A typical problem in environmental epidemiological studies concerns environmental exposure assessment. In this talk, we will discuss challenges to environmental exposure assessment and we will showcase and discuss statistical methods that have been developed to obtain estimates of environmental exposure (e.g. air pollution, temperature). Further we will discuss whether and how uncertainty in the environmental exposure has been and can be incorporated in health analyses.

1. Environmental exposure in environmental
epidemiological studies:
modeling approaches and challenges
Veronica J. Berrocal
Department of Biostatistics
University of Michigan
SAMSI Workshop on Remote Sensing, Uncertainty Quantification, and
Theory of Data Systems
Veronica J. Berrocal Air pollution exposure

2. Environmental epidemiological studies
• Environmental epidemiological studies aim to establish an
association (potentially, a causal one) between an health outcome
and an environmental exposure.
• Typically, health outcome refers to:
• mortality (all-cause non accidental deaths, or due to
cardiovascular diseases, respiratory diseases, etc.)
• hospitalizations/emergency visits
• pregnancy outcomes and birth defects
• ...
• Environmental exposure refers to:
• exposure to temperature, heat/heatwave, cold/cold waves
• air pollution/wildfires
• pesticides
• precipitation
• pollen
• ...
Veronica J. Berrocal Air pollution exposure

3. Environmental epidemiological studies:
this talk
• Focus only on air pollution and temperature as environmental
exposures.
• The statistical methods used are very similar:
• same type of health models are used to link health and
environmental exposure
• methods for air pollution exposure assessment are slighly
ahead of those for temperature, but the gap is closing
Veronica J. Berrocal Air pollution exposure

4. Health data
• Typically health data is obtained from:
• administrative database: mortality from the National Center
for Health Statistics; death and birth records from local and
State Departments of Health
−→ easier to obtain but aggregated over some areal unit
• hospital and emergency visit records: individual level data
−→ hard to obtain
• Department of Human Health and Services: Medicare and
Medicaid databases
−→ expensive to obtain; require a lot of data cleaning and
formatting
• cohort studies: individual level data, smaller sample size
−→ need a collaborator to obtain
• Earlier studies used mostly administrative databases aggregated over
counties or larger metropolitan areas.
• Now, common to use geocoded health data, e.g. individuals are
assigned specific geographical coordinates
Veronica J. Berrocal Air pollution exposure

5. Health data
• Typically health data is obtained from:
• administrative database: mortality from the National Center
for Health Statistics; death and birth records from local and
State Departments of Health
−→ easier to obtain but aggregated over some areal unit
• hospital and emergency visit records: individual level data
−→ hard to obtain
• Department of Human Health and Services: Medicare and
Medicaid databases
−→ expensive to obtain; require a lot of data cleaning and
formatting
• cohort studies: individual level data, smaller sample size
−→ need a collaborator to obtain
• Earlier studies used mostly administrative databases aggregated over
counties or larger metropolitan areas.
• Now, common to use geocoded health data, e.g. individuals are
assigned specific geographical coordinates =⇒ potential for
geocoding error
Veronica J. Berrocal Air pollution exposure

6. Environmental exposure data
• Typically environmental exposure data is obtained from:
• outdoor monitors (air pollution, temperature, humidity) -
sources: NOAA/NCEI, EPA
• dispersion model outputs (mostly for traffic related pollutants)
- sources: EPA, collaborators
• air quality model outputs - sources: EPA, collaborators
• satellite data (MODIS AOD, Aura OMI, etc.) - sources NASA
• personal monitors
• private monitors (e.g. Harvard Six City study, etc.) - sources:
NASA
• Temporal and spatial resolution varies across data sources.
• Informative sampling.
• Availability and access vary across data sources.
• Uncertainties and measurement errors vary across data sources.
Veronica J. Berrocal Air pollution exposure

7. Health analysis
• The statistical model used in the health model depends on the
spatial resolution of the health data.
• Most commonly used study design is a time series design
• Health outcome: number
of deaths on day t
aggregated over a unit
• Poisson regression
(GAM, overdispersion)
• logExpected mortalityt =
S(t;λ1)+
S(env expt;λ2)+
S(lagged env exp.;λ3)+
g(confound.)
• S(·;λ): smooth function
with λ d.f. Figure: From Bhaskaran et al. (2003)
Veronica J. Berrocal Air pollution exposure

