PRESENTATION: PROBABILISTIC RISK ASSESSMENT FOR … · Housatonic River Project Probabilistic Risk...
Transcript of PRESENTATION: PROBABILISTIC RISK ASSESSMENT FOR … · Housatonic River Project Probabilistic Risk...
Housatonic River Project
Probabilistic Risk Assessment for Human Ingestion of PCB-contaminated Fish from the
Housatonic River
Probabilistic Risk Assessment for Human Ingestion of PCB-contaminated Fish from the
Housatonic River
W. Troy Tucker and Scott FersonApplied Biomathematics
Housatonic River Project pg 2
OverviewOverview
• Uncertainty analysis• Monte Carlo simulation• Probability bounds analysis• Exposure metrics and equations• Assumptions• Input distributions and dependencies• Some results
• Uncertainty analysis• Monte Carlo simulation• Probability bounds analysis• Exposure metrics and equations• Assumptions• Input distributions and dependencies• Some results
Housatonic River Project pg 3
BackgroundBackground
• Most risk assessments are deterministic and deliberately conservative
• However ...– degree of conservatism is opaque,
unquantified, and can be inconsistent
– difficult to characterize risk, except in extreme situations
• Most risk assessments are deterministic and deliberately conservative
• However ...– degree of conservatism is opaque,
unquantified, and can be inconsistent
– difficult to characterize risk, except in extreme situations
Housatonic River Project pg 4
What’s neededWhat’s needed
An assessment should also tell us
• How likely the various consequences are
• How reliable the estimated likelihoods are
An assessment should also tell us
• How likely the various consequences are
• How reliable the estimated likelihoods are
Housatonic River Project pg 5
Why do an uncertainty analysis?Why do an uncertainty analysis?
• The only way to get at likelihoods• Produces better understanding of risk• Promotes transparency• Enhances credibility• Improves decision making• EPA guidance now available
• The only way to get at likelihoods• Produces better understanding of risk• Promotes transparency• Enhances credibility• Improves decision making• EPA guidance now available
Housatonic River Project pg 6
Types of uncertaintyTypes of uncertainty
VariabilityArises from natural stochasticityTemporal variation, genetics, etc.Not reducible by empirical effort
Incertitude Arises from incomplete knowledgeMeasurement error, small samples, censoring, etc.Reducible with empirical effort
Ambiguity, vagueness, confusion
VariabilityArises from natural stochasticityTemporal variation, genetics, etc.Not reducible by empirical effort
Incertitude Arises from incomplete knowledgeMeasurement error, small samples, censoring, etc.Reducible with empirical effort
Ambiguity, vagueness, confusion
Housatonic River Project pg 7
Basic conceptsBasic concepts
• Risk: The relationship between probability and magnitude of effect
• Exceedance risk: Probability that a variable is larger than some threshold value
• Sensitivity: How a model prediction changes when a parameter varies
• Robustness: Whether conclusions withstand changes in the model, data or assumptions
• Risk: The relationship between probability and magnitude of effect
• Exceedance risk: Probability that a variable is larger than some threshold value
• Sensitivity: How a model prediction changes when a parameter varies
• Robustness: Whether conclusions withstand changes in the model, data or assumptions
Housatonic River Project pg 8
Dual approachDual approach
• Monte Carlo analysis (MCA)– infer best estimates for probabilities– graphically illustrate distribution of risks
• Probability bounds analysis (PBA)– assess contributions of variability and incertitude– graphically illustrate state of knowledge
• Monte Carlo analysis (MCA)– infer best estimates for probabilities– graphically illustrate distribution of risks
• Probability bounds analysis (PBA)– assess contributions of variability and incertitude– graphically illustrate state of knowledge
Housatonic River Project pg 9
Parallel with point estimatesParallel with point estimates
Assessment of risk from fish consumption
Deterministic(points)
Probabilistic(distributions)
CTE RME MCA PBA
Housatonic River Project pg 10
Displaying probabilistic resultsDisplaying probabilistic resultsMean 1.75Median 1.68Variance 0.14Range [0.97, 2.58]95%ile 2.22
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Housatonic River Project pg 11
Methods to select distributionsMethods to select distributions• Default distributions
comes right out of the book• Empirical distributions
usually not enough data available• Extrapolations and surrogate data
requires professional judgement• Elicitation from experts
expensive, controversial when experts disagree• Maximum entropy criterion
inconsistent through changes of scale
• Default distributionscomes right out of the book
• Empirical distributionsusually not enough data available
• Extrapolations and surrogate datarequires professional judgement
• Elicitation from expertsexpensive, controversial when experts disagree
• Maximum entropy criterioninconsistent through changes of scale
Housatonic River Project pg 12
Monte Carlo simulationMonte Carlo simulation1
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A = lognormal(0.55, sqrt(0.005))B = triangular(0, 0.3, 0.5)
C = histogram(.2, .5, .6, .7, .75, .8)D = uniform(0, 1)
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assuming independenceA+B+C+D
Housatonic River Project pg 13
Probability boundsProbability bounds1
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A = {lognormal, mean=[.5,.6], variance=[.001,.01]}B = {min=0, max=.5, mode=.3}
C = {data = (.2, .5, .6, .7, .75, .8)}D = {shape = uniform, min=0, max=1}
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assuming independenceA+B+C+D
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with no assumptionsA+B+C+D
Housatonic River Project pg 14
How to specify PBA inputsHow to specify PBA inputs• Sample data
when there’s a lot, converges to a precise distribution• Moment information
mean, median, mode, variance, range, etc.• Structural information
unimodality, symmetry, positivity, (log)normality, etc.• Modeling and allometry
express the problem in terms of subproblems• Can also use precise distributions
fitted or assumed
• Sample datawhen there’s a lot, converges to a precise distribution
• Moment informationmean, median, mode, variance, range, etc.
