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CausalInference forAir Quality

Regulations

Corwin M.Zigler

Accountabilityfor Air Quality

PotentialOutcomesandInterference

SpatialHierarchicalModel

AssessingInterferenceAssumptions

Analysis ofthe 1990Clean Air ActAmendments

[email protected] 1 /21

Estimating Causal Effects of Air QualityRegulations Using Principal Stratification

for Spatially-Correlated MultivariateIntermediate Outcomes

Corwin M. Zigler

Department of Biostatistics, Harvard School of Public Health

May 24, 2012


Regulations

Corwin M.Zigler







Air Quality, Health, andRegulation

Accountability Assessment

• Long term exposure to air pollution is bad for health.• EPA estimates ≈ $25 billion per year on air quality

management.• 1970 Clean Air Act.

• For a specific regulatory action:• What were the causal effects on air quality?• What were the causal effects on health?


Regulations

Corwin M.Zigler







1990 Clean Air ActAmendments (CAAA)

EPA designates counties as:

1 Attainment of air quality standards for PM10 .2 Nonattainment of air quality standards for PM10 :

• Required states to implement plans to achievestandards.

What were the causal effects of the 1990nonattainment designations for PM10 on:

• Pollution• Ambient concentrations of PM10 and O3 in 1999-2001.

• Health• All-cause Medicare mortality in 2001.


Regulations

Corwin M.Zigler







Causal Inference for Air QualityRegulations

1 Potential outcomes in the EPA regulatory environment.

2 Air quality is a posttreatment concomitant variable.• ⇒ Principal stratification.

3 Regulations affect multiple pollutants.• ⇒ Multivariate continuous intermediate variable.

4 Pollution is spatially correlated.• Hierarchical spatial model.

5 Interference between observations (no SUTVA).


Regulations

Corwin M.Zigler








1 Potential outcomes in the EPA regulatory environment.2 Air quality is a posttreatment concomitant variable.

• ⇒ Principal stratification.

3 Regulations affect multiple pollutants.• ⇒ Multivariate continuous intermediate variable.




Regulations

Corwin M.Zigler









• ⇒ Principal stratification.3 Regulations affect multiple pollutants.

• ⇒ Multivariate continuous intermediate variable.




Regulations

Corwin M.Zigler









• ⇒ Principal stratification.3 Regulations affect multiple pollutants.

• ⇒ Multivariate continuous intermediate variable.4 Pollution is spatially correlated.

• Hierarchical spatial model.



Regulations

Corwin M.Zigler







Observed Regulation Programand Overall Causal Effect

Observed Regulation Program

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Observational unit:pollution monitor(point-referenced data)

Overall Causal Effect

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No EPA Action


Regulations

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Corwin M.Zigler









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No EPA Action


Regulations

Corwin M.Zigler







Potential Outcomes

Regulation program vector: A = [A(si)]ni=1

• n = 362 locations.• A(si) = 1⇒ i th location nonattainment.• Specific regulation program A = a.

Potential Outcomes• Pollution Xa(s): vector of pollutant concentrations.

• PM10 and O3 .• Mortality Ya(s): all-cause mortality among Medicare

beneficiaries living near a monitor.• ≈ 7 million people aged 65+.


Regulations

Corwin M.Zigler







Potential Outcomes

Regulation program vector: A = [A(si)]ni=1

• n = 362 locations.• A(si) = 1⇒ i th location nonattainment.• Specific regulation program A = a.

Potential Outcomes• Pollution Xa(s): vector of pollutant concentrations.

• PM10 and O3 .• Mortality Ya(s): all-cause mortality among Medicare

beneficiaries living near a monitor.• ≈ 7 million people aged 65+.


Regulations

Corwin M.Zigler







Spatial Correlation→Interference

• Typical assumption of no interference (SUTVA) likelyviolated.

• Regulations can affect air quality in other areas.

• Full interference: every location interferes with everyother location.

• 2n potential outcomes for each location.• Partial interference.

• Some locations interfere with some other locations.• How to define the interference groups?


Regulations

Corwin M.Zigler









• Regulations can affect air quality in other areas.• Full interference: every location interferes with every

other location.• 2n potential outcomes for each location.

• Partial interference.• Some locations interfere with some other locations.• How to define the interference groups?


Regulations

Corwin M.Zigler









• Regulations can affect air quality in other areas.• Full interference: every location interferes with every

other location.• 2n potential outcomes for each location.

• Partial interference.• Some locations interfere with some other locations.• How to define the interference groups?