8. Health analysis
• In time series study, the environmental exposure is
representative of the entire areal unit
−→ usually, area-wide average from outdoor monitors
Veronica J. Berrocal Air pollution exposure

9. Health analysis
• In time series study, the environmental exposure is
representative of the entire areal unit
−→ usually, area-wide average from outdoor monitors
• No accounting for intra-urban variation in exposure
• Usually fit at individual locations separately and then
combined together through a hierarchical approach
• Effect of environmental exposure at each areal unit linked to
areal unit characteristics
−→ use multiple data sources (Census, National Land Cover
Dataset, etc.)
Veronica J. Berrocal Air pollution exposure

10. Health analysis
• In time series study, the environmental exposure is
representative of the entire areal unit
−→ usually, area-wide average from outdoor monitors
• No accounting for intra-urban variation in exposure
• Usually fit at individual locations separately and then
combined together through a hierarchical approach
• Effect of environmental exposure at each areal unit linked to
areal unit characteristics
−→ use multiple data sources (Census, National Land Cover
Dataset, etc.)
• If individual lavel health data is available, other study design
are possible
• case-crossover design
• Cox proportional hazard models
• linear regression models
Veronica J. Berrocal Air pollution exposure

11. Environmental exposure
• Earlier studies on the health effect of air pollution or
temperature used area-wide averages from monitors as
exposure
=⇒ this approach ignores intra-urban variation in exposure.
• Exploiting intra-urban contrasts has several advantages:
• increased power
• rule out unmeasured confounders
• differentiate between different environmental exposures (e.g.
pollutant, temperature vs dew point, etc.)
• Environmental exposure assessment methods are used more
frequely for air pollution exposure, but are starting to be more
routinely used also for temperature
Veronica J. Berrocal Air pollution exposure

12. Environmental exposures: modeling
approaches
• Several different strategies are used to assign environmental
exposure to locations/individual subjects:
1 Nearest monitor(s)/Average over a buffer: derive exposure
using measurement from the nearest monitor or the monitors
within a buffer.
• Pro: simple
• Cons: too simplistic; does not capture small-scale spatial
variation
Veronica J. Berrocal Air pollution exposure

13. Environmental exposures: modeling
approaches
• Several different strategies are used to assign environmental
exposure to locations/individual subjects:
3 Land use regression (LUR): predict environmental exposure
using a linear regression model with predictors GIS covariates,
e.g. type of roads within a buffer, air conditioning (Briggs et al.
1997, 2000; Brauer et al. 2003; Ross et al. 2006).
• Pro: simple
• Cons: large number of GIS covariates (variable selection
technique needed: backward/forward selection; LASSO; PLS),
limited transferability to different locations, residual
independence between sites.
Veronica J. Berrocal Air pollution exposure

14. Environmental exposures: modeling
approaches
• Several different strategies are used to assign environmental
exposure to locations/individual subjects:
3 Land use regression (LUR): predict environmental exposure
using a linear regression model with predictors GIS covariates,
e.g. type of roads within a buffer, air conditioning (Briggs et al.
1997, 2000; Brauer et al. 2003; Ross et al. 2006).
• Pro: simple
• Cons: large number of GIS covariates (variable selection
technique needed: backward/forward selection; LASSO; PLS),
limited transferability to different locations, residual
independence between sites.
• In recent studies, satellite data has also been used (Kloog et
al. 2011).
• Multiple-stage models needed to account for extensive missing
satellite data.
• Uncertainty in each model stage is not properly accounted for.
Veronica J. Berrocal Air pollution exposure

15. Using satellite data (Kloog et al. 2017)
• (1) Daily average temperature from monitoring stations from M´et´o
France, (2) daily temperature data from MODIS, Terra instrument,
at 1km resolution
• Two step-model:
1 Calibration of satellite data
2 Prediction
Veronica J. Berrocal Air pollution exposure

