes

14. SAMSI Workshop: September 15, 2009 Sampling 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

15. SAMSI Workshop: September 15, 2009 Spatial Sampling Plans RandomMaximize var(W) Maximize min(info) Maximize min(dist) Thomas, Lifetime Data Analysis 2007; 13: 565-81

16. SAMSI Workshop: September 15, 2009 Additional 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

17. SAMSI Workshop: September 15, 2009 Methodologic Research Framework in the CHS Exposure Determinant True Exposure Measurements Genes Asthma Lung Function Biomarker Oxidative Stress & Inflammation Aim 1 Aim 2 Aim 3 Aim 4

18. SAMSI Workshop: September 15, 2009 Further Extensions of the Integrated Research program

19. SAMSI Workshop: September 15, 2009 Details Spatio-temporal pollution field: x(s,t) = X(s) T(t) where X = CAR(W a,s x 2,t 2,r,D) Ambient measurements: Z(t) ~ LN(T(t), Z 2 ) Local measurements: z(s) ~ LN(x(s,t s ), z 2 ) True personal exposure: X i = m im X(s im ) e im Personal exposure measurements: Z i ~ LN(X i, X 2 ) Time in MEs: (p i, P i ) ~ MN( i, (n,N)), i ~ MN( ) Activity in MEs: (v im,V im ) ~ LN( im, v 2 ), im ~ LN( m, 2 ) Latent disease: L i ~ LN( 0 + 1 X i + 2 G i + 3 X i G i, L 2 ) Biomarker measurements: B i ~ LN(L i, B 2 ) Disease: Y i ~ N( 0 + 1 L i, Y 2 )

20. SAMSI Workshop: September 15, 2009 Discussion 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?

21. SAMSI Workshop: September 15, 2009

22. THANK YOU! Contact me at kiros@usc.edu