Health effects modeling

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Health effects modeling
Lianne Sheppard University of Washington
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Outline

• Introduction
• Conceptual overview for health effect studies
• Disease and risk model
• Exposure and measurement models
• Health effects study designs and relationship to
  exposure assessment
• Measured exposure focused through the lens of
  study design
• Challenges in health modeling
• Example 1 Cohort study implications of
  predicted exposure
• Example 2 Time series study understanding the
  estimated health effect parameter
• Discussion

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Introduction

• Epidemiological study interpretation
• Estimates of association in the context of the
  particular study
• Study population
• Health outcome
• Exposure metric and data
• Confounders and other adjustment variables
• Study design
• Cant infer causality from observational studies
• Goal Understand properties of health effect
  estimates in epidemiological studies
• Context Health effects of ambient air pollution
• My interests
• Impact and implications of specific study designs
  in the context of the exposure data study
  design as a lens to focus the data
• Role of exposure assessment and data on health
  effect estimates

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Conceptual framework for health effect studies

• Disease model
• Relates the true environmental exposure to the
  disease outcome
• Includes the health effect parameter(s) of
  interest
• Exposure model
• Describes the distribution of exposure over
  space, time, and individuals
• Measurement model
• Relates measured exposures to the true unknown
  exposure
• Study design
• Sources of exposure variation should frame the
  design of any epidemiological study
• Limitations in exposure assessment that will lead
  to measurement error bias must also be considered

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Disease model

• Relates the exposure to the disease model, e.g.
• E(Yit) exp(XPitßZit?)
• for
• the outcome Yit on individual i at time t,
• personal exposures XPit and
• health effect parameter ß
• ß is the parameter of interest toxicity
• Also includes
• Confounders and other adjustment variables (Zit)
• A dependence model (as needed)

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Risk model

• The disease model includes the risk model a
  model to reflect risk over time
• Under an expanded risk model, the disease model
  is
• where
• ß(ts) denotes the influence of exposure at time
  s on risk at time t.

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Risk model examples

• Current risk Risk at time t is affected by
  exposure at time t
• Cumulative constant risk Risk is determined by
  cumulative exposure during the previous m days
• Lagged constant risk Risk is determined by
  cumulative exposure during the previous m days
  lagged n days
• Cumulative time-varying risk Risk varies over
  time and is determined by cumulative exposure
  during the previous m days

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Basic personal air pollution exposure model (e.g.
particulate matter PM)

• Total personal exposure

Person i Time t
Total personal exposure
Non-ambient source exposure
Fraction of ambient
Ambient source concentration



XPit XNit ait Cit

• Ambient source exposure XAit aitCit
• We can measure Cit and XPit,
• Assume ambient and non-ambient sources are
  independent

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Exposure model component a

• Fraction of ambient concentration experienced as
  exposure

ait oit (1-oit) Finf(it)

• oit is the fraction of time spent outdoors
• Finf(it) is the infiltration efficiency (building
  filter)
• Varies by season, person/building, region,
  species (or characteristic)
• Note

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Measurement model

• Needed because typically only measurements of Cit
  are available while XPit or XAit are of interest
• The measurement model defines sources of
  variation
• The data dont capture (Berkson)
• The data capture but arent of interest
  (classical)
• Measurement models
• Are needed to avoid bias
• Are assumed to not provide additional information
  about health effects

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Health effect study designs Ambient source air
pollution exposure

• Rely most on short-term temporal exposure
  variation
• Panel studies
• Time series studies
• Case-crossover studies
• Rely most on spatial exposure variation
• Cohort studies
• Migration studies
• Rely on either or both temporal and spatial
  variation
• Medium term longitudinal studies
• Cross-sectional studies

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Panel studies

• Enroll a panel of subjects and observe them
  repeatedly over time
• Strengths
• Possible to collect comprehensive personal, home
  indoor, and home outdoor exposure data on every
  subject
• Uniquely suited to study personal exposure
  effects
• Can directly measure health outcomes
• Challenges
• High effort for a limited number of subjects
• Power limited for affordable studies and rare
  outcomes
• Significant feasibility issues need to be
  overcome
• Can be very difficult to detect small effects
  because of the large heterogeneity in individual
  responses and uneven compliance to study protocol
  (medication use, data collection)
• Heterogeneity between subjects can swamp the
  small effects of air pollution ? Analysis
  approach can affect conclusions, particularly
  with typical small panel sizes