16. Environmental exposures: modeling
approaches
• Several different strategies are used to assign environmental
exposure to locations/individual subjects:
4 Universal kriging (UK) models/Hybrid models: predict
exposure using a spatial statistical model with predictors GIS
covariates (Mercer et al. 2011; Bergen et al., 2013; Kloog et
al. 2012 - includes satellite data).
• Pro: accounts for spatial dependence between sites
• Cons: requires knowledge of spatial statistics; cannot be
implemented directly in ArcGIS, although possible through a
two-stage approach.
Still requires use of variable selection techniques to reduce
number of GIS covariates.
• UK has been shown to yield better predictions than LUR
(Beelen et al. 2009; Mercer et al. 2011)
Veronica J. Berrocal Air pollution exposure

17. Environmental exposures: modeling
approaches
• Several different strategies are used to assign environmental
exposure to location/individual subjects:
5 Dispersion modeling/Regional climate model: use as exposure
the output of a dispersion model/regional climate model
(Nafstad et al. 2004; Penard-Morand et al. 2006).
• Pro: Based on physical principles; non-linearity; better than
LUR for specific-source related component.
• Cons: output often uncalibrated; smooth exposure surfaces;
different spatial resolution.
Veronica J. Berrocal Air pollution exposure

18. Environmental exposures: modeling
approaches
• Several different strategies are used to assign environmental
exposure to locations/individual subjects:
6 Statistical downscaling/data fusion models: predict exposure
combining the output of air quality/dispersion/regional climate
models with monitoring data (Fuentes and Raftery 2005;
McMillan et al.2010; Berrocal et al. 2010a,b, 2012, 2014;
Reich et al. 2014; Rushworth et al. 2014; Lee et al. 2016).
• Pro: accounts for physical and chemical processes; no need to
include GIS covariates (Lindstrom et al. 2014); can account
for complicated spatio-temporal dependence structure.
• Cons: numerical model output not easily/publically available;
requires knowledge of spatial, spatio-temporal and Bayesian
statistics; software not always available.
Veronica J. Berrocal Air pollution exposure

19. Downscaler/data fusion models (Berrocal et al., 2010,
2011, 2012, 2014):
100 95 90 85 80 75 70
30354045
Longitude
Latitude
20
40
60
80
100
120
140
Observed ozone concentration
August 1, 2001
100 95 90 85 80 75 70
30354045
Longitude
Latitude
20
40
60
80
100
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CMAQ estimate of ozone concentration
August 1, 2001
• Main idea: leverage two sources of information:
• the true sparse, point-referenced monitors measurements:
Y (s), s ∈ S
• the spatially dense, grid-based, potentially uncalibrated, model
output X(B) with B 12-km grid cell
Veronica J. Berrocal Air pollution exposure

20. Data fusion model (Berrocal et al. 2012)
• Our most recent data fusion model is:
Observed concentration at s = β0(s)+β1 · ˜X(s)+ε(s)
Y (s)
with
• β0(s) modeled as a spatial process (e.g. Gaussian process with
a given covariance function).
• ˜X(s) smoothed version of model output at each point s,
obtained using random, directional, spatially-varying and
spatially correlated weights.
• ε(s) ∼ N(0,τ2
).
Veronica J. Berrocal Air pollution exposure

21. Data fusion model (Berrocal et al. 2012)
• Our most recent data fusion model is:
Observed concentration at s = β0(s)+β1 · ˜X(s)+ε(s)
Y (s)
with
• β0(s) modeled as a spatial process (e.g. Gaussian process with
a given covariance function).
• ˜X(s) smoothed version of model output at each point s,
obtained using random, directional, spatially-varying and
spatially correlated weights.
• ε(s) ∼ N(0,τ2
).
• Other extensions of this data fusion model have been proposed.
• Used by EPA to derive fused surfaces of daily average PM2.5 and
daily 8-hour maximum ozone concentration at census tract
centroids for US
• Website https://www.epa.gov/air-research/
downscaler-model-predicting-daily-air-pollution)
provides predictions and their standard deviations
Veronica J. Berrocal Air pollution exposure

