Outline Background on dose response (concentration response) - PDF document

6/27/2016 Dose ‐ Response Modeling: An Example Using Ozone and Mortality Statistical Methods and Analysis of Health Data Workshop Mumbai, India May 30, 2016 Michelle L. Bell , Yale University Outline • Background on dose ‐ response (concentration ‐ response) – Different types of curves and approaches • Example of modeling exposure ‐ response curve for risk of mortality from ozone in 98 U.S. cities • Concluding thoughts 1

6/27/2016 Dose ‐ Response Curve (Exposure ‐ Response Curve) Shows the relationship between different levels of exposure and different levels of risk Response Concentration •Curves can be a wide variety of shapes. •Curves can cross: Substance A may be more toxic at low doses, Substance B more toxic at high doses. May have some data points, but not the whole curve (may not know the true shape) x Health Response x x x ? x One approach: x Statistical modeling x through sets of points Dose (or pollutant concentration) 2

6/27/2016 May have data at high exposures, but not lower exposures (or vice versa). x x x x x x Health Response x Known x x x x x One approach: Extrapolation ? Unknown Dose (or pollutant concentration) Often Summary Measures are Reported mortality 100 One approach: Percent Response Summarize one point of the curve 50% response dose at LD 50 = 50 which 50% of subjects respond 0 LD 50 Dose 3

6/27/2016 Example of a curve with little concentration-dependence. Shows little dose-response. Health Risk Still there is an effect. Concentration Resistant and Sensitive Populations Resistant Populations Health Response Hypersensitive Populations Concentration 4

6/27/2016 Does the effect persist at very low concentrations? Exposure ‐ response curve study • How does risk change with level of exposure? • Are there “safe” Mortality Risk ? levels? • If so, are they at or below current regulations? O 3 Concentration Threshold? Background • Here, we focus on short ‐ term exposure (a day or a few days) • Epidemiological studies: – Estimate association between exposure and risk of health outcome – E.g., A 10 ppb increase in daily 8 ‐ hour maximum O 3 is associated with a 0.52% increase in risk of daily mortality 5

6/27/2016 Original Model (city ‐ specific) number of concentration day of the variables lag days in city c on day week for representing considered t at lag l day t temporal trends     L       c c c c E x y DOW ns time year ln ( , 7 / )  t l t l t t  l regression 0 regression coefficient for mortality in coefficient for city c for day of city c on day t city c and lag l the week     c c c c ns T ns T ns D ns D ( , 6 ) ( , 6 ) ( , 3 ) ( , 3 )     t t l t t t l t , 3 , 3 non ‐ linear non ‐ linear functions for functions for dew temperature point temperature  interactio n terms for age and time Epidemiological Model Time ‐ series model (city ‐ specific)     L  c  c c  E μ β x ln . . .  t l t l  l 0  c = Expected mortality in city c on day t t c x  = Pollution level in city c on day t at lag l t l  c = Regression coefficient for city c and pollution at lag l l L = maximum number of days considered for lags 6

6/27/2016 Exposure ‐ response curve models     L    c c c E μ β x ln . . . 1. Original model  t l t l  l 0 Exposure ‐ response curve models     L    c c c E μ β x ln . . . 1. Original model  t l t l  l 0     L   c  c c  2. Subset approach E μ β x ln . . .  t l t l c  l x s 0 ,  t l s = specified subset value Generates effect estimates only for concentrations below s Vary level of s 7

6/27/2016 Results – Subset Approach % Increase in Mortality Risk s : for daily Lag 01 O 3 (ppb) Threshold: level below which no adverse health effect occurs (safe level) 100 Health Risk ? 50 0 Concentration Threshold 8

6/27/2016 Exposure ‐ response curve models     L    c c c E μ β x ln . . . 1. Original model  t l t l  l 0     L   c  c c  2. Subset approach E μ β x ln . . .  t l t l c  l x s 0 ,  t l 3. Threshold model     L    c c c E μ β x - h) . . . ln (   t l t l  l 0     c c c x h x h x h ( ) ( ) if , 0 o/w where     t l t l t l Assumes no health effect for h = specified threshold value concentrations < h , effect for > h Exposure ‐ response curve models     L    c c c E μ β x ln . . . 1. Original model  t l t l  l 0     L   c  c c  2. Subset approach E μ β x ln . . .  t l t l c  l x s 0 ,  t l 3. Threshold model     L    c c c E μ β x - h) . . . ln (   t l t l  l 0     c c c x h x h x h ( ) ( ) if , 0 o/w where     t l t l t l     L    c c E μ ns x 4. Spline model ln ( ) . . .  t t l  l 0 9

6/27/2016 Exposure ‐ Response Curve Study Conclusions • Consistent evidence that if a threshold exists, it is at very low levels • Consistent results under multiple methods • Any “safe” level would be below current regulations at the time of the study – Strong effects under compliance with U.S. EPA, WHO, CA, Canada, and European Commission • Health benefit from reduced O 3 , even in areas meeting current regulations 10

6/27/2016 Concluding Thoughts • Not all air pollution ‐ health relationships may follow the traditional exposure ‐ response model form • This example: O 3 and mortality – effects and low levels (see reference) • Similar approaches – applications for other air pollutants, other health effects, other aspects of the exposure ‐ response curve (e.g., high pollution levels) Michelle L. Bell, Roger D. Peng, and Francesca Dominici. The exposure ‐ response curve for ozone and risk of mortality and the adequacy of current ozone regulations . Environmental Health Perspectives 2006 114, p. 532 ‐ 536. 11