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Time series studies

• Estimate the association between time-varying
  ambient concentration and time-varying population
  event counts
• Rely on temporal exposure variation
• Strengths
• Simple and inexpensive (use administrative data)
• Powerful -- can target huge populations
• Appear uniquely suited to estimate acute health
  effects of ambient pollutants for rare events
• Bias due to spatial variation in PM is likely to
  be small
• Challenges
• Sources of bias not well understood (Is an
  ecological design gt possible ecological bias)
• However individuals are crossed with time so
  ecological biases much less likely to dominate
  than when individuals are nested
• Results can be sensitive to modeling choices (and
  software)
• Confounding removed through modeling
• Dont capture chronic effects, non-ambient
  exposures
• Dont estimate toxicity (rather estimate
  attenuated toxicity, attenuated for building
  characteristics and population behavior)

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Case-crossover studies

• Assess acute effects of air pollution by
  comparing exposures on the day with an event
  (index day) to days without the event (referent
  days)
• Essentially time series studies with a different
  approach to confounding control
• Confounding controlled by matching (and modeling)
  rather than modeling alone
• Some approaches to referent selection lead to
  biased health effects (overlap bias)
• Time-stratified referent selection recommended
• Commonly used symmetric bidirectional referents
  are subject to overlap bias
• Similar scientific considerations as time series
  studies

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Cohort studies

• Follow subjects over time to relate some measure
  of usual exposure to health events
• Rely on variation in exposure over space (shared
  exposure) and individual (total exposure,
  including unshared components)
• Incomplete exposure ascertainment implies
• Need to rely on an exposure prediction model
• Because of limited exposure assessment, these are
  semi-individual studies
• Cant rule out ecological biases
• Individuals are nested within areas
• Unclear how to best accumulate exposure over
  time. What are the implications? e.g.,
• Average exposure
• Time-varying risk model

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Challenges in analysis and interpretation of
epidemiological studies Bias

• Air pollution health effects are small and thus
  can be easily swamped by even small biases
• Confounding is
• A major source of bias
• Orders of magnitude larger than the air pollution
  effect of interest
• Other less well understood issues
• Exposure vs. concentration and attenuation of
  ambient exposure (recall ambient exposureambient
  concentrationa)
• Loss of information
• Bias
• Policy implications
• Specification, cross-level, and overlap biases
• Model selection

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Small Effects and Large Confounders Air
pollution signal is an order of magnitude smaller
than confounder effects (time series study
example)
Courtesy of Francesca Dominici and NMMAPS
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Challenges in analysis and interpretation of
epidemiological studies Uncertainty

• Uncertainty of the model key features
• Linearity of the exposure-response model
• Which single or distributed lags in the risk
  model?
• Multiple pollutants
• Confounder control
• Exposure data, metrics, and measurement error
• How does measured exposure relate to true
  exposure?
• Additional model selection issues
• Model selection process often not disclosed
• Model averaging as an alternative

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Exposure data considerations for health effects
analyses

• Considerations in study planning
• Source of variation needed for study design
• Measurements available or feasible to collect
• Predicted exposure required?
• Interpretation of estimated health effects
  depends on exposure data used in the analysis
• Example 1 Effect of prediction on cohort study
  health effect estimates
• Example 2 Time series study health effects
  estimates Interpretation and relevant features
  of personal exposure when concentration is used
  in the analysis

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Cohort study and predicted exposure example
Simulation set-up
Purpose To investigate how prediction of
pollutants over space affects estimated relative
risk in a cohort study

• Realistic setting
• Monitored PM2.5 data
• Outcome model based on cardiovascular events
  using published estimates (Womens Health
  Initiative, Miller et al 2007)
• Los Angeles geography
• Compare exposure prediction models Nearest
  monitor vs. universal kriging
• Simulation structure
• Simulate spatially dependent exposure for subject
  residences and monitoring sites
• Explore a variety of exposure models
• Use true exposure to generate the health outcome
  data
• Predict exposure from monitoring site data only
• Estimate health effects conditioned on modeled
  (and true) exposure