22. More monitoring data? Caution!
(Berrocal and Holland, 20XX)
• The downscaler model uses monitoring data to calibrate the
air quality model output.
• We used data from the Federally Regulated Monitors for
PM2.5: the FRM monitors.
• Measurements of PM2.5 are nowadays available also from
other monitors. Are they useful?
• Here we consider “new”, automated monitors that measure
PM2.5 semi-continuously, the SC-FEM monitors, and we
evaluate whether adding these set of monitors in a downscaler
model leads to better predictions.
Veronica J. Berrocal Air pollution exposure

23. Is more monitoring data helpful?
−120 −110 −100 −90 −80 −70
253035404550
Longitude
Latitude
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FRM
SC/FEM
• We apply a downscaler model to daily
average PM2.5 concentration in the US
for year 2011.
• Each day we fit the model to the data,
using 80% of the observations
and holding 20% for validation of the
predictions.
• We compare a model that uses both
FRM and SC/FEM monitoring data
vs one that uses only FRM data.
Veronica J. Berrocal Air pollution exposure

24. Results
• MSE= Average of (observed−predicted)2
.
• MAE= Average of |observed−predicted|.
MSE MAE Width 95% CI Coverage 95% CI
Monitors (µg/m3
) (µg/m3
) (µg/m3
) (%)
Only
FRM 4.09 2.28 16.82 95.59
FRM and
SC/FEM 4.03 2.09 17.45 96.29
• Moderate improvement overall.
• Larger improvements when stratified by season, with large gains in
Summer and Fall.
Veronica J. Berrocal Air pollution exposure

25. Caution with monitoring data!
• Reduction in Mean Absolute Error by state when we compare the
model that uses FRM + SC/FEM data vs a model that uses only
FRM data.
• Positive means better predictions using FRM + SC/FEM data.
Percent reduction in MAE:
SC/FEM + FRM data vs FRM only
Fall
PercentreductioninMeanAbsoluteError(%)
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
DistrictOfColumbia
Florida
Georgia
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
NewHampshire
NewJersey
NewMexico
NewYork
NorthCarolina
NorthDakota
Ohio
Oklahoma
Oregon
Pennsylvania
RhodeIsland
SouthCarolina
SouthDakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
WestVirginia
Wisconsin
Wyoming
−40−20020
Veronica J. Berrocal Air pollution exposure

26. Challenges: measurement error
• Predicted exposure is not the true exposure.
• Using predicted exposure in a health model introduces two
sources of measurement errors:
• Berkson error: from smoothing the exposure surface =⇒
inflated SE of health effect estimates.
• Classical measurement error: from estimation of the
parameters in the exposure model =⇒ bias and SE inflation.
• Not easy to separate the two.
Veronica J. Berrocal Air pollution exposure

27. How to correct for measurement error
• Various papers have addressed this issue (Gryparis et al. 2009;
Szpiro et al. 2011; Szpiro and Paciorek, 2013; Alexeef et al.
2015; etc).
• Proposed approaches include:
1 Bayesian joint model of exposure and disease: this uses the
correct imputation scheme (see missing data literature - Rubin
1987, Little 1992).
2 Two-stage Bayesian approach: exposure model first, then
health model.
Posterior distribution for exposure is the prior in the health
model.
=⇒ Does not cut the feedback between exposure and health
outcome.
3 Bootstrap approximation: resample health and exposure datat.
• Option 1 is the ideal, but most computationally intensive.
Veronica J. Berrocal Air pollution exposure

28. Accounting for uncertainty in personal
exposure
• Personal exposure is not the same as ambient exposure
• Using ambient exposure as a proxy for personal exposure
1 Biased estimates of the effect of air pollution (Zeger et al.
2000)
2 Wrong assessment of its uncertainty (Zeger et al. 2000;
Gryparis et al. 2009)
• Prototype analysis that shows how to account for exposure
uncertainty in a study on the effect of personal or ambient
maternal exposure to PM2.5 on birthweight.
Veronica J. Berrocal Air pollution exposure

29. Personal exposure
Veronica J. Berrocal Air pollution exposure

30. Ambient vs personal exposure
• Given a day d, let Cj (d) be outdoor concentration of PM2.5 at
the location where subject j lives .
• Ambient exposure for individual j on day d is the outdoor
concentration Cj (d).
Veronica J. Berrocal Air pollution exposure

