Skill of Generalized Additive Model to Detect PM 2.5 Health Signal in the Presence of Confounding Variables Office of Research and Development Garmisch 2014 Valerie Garcia 1, P.S. Porter 2, E. Gego 2, S.T. Rao 3 1 US EPA, Office of Research and Development, Raleigh NC 2 Porter-Gego, Idaho Falls, ID, 3 NCSU, Raleigh, NC

1 Does Confounding Affect the Detection of Air Pollution Health Effect in New York City (NYC)? However, other related variables (temperature, relative humidity, other air pollutants) are also thought to affect respiratory health Fine particulate matter (< 2.5 microns in size; PM2.5) is known to affect respiratory health Source: modified, Air Pollution and the Health of New Yorkers, 2011 (Silverman and Ito, 2010) The risk of hospitalization for asthma increases with increases in daily levels of PM 2.5 and O 3 in New York City

2 Confounding: relationships between main health effect (independent variable) and health outcome (dependent variable) May result in spurious relationships (e.g., association between independent and dependent variable that doesn’t exist) Does Confounding Affect the Detection of Air Pollution Health Effect in NYC? Temperature Humidity Ozone Time PM2.5Respiratory- Related HA Confounding: Co-variables in model are related to main health effect (PM2.5) and health endpoint (hospital admissions)

1. Emperical health (hospital admissions; HA) and air quality data (PM) used to parameterize simulations of several realizations of PM2.5 concentrations and respiratory-related hospital admissions 2. Run Simulations ( 10 PM + ε) x [(5 HA 1-mo + 5 HA 3-mo) x 2 HA random] = 200 a.PM2.5 (24-hr avg; PM) estimated as a function of O 3 (O3), temperature (TEMP), relative humidity (RH) plus noise (ε) to ensure collinearity b.Hospital admissions (daily total; HA) in correspondence to PM2.5 simulated for 3 health effect values. 3. GAM systematically run with simulated datasets 3 Study Approach Overall approach: Simulated health response to PM2.5 in Generalized Additive Model (GAM) Framework

Spatial and temporal extent: daily values for NYC metropolitan area from Jan 1st 2000 to Dec 31 st 2006 Hospital Admissions: Daily total for asthma, chronic bronchitis, emphysema, and chronic obstructive pulmonary disease from NYS Department of Health Statewide Planning & Research Cooperative (SPARCS) 4 1. Actual health and air quality data used to parameterize simulations Met Data: Max. temperature and relative humidity averaged across 3 monitors (Bronx, Queens, Richland) Air Quality Data: US EPA AIRS database for NY (Region 2) 4 Kings Pop. 2,465,326 Queens Pop. 2,229,379 Bronx Pop. 1,332,650 New York Pop. 1,537,195

5 2. PM2.5 (24-hr avg) estimated as a function of O3, TEMP, RH plus noise to ensure collinearity 10 simulations of PM2.5 (24-hr avg) estimated as a function of O3, TEMP, RH plus noise (modified daily) to ensure collinearity Confounders kept stable for all 10 simulations, while timeseries (ts) for PM2.5 and HA were systematically modified

6 3. Hospital admissions (daily total) in correspondence to PM2.5 simulated for 3 health effect values  Y-intercept (β 0 = 4.74); baseline incidence rate (average considering all independent variables)  Slope (β PM = 0.0, or ); Increase in HA due to PM2.5; β PM = means increase in 10 ppb in PM2.5 causes a rise in HA of about 4%  ‘Flu’ variable (time seasonal = 1 month or 3 months); to account for a more persistent flu/allergy Ln(y) = Ln(B) + ß(PM) Incidence (log scale) PM concentration Ln(B) Epidemiology Study Source: N. Fann, 2009 CMAS presentation 10 simulations (5 for each ‘flu’ scenario) of hospital admissions corresponding to PM2.5 simulations; 3 parameters:

3. Hospital admissions (daily total) in correspondence to PM2.5 simulated for 3 health effect values

Examined the impact of collinearity between PM2.5 and 4 confounding variables on the relative risk HA ~ β 0 + β PM PM2.5 + s(time) + s(O3) + s(TEMP) + s(RH) family=quasi-poisson –Spline function (s) –Calendar time (time) –Ozone 8-hr daily max. concentration (O3) –Daily maximum temperature (TEMP) –Relative humidity (RH) 4. GAM systematically run with simulated datasets Series of 100 simulations (10 PM2.5 realizations x 10 HA [5 each 1- mo flu and 3-mo flu]) realizations Randomly selected 2 HA realizations for a total of 200 simulations Also examined effect of knots on ‘time’ variable as this variable has the strongest association with hospital admissions

Note on smoothing ‘time’ variable and number of knots 4. GAM systematically run with simulated datasets More knots equates to constraining the model more tightly In the example to the right, more knots required to characterize ‘seasonal’ than long-term ‘trend’ Source graphic: Stats.stackexchange.com

Results - Change in β PM (Health Effect) k = knots

Analysis of β PM parameter –GAM is successful at extracting/re-estimating health effect (HA) with three ‘true’ β PM values (0.000, and 0.004) –This is true with year-long data or when data for summers only used; summer-only information leads to less precision (likely from smaller sample size) –Narrowing of β PM interquartile ranges from top (k-10) to bottom (k-49) panels shows increasing number of knots in ‘time’ smooth function leads to less variability in β PM –GAM is skilled at detecting no signal as well as extracting the true health signal Results

Results - Change in Standard Error (Related to Statistical Relevance) Standard error of β PM

Results - Change in Correlation Coefficient (Goodness of Fit) Correlation Coefficient

Results – 4 confounders vs time-variant confounder only

Analysis of standard error (se) –Range of se for 3 different health effects similar for same number of knots indicating incremental HA variability caused by health signals is not a major factor in the overall variability of HA –Increasing smoothness of time confounder leads to smaller se –Loss in accuracy is seen with “summer only” dataset due to limiting data Analysis of correlation coefficient (goodness of fit) –Correlation coefficient increases with number of knots –Correlation coefficients characterizing 3 true slopes are similar; again indicating that the overall affect of PM pollution on HA is rather small in comparison to the other factors such as seasonality Results

16 Summary GAM detects the absence or the existence of a very weak signal (β PM ) effectively, regardless of confounding health effect covariates –Better detects signal (tighter IQR, less error) using year- round data (with time variant function) as opposed to summers only Relationship with time variant variable swamps more subtle pollution and meteorology relationships with health outcome Modifying the knots (or degrees of freedom) for this variable can drastically alter results Increasing knots resulted in better goodness of fit measures and tighter confidence intervals