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Cohort study and predicted exposure example
Simulation study area
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Underlying PM2.5 AQS monitoring data

• PM2.5 Air Quality Standard (AQS) monitors
• 22 monitors in five counties in greater Los
  Angeles
• PM2.5 concentration
• in year 2000
• (black lt red lt
• green lt blue)
• Spatial analysis to estimate parameters
• Mean (using geographic covariates)
• Variance
• Range
• Partial sill
• Nugget

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Exposure (concentration) models

• Multivariate normal distribution with spatial
  autocorrelation using assumed mean and covariance
  model parameters
• Realizations of PM2.5 at 2,000 residences and 22
  monitoring sites
• Five underlying exposure models using different
  spatial structures

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Examples of spatial surfaces
Medium range
Geographic characteristics

• Spatial surface of five exposure models
  (lighter higher concentration)

Measurement error only
Short range
One realization of each surface
Long range
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True and predicted PM2.5
True vs. Kriged
Nearest v.s Kriged
True vs. Nearest

• Relationship between true and predicted PM2.5 at
  2,000 individual sites in one simulation
• Observations
• Better association between predictions and true
  values when there is more spatial structure
• Spatial structure can be
• In the mean model (TEM 1)
• In the variance model (TEM 5)
• Models 1 and 2 were based on different estimated
  fits to the same data, with model 1 allowing a
  spatially varying mean and model 2 assuming a
  constant mean. Model 1 appears to capture
  spatial structure better.

Geog Char
Med Range
Meas Error Only
Short Range
Long Range
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Health effect estimates Geographical
characteristics exposure

• Comparison of ß estimates for true and modeled
  PM2.5

True exposure vs. nearest neighbor
True exposure vs. kriged
Nearest neighbor vs. kriged
N e a r e s t
K r i g e d
K r i g e d
Nearest neighbor
True exposure
True exposure
xy line best fit line
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Health effect estimates Exposures with little
spatial structure
Measurement error only
Short Range Low spatial correlation
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Health effect estimates Spatially dependent
exposures only in the variance model
Medium range medium spatial correlation
Long range High spatial correlation
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Health effect estimates Summary
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Conclusions Impact of predicted exposure on
cohort study health effect estimates

• Exposure prediction
• Kriging prediction gave better estimates of PM2.5
  than nearest monitor prediction
• Less biased
• Generally smaller prediction error
• Kriging predictions were less variable than
  nearest monitor predictions
• Health effect estimates
• Kriged PM2.5 as compared to nearest monitor PM2.5
  had
• Better coverage (in most cases)
• Less biased health effect estimates
• More variable health effect estimates (and thus
  worse MSE)
• Underlying exposure models with higher spatial
  dependence had better coverage
• Results more consistent with prior expectations
  for a Berkson measurement error model
• Less that 95 coverage with predicted exposure
• Not incorporating uncertainty of prediction in
  this analysis

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Discussion Impact of predicted exposure on
cohort study health effect estimates

• Other lessons learned
• More dense monitoring doesnt change these
  results
• Only 22 monitor measurements
• Same results for up to 42 monitors
• Not all the kriging results were believable
• Spatial statistics is iterative, uses judgment
  and thus is not well suited to our nonjudgmental
  approach to the simulations
• Some realizations of kriging parameter estimates
  were unacceptably large
• Universal kriging performed better on average
  than ordinary kriging
• Fewer poor estimates of kriging parameters, even
  when the true exposure had a constant mean
• Better coverage for health effects
• Spatial pollution structure best suited to
  modeling and good health effect estimates
• High spatial variability
• Spatial variability characterized in the mean
  model
• Spatial variability in the variance model should
  have long range and a smaller partial sill so
  there is relatively small prediction error
  variance.