31. Ambient vs personal exposure
• Given a day d, let Cj (d) be outdoor concentration of PM2.5 at
the location where subject j lives .
• Ambient exposure for individual j on day d is the outdoor
concentration Cj (d).
• Personal exposure for individual j on day d is the sum of
contributions from the various “microenvironments” the
individual visits during the day:
Personal exposure =
m
∑
k=1
wjk (d)·Cik,amb.(d)+wjk (d)·Cjk,non-amb.(d)
• wjk(d): time individual i spent in microenvironment k on day d
• Cjk,amb.(d): PM2.5 concentration in microenvironment k on
day d due to outdoor sources
• Cjk,non-amb.(d): PM2.5 concentration in microenvironment k
on day d due to indoor sources
Veronica J. Berrocal Air pollution exposure

32. Exposure simulators
• How to derive estimates of personal exposure if we don’t have
data on individuals’ movement?
• Exposure simulators are stochastic models that estimate the
distribution of average personal exposure to a contaminant
• Initially developed for regulatory purposes: pNEM (Law et al.
1997), SHEDS-PM (Burke et al. 2001), APEX, pCNEM
(Zidek et al. 2003, 2007)
Veronica J. Berrocal Air pollution exposure

33. SHEDS-PM
• Given a day d
• SHEDS-PM simulates individuals with certain demographic
characteristics (i.e. age, sex, smoking status, etc.) living in a
spatial unit (usually, census tracts) according to proportions
obtained from the Census.
Veronica J. Berrocal Air pollution exposure

34. SHEDS-PM
• Given a day d
• SHEDS-PM simulates individuals with certain demographic
characteristics (i.e. age, sex, smoking status, etc.) living in a
spatial unit (usually, census tracts) according to proportions
obtained from the Census.
• To each simulated individual, SHEDS-PM assigns an activity
diary. The activity diaries come from the CHAD database.
Veronica J. Berrocal Air pollution exposure

35. SHEDS-PM
• Given a day d
• SHEDS-PM simulates individuals with certain demographic
characteristics (i.e. age, sex, smoking status, etc.) living in a
spatial unit (usually, census tracts) according to proportions
obtained from the Census.
• To each simulated individual, SHEDS-PM assigns an activity
diary. The activity diaries come from the CHAD database.
• SHEDS-PM simulates values for the input parameters, uses
PM2.5 concentration for the given day and derives PM2.5
concentration within each “microenvironment”.
Veronica J. Berrocal Air pollution exposure

36. SHEDS-PM
• Given a day d
• SHEDS-PM simulates individuals with certain demographic
characteristics (i.e. age, sex, smoking status, etc.) living in a
spatial unit (usually, census tracts) according to proportions
obtained from the Census.
• To each simulated individual, SHEDS-PM assigns an activity
diary. The activity diaries come from the CHAD database.
• SHEDS-PM simulates values for the input parameters, uses
PM2.5 concentration for the given day and derives PM2.5
concentration within each “microenvironment”.
• Finally, SHEDS-PM derives a personal exposure for the
simulated individual on the given day d.
Veronica J. Berrocal Air pollution exposure

37. Example: metrics of ambient exposure
without uncertainty
Day
DailyambientexposuretoPM2.5
0102030
2001−01−20 2001−04−21 2001−07−21 2001−10−27
• Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
Veronica J. Berrocal Air pollution exposure

38. Example: metrics of ambient exposure
without uncertainty
Day
DailyambientexposuretoPM2.5
0102030
2001−01−20 2001−04−21 2001−07−21 2001−10−27
• Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
1 Average exposure:
13.36µg/m3
Veronica J. Berrocal Air pollution exposure

39. Example: metrics of ambient exposure
without uncertainty
Day
DailyambientexposuretoPM2.5
0102030
2001−01−20 2001−04−21 2001−07−21 2001−10−27
Threshold: 15µg/m3
• Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
1 Average exposure:
13.36µg/m3
2 Percentage of days over
threshold: 35.92%
Veronica J. Berrocal Air pollution exposure

