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

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Dose‐Response Modeling: An Example Using Ozone and Mortality

Michelle L. Bell, Yale University Statistical Methods and Analysis of Health Data Workshop

Mumbai, India May 30, 2016

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

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Dose‐Response Curve (Exposure‐Response Curve)

• 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.

Concentration Response Shows the relationship between different levels of exposure and different levels of risk

Health Response Dose (or pollutant concentration)

x x x x x x

?

x

May have some data points, but not the whole curve (may not know the true shape)

One approach: Statistical modeling through sets of points

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Health Response Dose (or pollutant concentration)

x x x x x x x x x x x x

Known Unknown

?

May have data at high exposures, but not lower exposures (or vice versa).

One approach: Extrapolation

50 100

Percent Response

50% response

LD50 mortality

Dose

Often Summary Measures are Reported

dose at which 50%

• f subjects

respond LD50 =

One approach: Summarize one point

• f the curve

SLIDE 4

6/27/2016 4 Health Risk Concentration Shows little dose-response. Still there is an effect.

Example of a curve with little concentration-dependence.

Health Response Concentration Hypersensitive Populations Resistant Populations

Resistant and Sensitive Populations

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Does the effect persist at very low concentrations? Exposure‐response curve study

Mortality Risk O3 Concentration

Threshold?

• How does risk

change with level of exposure?

• Are there “safe”

levels?

• If so, are they at or

below current regulations?

?

Background

• Here, we focus on short‐term exposure (a day
• r 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 O3 is associated with a 0.52% increase in risk of daily mortality

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Original Model (city‐specific)

   

) / 7 , ( ln year time ns DOW y x E

t t c c l t L l c l c t

  

 



 ) 3 , ( ) 3 , ( ) 6 , ( ) 6 , (

3 , 3 , c t l t c t c t l t c t

D ns D ns T ns T ns

   

   

concentration in city c on day t at lag l

time and age for n terms interactio 

day of the week for day t variables representing temporal trends regression coefficient for city c and lag l number of lag days considered non‐linear functions for dew point temperature mortality in city c on day t non‐linear functions for temperature regression coefficient for city c for day of the week

Epidemiological Model

Time‐series model (city‐specific)

   

. . . ln  

 



c l t L l c l c t

x β μ E

= Expected mortality in city c on day t = Pollution level in city c on day t at lag l = Regression coefficient for city c and pollution at lag l = maximum number of days considered for lags

c t



c l t

x 

c l



L

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Exposure‐response curve models

• 1. Original model

   

. . . ln  

 



c l t L l c l c t

x β μ E

Exposure‐response curve models

• 1. Original model

   

. . . ln  

 



c l t L l c l c t

x β μ E

• 2. Subset approach

   

. . . ln

,

 

  



c l t L s x l c l c t

x β μ E

c l t

s = specified subset value Generates effect estimates only for concentrations below s Vary level of s

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Results – Subset Approach

% Increase in Mortality Risk s: for daily Lag 01 O3 (ppb)

50 100 Health Risk Concentration

Threshold Threshold: level below which no adverse health effect occurs (safe level)

?

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Exposure‐response curve models

• 1. Original model

   

. . . ln  

 



c l t L l c l c t

x β μ E

• 2. Subset approach

   

. . . ln

,

 

  



c l t L s x l c l c t

x β μ E

c l t

• 3. Threshold model
• /w

, if ) ( ) ( h x h x h x

c l t c l t c l t

   

   

   

. . . h)

• x

β μ E

c l t L l c l c t

 

  



( ln

where h = specified threshold value Assumes no health effect for concentrations <h, effect for >h

Exposure‐response curve models

• 1. Original model

   

. . . ln  

 



c l t L l c l c t

x β μ E

• 2. Subset approach

   

. . . ln

,

 

  



c l t L s x l c l c t

x β μ E

c l t

• 3. Threshold model
• /w

, if ) ( ) ( h x h x h x

c l t c l t c l t

   

   

   

. . . h)

• x

β μ E

c l t L l c l c t

 

  



( ln

• 4. Spline model

   

. . . ) ( ln  



  L l c l t c t

x ns μ E

where

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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 O3, even in areas

meeting current regulations

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Concluding Thoughts

• Not all air pollution‐health relationships may

follow the traditional exposure‐response model form

• This example: O3 and mortality – effects and

low levels (see reference)

• Similar approaches – applications for other air

pollutants, other health effects, other aspects

• f 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

• f current ozone regulations.

Environmental Health Perspectives 2006 114, p. 532‐536.