Regulations

Corwin M.Zigler







Never Observe PotentialOutcomes Under Regulation

Programs of Interest

Observed Regulation No Regulation Full RegulationA = aobs A = 0 A = 1

i Aobs(si ) Xaobs (si ) Yaobs (si ) X0(si ) Y0(si ) X1(si ) Y1(si )

Observed 1 0 obs obs

obs∗

obs∗ ? ?

Attainment 2 0 obs obs

obs∗ obs∗ ? ?

(black dots)...

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Observed...

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.nonattainment n − 1 1 obs obs

? ? obs∗ obs∗

(red dots) n 1 obs obs

? ? obs∗ obs∗


Regulations

Corwin M.Zigler







Never Observe PotentialOutcomes Under Regulation

Programs of Interest

Observed Regulation No Regulation Full RegulationA = aobs A = 0 A = 1

i Aobs(si ) Xaobs (si ) Yaobs (si ) X0(si ) Y0(si ) X1(si ) Y1(si )

Observed 1 0 obs obs obs∗ obs∗ ? ?Attainment 2 0 obs obs obs∗ obs∗ ? ?

(black dots)...

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Observed...

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.nonattainment n − 1 1 obs obs ? ? obs∗ obs∗

(red dots) n 1 obs obs ? ? obs∗ obs∗


Regulations

Corwin M.Zigler







Assignment Group InterferenceAssumption (AGIA)

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Interference implicitin EPA decisions

⇓Black dots don’tinterfere withRed dots


Regulations

Corwin M.Zigler







Estimation

Models• Potential pollution outcomes.

• Multivariate spatial hierarchical model.• Mortality outcomes, conditional on pollution.

• Poisson regression.

• Estimation with data augmentation / MCMC.

Average Causal Effects

• Expected K-Dissociative Effect:• Average effect on mortality in areas where regulation

did not affect pollution.• Expected K-Associative Effect:

• Average effect on mortality in areas where regulationdecreased pollution.


Regulations

Corwin M.Zigler







Estimation







did not affect pollution.

• Expected K-Associative Effect:• Average effect on mortality in areas where regulation

decreased pollution.


Regulations

Corwin M.Zigler







Estimation







did not affect pollution.• Expected K-Associative Effect:

• Average effect on mortality in areas where regulationdecreased pollution.


Regulations

Corwin M.Zigler







Spatial Hierarchical Model

X (s) = Z T (s)β + W (s) + ε(s)

• s ≡ specific location.

• X (s) ≡ 4−dimensional vector of pollution concentrations underboth regulations (XA=0(s),XA=1(s)).

• Z (s) ≡ covariates.

• ε(s) ≡ nonspatial (”nugget”) error.

• W (s) ≡ spatially-varying random intercepts.

• W (s) ∼ Multivariate Gaussian Process (MVGP).• Cross-covariance: K (s, s′; ν).

• ν governs spatial decay and smoothness.


Regulations

Corwin M.Zigler







Spatial Hierarchical Model

X (s) = Z T (s)β + W (s) + ε(s)

• s ≡ specific location.

• X (s) ≡ 4−dimensional vector of pollution concentrations underboth regulations (XA=0(s),XA=1(s)).

• Z (s) ≡ covariates.

• ε(s) ≡ nonspatial (”nugget”) error.

• W (s) ≡ spatially-varying random intercepts.

• W (s) ∼ Multivariate Gaussian Process (MVGP).• Cross-covariance: K (s, s′; ν).

• ν governs spatial decay and smoothness.


Regulations

Corwin M.Zigler







K (s, s′; ν)

Not RegulatedRegulated

sPM

O3

PM

O3

s'PM

O3

PM

O3

K (s, s; ν)

?

K (s′, s′; ν)

?K (s, s; ν) =K (s′, s′; ν)⇒ stationary

K (s, s′; ν) =( · · · ·· · · ·· · · ·· · · ·

)@@@R

��n

n@@@R

��

K (s, s′; ν) =( • · · ·· · · ·· · · ·· · · ·

)Corr(PM(s),PM(s′)) = e−ν||s−s′|| (isotropic)


Regulations

Corwin M.Zigler







K (s, s′; ν)


sPM

O3

PM

O3

s'PM

O3

PM

O3K (s, s; ν)

?

K (s′, s′; ν)


K (s, s′; ν) =( · · · ·· · · ·· · · ·· · · ·

)@@@R

��n

n@@@R

��

K (s, s′; ν) =( • · · ·· · · ·· · · ·· · · ·



Regulations

Corwin M.Zigler







K (s, s′; ν)


sPM

O3

PM

O3

s'PM

O3

PM

O3

K (s, s; ν)

?