40. Example: metrics of ambient exposure
without uncertainty
Day
DailyambientexposuretoPM2.5
0102030
2001−01−20 2001−04−21 2001−07−21 2001−10−27
Threshold: 15µg/m3
• Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
1 Average exposure:
13.36µg/m3
2 Percentage of days over
threshold: 35.92%
3 Area above a threshold:
1.98(µg/m3)2
Veronica J. Berrocal Air pollution exposure

41. Example: metrics for personal exposure
Day
PersonalexposuretoPM2.5
05101520253035
2001−01−20 2001−04−21 2001−07−21 2001−10−27
• Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
• Set of 30 simulated individuals
Veronica J. Berrocal Air pollution exposure

42. Example: metrics for personal exposure
Day
PersonalexposuretoPM2.5
05101520253035
2001−01−20 2001−04−21 2001−07−21 2001−10−27
• Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
• Set of 30 simulated individuals
• For each simulated individual, we
compute the 3 metrics of exposure.
• The 30 values are considered
equally likely and represent
the distribution of metrics of
personal exposure for this particular
subject.
Veronica J. Berrocal Air pollution exposure

43. Example: metrics for personal exposure
0 10 20 30 40 50 60
0.000.050.100.15
Average personal exposure to PM 2.5
Density
Average personal exposure • Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
• Set of 30 simulated individuals
• For each simulated individual, we
compute the 3 metrics of exposure.
• The 30 values are considered
equally likely and represent
the distribution of metrics of
personal exposure for this particular
subject.
Veronica J. Berrocal Air pollution exposure

44. Example: metrics for personal exposure
0 20 40 60 80 100
0.000.010.020.03
Percentage days personal exposure over 15µg/m3
Density
Percentage of days over threshold • Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
• Set of 30 simulated individuals
• For each simulated individual, we
compute the 3 metrics of exposure.
• The 30 values are considered
equally likely and represent
the distribution of metrics of
personal exposure for this particular
subject.
Veronica J. Berrocal Air pollution exposure

45. Example: metrics for personal exposure
0 5 10 15
0.000.050.100.150.200.250.30
Normalized area personal exposure over 15µg/m3
Density
Area above threshold • Spatial unit: census tract in
North Carolina
• Period of exposure (Tij ):
January 20 to October 27, 2001
• Set of 30 simulated individuals
• For each simulated individual, we
compute the 3 metrics of exposure.
• The 30 values are considered
equally likely and represent
the distribution of metrics of
personal exposure for this particular
subject.
Veronica J. Berrocal Air pollution exposure

46. Birthweight and air pollution
• Health outcome: birthweight (gr) of children born between 2001
and 2002 in 14 counties in North Carolina (N=49,689).
• Exposure: predicted ambient maternal exposure to PM2.5 using a
data fusion model, and personal exposure using SHEDS-PM.
• Considered different exposure metric and time window of exposure.
• Window of exposure: entire pregnancy.
• Estimates of coefficients with 95% credible intervals.
Exposure metric Personal exposure Ambient exposure
Average exposure 11.04g (-193.74g; 160.65g) 20.27g (-179.23g; 209.42g)
Percentage days
above threshold 0.27g (-0.28g; 0.82g) 0.28g (-0.25g; 0.84g)
Area
above threshold 19.57g (-89.17g; 135.18g) 32.05g (-28.04g; 96.18g)
Veronica J. Berrocal Air pollution exposure

47. Discussion
• Environmental epidemiologists use multiple data sources
• Varying spatial and temporal resolution
• Varying level of precision and quality (what data to use? and
where?)
• Some are provided with measures of uncertainty (e.g. Census
estimates), most are not
• Some data formats are not easy to use
• Many unresolved issues (and new potential data sources)
• What metric of exposure? Avg vs apparent temperature? Etc.
• Spatially resolved estimates of exposure, but how to account
for uncertainty?
• Data on individuals’ movement to derive personal exposure
• How to handle multiple environmental exposures?
• Larger spatial datasets, long time series: computational burden.
• Privacy issues with health data.
• Typical to do sensitivity analyses, changing definitions of exposure
metrics.
Veronica J. Berrocal Air pollution exposure