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Acute Air Pollution Health EffectsSources of
Bias in Time Series Studies

• Use of concentration when exposure is of interest
• Not estimating toxicity
• Not accounting for time-varying ambient
  attenuation
• Substitution of measured for true concentration
  
• Classical measurement error
• Dropping the within-day component of exposure
  variation by using central site concentration
  measurements
• Specification bias (small because the effects are
  small)
• Cross-level bias (inference on effects in
  individuals when the data only come from groups)
• Inadequate adjustment for covariates
• Uncontrolled confounding
• Multipollutant exposures

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Time series study example Impact of aspects of
personal exposure Set-up

• We conducted simulation studies to assess the
  behavior of time series study estimates under
  differing exposure and measurement models
• Assume
• Acute risk model (same day exposure only)
• Total personal exposure affects true disease risk
• Only ambient concentration is measured and used
  in the time series study analysis
• Simulate individual data analyze using a time
  series study design

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Time series study example Impact of aspects of
personal exposure Set-up

• Assume a true individual-level disease model with
  personal exposure
• Personal exposure model
• Generate NT personal exposures and binary events
  for N100,000 individuals on T1,000 days
• Use a time series study analysis with ambient
  concentration measurements, i.e. fit
• Assess the impact of
• Major independent non-ambient exposure
  contributions
• Seasonally varying ambient attenuation a
• Varying characterizations of daily exposure or
  concentration measurements

XPit nonambient source it aitCit
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Time series study example Impact of aspects of
personal exposure Results

• Time series studies estimate aß toxicity times
  ambient attenuation
• Non-ambient source exposure doesnt affect
  estimates when it is independent of ambient
  concentration
• Variation in a affects time series study results
  when it is seasonal and correlated with ambient
  concentration (supported by data see next
  slide)
• Larger estimates if a is high when concentration
  is high
• Smaller estimates if a is low when concentration
  is high
• Average concentration from multiple monitors
  improves estimates slightly (reduction in
  classical measurement error)

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Regression Coefficients for CVD-Related Hospital
Admissions vs. Ambient PM10
0.0025
0.0020
0.0015
CVD Coefficient
0.0010
0.0005
0.0000
0
10
20
30
40
50
60
70
80
? gt smaller summer a
Central Air Conditioning ()
Slide courtesy of Doug Dockery
Janssen N, Schwartz J, Zanobetti A, Suh H (2002).
Environ. Health Perspect.
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Time series study example Impact of aspects of
personal exposure Summary

• Measurements effect on health effect parameter
  interpretation
• Models with concentration as the predictor dont
  estimate toxicity alone
• When the disease model has a simple form, e.g.
• E(Y)exp(XAß) exp(Caß)
• ß is toxicity
• Assuming XACa, the disease model with ambient
  concentration has parameter aß.
• Differences between estimates of aß can be due to
  variations in a (e.g. due to season, region or
  individual)
• Huge policy implications that variation in time
  series study health effect estimates is not
  (only) toxicity

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Time series study example Impact of aspects of
personal exposure Discussion

• Ambient attenuation (a) is not just measurement
  error
• In models with concentration as the predictor, it
  changes the interpretation of the estimated
  health effect parameter (not just toxicity)
• a has structure that varies by season, region,
  person, species (due to e.g. size, reactivity)
• Averaging exposure over time or area averages
  over a
• a is not measured and properties (e.g.
  seasonality, population patterns) not well
  understood Important area for exposure
  assessment research

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Discussion Health modeling in the context of
exposure data

• These two examples illustrate ways study design
  and exposure data influence
• The health effect parameters estimated
• The characteristics of the health effect
  estimates
• Design of choice depends on
• Health outcome of interest
• Exposure characteristics of interest (e.g. is
  exposure usual or unusual?)
• What sources of variation in exposure do
  available exposure data capture?
• If an exposure prediction model is needed, are
  there sufficient data to produce a good model
  that captures the key sources of variation?
• Feasibility

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Discussion Other research directions

• Link health effect parameters from acute and
  chronic exposures
• Ascertain time-varying risk in cohort studies
• Incorporation of complex risk models into policy
  estimates
• Effect of exposure structure on estimates in
  single vs. distributed lag models
• Multipollutant exposures
• More complete estimates of uncertainty.
  Uncertainty due to
• Model selection
• Exposure assessment and predicted exposure
• Form of the distributed risk model
• Confounder selection
• Subgroup selection

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