Health effects modeling

Lianne Sheppard University of Washington

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

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

Can’t 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

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

Disease model

Relates the exposure to the disease model, e.g.

E(Yit) = exp(XPitβ+Zitγ)

for the outcome Yit on individual i at time t,

personal exposures XPit and

health effect parameter β β is the parameter of interest – “toxicity” Also includes

Confounders and other adjustment variables (Zit) A dependence model (as needed)

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 β(t;s) denotes the influence of exposure at time s on

risk at time t.

E( ) = exp ( ; )Pit is it

s t

Y X t s Z

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

1E( ) = exp Pit it itY X Z

2( 1)

E( ) = expt

Pit is it

s t m

Y X Z

3( 1)

E( ) = expt n

Pit is it

s t n m

Y X Z

( 1)

E( ) = expt

Pit is s it

s t m

Y X Z

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

Total personal exposure :

Total personal exposure

=Non-ambient source exposure

+ Fraction of ambient * Ambient source

concentration

XPit = XN

it + αit * Cit

• Ambient source exposure: Ambient source exposure: XXAAitit= = αitCit

• We can measure We can measure Cit and and XPit,,

• Assume ambient and non-ambient sources are Assume ambient and non-ambient sources are independentindependent

Person i

Time t

Exposure model component: α

Fraction of ambient concentration experienced as exposure:

αit = oit + (1-oit) Finf(it)

• oit is the fraction of time spent outdoorsis the fraction of time spent outdoors

• Finf(it) is the infiltration efficiency is the infiltration efficiency (building filter)(building filter)

• Varies by season, person/building, region, Varies by season, person/building, region, species (or characteristic)species (or characteristic)

• Note Note 0 1it

Measurement model

Needed because typically only measurements of Cit are available while XP

it or XAit are of interest

The measurement model defines sources of variation: The data don’t capture (“Berkson”) The data capture but aren’t of interest (“classical”)

Measurement models Are needed to avoid bias Are assumed to not provide additional information

about health effects

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

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

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 => 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 Don’t capture chronic effects, non-ambient exposures

Don’t estimate toxicity (rather estimate attenuated toxicity, attenuated for building characteristics and population behavior)

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

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 Can’t 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

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 exposure=ambient concentration*α)

Loss of information Bias Policy implications

Specification, cross-level, and overlap biases Model selection

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

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

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

Cohort study and predicted exposure example: Simulation set-up

Realistic setting: Monitored PM2.5 data Outcome model based on cardiovascular events using published

estimates (Women’s 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

Purpose: To investigate how prediction of pollutants over space affects estimated relative risk in a cohort study

Cohort study and predicted exposure example: Simulation study area

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 < red < green < blue) Spatial analysis to

estimate parameters: Mean (using

geographic covariates)

Variance Range Partial sill Nugget

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:

True exposure Source of spatial variability Initial parameters

Model (TEM) RangePartial sill

Nugget Mean

TEM 1 Geographic characteristics Short Small Small 2nd order

TEM 2 Medium range Middle Large Small Constant

TEM 3 Measurement error only Short Small Large Constant

TEM 4 Short rangeShortest

Large Small Constant

TEM 5 Long range Long Large Small Constant

Examples of spatial surfaces

Spatial surface* of five exposure models (lighter = higher concentration):

Geographic characteristics Medium range

Measurement error only Short range

Long range

*One realization of each surface

True and predicted PM2.5

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.

True vs. Nearest True vs. Kriged Nearest v.s Kriged

Geog Char

Med Range

Meas ErrorOnly

ShortRange

LongRange

Health effect estimates – Geographical characteristics exposure Comparison of β estimates for true and modeled PM2.5

True exposure True exposure Nearest neighbor

True exposure vs. nearest neighbor

True exposure vs. kriged

Nearest neighbor vs. kriged

Kriged

Nearest

Kriged

x=y line best fit line

Health effect estimates – Exposures with little spatial structure

Measurement error only

Short Range – Low spatial correlation

Health effect estimates – Spatially dependent exposures only in the variance model

Medium range – medium spatial correlation

Long range – High spatial correlation

Health effect estimates – Summary

True exposure Fitted exposure Bias2 VarianceMean squared

errorCoverage probability

Geographical True 0 56 56 0.96characteristics Nearest 34 105 139 0.85

Kriging 0 153 153 0.92Medium range – True 0 31 31 0.95Medium spatial Nearest 33 58 91 0.76

correlation Kriging 1 734 735 0.74Measurement error True 0 9 9 0.95

Nearest 465 15 480 0.00Kriging 469 346 815 0.54

Short range – Low True 0 9 9 0.95spatial correlation Nearest 327 23 350 0.03

Kriging 342 778 1120 0.58Long range – High True 0 69 69 0.95spatial correlation Nearest 30 125 155 0.87

Kriging 1 426 427 0.89

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

Discussion: Impact of predicted exposure on cohort study health effect estimates

Other lessons learned: More dense monitoring doesn’t 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.

Acute Air Pollution Health Effects:Sources 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

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

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 N=100,000 individuals on T=1,000 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 α Varying characterizations of daily exposure or concentration

measurements

E( ) exp( )Pit itY X

ˆE( ) exp( [ ])t tY C

XPit= [nonambient source ]it+ αitCit

Time series study example: Impact of

aspects of personal exposure – Results Time series studies estimate αβ – toxicity times

ambient attenuation Non-ambient source exposure doesn’t affect

estimates when it is independent of ambient concentration

Variation in α affects time series study results when it is seasonal and correlated with ambient concentration: (supported by data – see next slide) Larger estimates if α is high when concentration is high Smaller estimates if α is low when concentration is high

Average concentration from multiple monitors improves estimates slightly (reduction in classical measurement error)

Central Air Conditioning (%)

0 10 20 30 40 50 60 70 80

CV

D C

oeffi

cie

nt

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

Regression Coefficients for CVD-Related Hospital Admissions vs. Ambient PM10

Janssen N, Schwartz J, Zanobetti A, Suh H (2002). Environ. Health Perspect.

Summer peaking citiesWinter peaking cities

Slide courtesy of Doug Dockery

↑ => smaller summer α

Time series study example: Impact of

aspects of personal exposure – Summary

Measurements’ effect on health effect parameter interpretation:

Models with concentration as the predictor don’t estimate toxicity alone: When the disease model has a simple form, e.g. E(Y)=exp(XAβ) =exp(Cαβ) β is toxicity Assuming XA=Cα, the disease model with ambient

concentration has parameter αβ. Differences between estimates of αβ can be due to

variations in α (e.g. due to season, region or individual) Huge policy implications that variation in time series study

health effect estimates is not (only) toxicity

Time series study example: Impact of

aspects of personal exposure – Discussion Ambient attenuation (α) 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)

α has structure that varies by season, region, person, species (due to e.g. size, reactivity)

Averaging exposure over time or area averages over α

α is not measured and properties (e.g. seasonality, population patterns) not well understood – Important area for exposure assessment research

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

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