K (s′, s′; ν)


K (s, s′; ν) =( · · · ·· · · ·· · · ·· · · ·

)@@@R

��

nn@

@@R

��

K (s, s′; ν) =( • · · ·· · · ·· · · ·· · · ·



Regulations

Corwin M.Zigler







K (s, s′; ν)


sPM

O3

PM

O3

s'PM

O3

PM

O3

K (s, s; ν)

?

K (s′, s′; ν)


K (s, s′; ν) =( · · · ·· · · ·· · · ·· · · ·

)@@@R

��

nn@

@@R

��

K (s, s′; ν) =( • · · ·· · · ·· · · ·· · · ·

)

Corr(PM(s),PM(s′)) = e−ν||s−s′|| (isotropic)


Regulations

Corwin M.Zigler







K (s, s′; ν)


sPM

O3

PM

O3

s'PM

O3

PM

O3

K (s, s; ν)

?

K (s′, s′; ν)


K (s, s′; ν) =( · · · ·· · · ·· · · ·· · · ·

)@@@R

��

nn@

@@R

��

K (s, s′; ν) =( • · · ·· · · ·· · · ·· · · ·

)

Corr(PM(s),PM(s′)) = e−ν||s−s′|| (isotropic)


Regulations

Corwin M.Zigler







Specifying Spatial Structure

1 Specify K (s, s; ν)• Covariance matrix for potential pollution concentrations

within a location.• Nonidentifiability⇒ sensitivity parameter.

2 Specify spatial decay for each individual pollutionconcentration.

• Separate isotropic exponential decay functions for eachpollutant.

3 Combine 1. and 2. ⇒ cross-covariance function forMVGP.

• Computational feasibility.• Isoloate nonidentifiable associations between potential

outcomes.


Regulations

Corwin M.Zigler







Why a Spatial Model?

Predicting potential outcomes:

• Predict missing potential outcomes at s usinginformation at surrounding locations.

• Use estimates of ν to assess interference assumption.


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s

iν

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ν &%'$

ν


Regulations

Corwin M.Zigler












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Regulations

Corwin M.Zigler












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iν ��

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ν


Regulations

Corwin M.Zigler







Assess Interference Assumption

ν̂ has implications of interference

• ν̂ ⇒ estimated correlation between measurements attwo locations.

• Examine correlations between observations assumednot to interfere.

• Substantial correlation⇒ violation of AGIA.


Regulations

Corwin M.Zigler







Assessment of AGIA for PM10

Figure: PM10 , ν̂ = 3.13

Correlation at distance ds

Freq

uenc

y

0.0 0.1 0.2 0.3 0.4 0.5 0.6

020

4060

8010

0

Correlation > 0.2530 locations


Regulations

Corwin M.Zigler







Assessment of AGIA for O3

Figure: O3 , ν̂ = 2.68

Correlation at distance ds

Freq

uenc

y

0.0 0.1 0.2 0.3 0.4 0.5 0.6

010

2030

4050

60

Correlation > 0.2554 locations


Regulations

Corwin M.Zigler







Associative and DissociativeEffects for PM10

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Dea

ths/

1000

EDE EAE

−8−6

−4−2

02

4

ω=0 ω=0.3 ω=0.6 ω=0.9 ω=0 ω=0.3 ω=0.6 ω=0.9

Causal effect on heath in areas where:regulation does not

affect PM10regulation causally

reduces PM10


Regulations

Corwin M.Zigler







Associative and DissociativeEffects for joint effect on both

PM10 and O3

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Dea

ths/

1000

EDE EAE−1

0−8

−6−4

−20

24

68

ω=0 ω=0.3 ω=0.6 ω=0.9 ω=0 ω=0.3 ω=0.6 ω=0.9

Causal effect on heath in areas where:regulation does not

affect PM10 or O3regulation causally

reduces PM10 and O3


Regulations

Corwin M.Zigler







Summary

Causal inference for accountability assessment

• Complex regulatory environment.• Causal inference with spatial data.• Principal stratification

• Multivariate intermediate variable.• Multipollutant approach.

• Assumptions about interference between observations.• What do we assume?• How do we assess?• What are the implications of violations?


Regulations

Corwin M.Zigler







Thank You

Acknowledgments

• Francesca Dominici• Yun Wang• Funding: Health Effects Institute.• Publication: Zigler CM, Dominici F, and Wang Y.

Estimating causal effects of air quality regulations usingprincipal stratification for spatially-correlatedmultivariate intermediate outcomes. Biostatistics 2012;13(2): 289–302.