• Structural informationunimodality, symmetry, positivity, (log)normality, etc.
• Modeling and allometryexpress the problem in terms of subproblems
• Can also use precise distributionsfitted or assumed
Housatonic River Project pg 15
Why not second-order?Why not second-order?• PBA conveniently and comprehensively
handles– distribution shape uncertainty– model uncertainty– uncertainty about intervariable dependencies
• PBA is computationally cheaper and analytically simpler
• PBA’s output is easier for non-technical readers to understand
• PBA conveniently and comprehensively handles– distribution shape uncertainty– model uncertainty– uncertainty about intervariable dependencies
• PBA is computationally cheaper and analytically simpler
• PBA’s output is easier for non-technical readers to understand
Housatonic River Project pg 16
Data sourcesData sources
• Open literature, NHANES, EPA’s EFH• MADPH• Maine angler data (Ellen Ebert)• Fish contamination measurements
• Open literature, NHANES, EPA’s EFH• MADPH• Maine angler data (Ellen Ebert)• Fish contamination measurements
Housatonic River Project pg 17
DesignDesign• Four sites• Four sites
Reaches 5&6, Rising Pond, two sites in Connecticut
• Two receptor populationsAdults and Children
• Two measuresTotal PCB and TEQ (Toxicity Equivalence Quotient)
• Two endpointsCancer and Non-cancer
• Two analysesMonte Carlo and Probability Bounds Analysis
• Two scenariosOne-dimensional exposures and Microexposure scenarios
Reaches 5&6, Rising Pond, two sites in Connecticut
• Two receptor populationsAdults and Children
• Two measuresTotal PCB and TEQ (Toxicity Equivalence Quotient)
• Two endpointsCancer and Non-cancer
• Two analysesMonte Carlo and Probability Bounds Analysis
• Two scenariosOne-dimensional exposures and Microexposure scenarios
Housatonic River Project pg 18
Same plate of fishSame plate of fish
• Simple scaling of the point estimate formula is questionable in a probability context
It essentially says a person eats the same plate of fish over his whole lifetime
• In fact, different years and different meals may be different
• Microexposure modeling is useful
• Simple scaling of the point estimate formula is questionable in a probability context
It essentially says a person eats the same plate of fish over his whole lifetime
• In fact, different years and different meals may be different
• Microexposure modeling is useful
Housatonic River Project pg 19
Two scenariosTwo scenarios
• One-dimensional exposures• cooking loss the same from meal to meal• exposure frequencies the same each year
• Microexposures• cooking losses independent in sequential meals• exposure frequencies independent from year to year
• Each scenario was used in both MCA and PBA• Results not very different (IR, Cfish were points)
• One-dimensional exposures• cooking loss the same from meal to meal• exposure frequencies the same each year
• Microexposures• cooking losses independent in sequential meals• exposure frequencies independent from year to year
• Each scenario was used in both MCA and PBA• Results not very different (IR, Cfish were points)
Housatonic River Project pg 20
Microexposure via Monte CarloMicroexposure via Monte Carlo
Simulate a yearSample EFSimulate EF meals
Simulate a yearSample EFSimulate EF meals Simulate a meal
Sample Cfish, IR, LOSSslug = Cfish × (1−ς.LOSS) × IR × CFacute = slug / BWtotal = total + slug
Monte Carlo simulationSimulate many anglersMonte Carlo simulationSimulate many anglers
Simulate an anglerSimulate an angler
Simulate a yearSample EFSimulate EF meals
Sample BW, EDSimulate ED yearsSample BW, EDSimulate ED years
Simulate a meal
slug = Cfish × (1− ) × IR × CFtotal = total + slug
Set Cfish = EPC, Set IRSample LOSS
LOSS
Housatonic River Project pg 21
Expression for cancer riskExpression for cancer risk
Risk = CSF·Cfish·(1−LOSS)·CF·Σ(EFa·EDa·IRa/BWa) / AT
Risk = cancer risk (unitless),CSF = cancer slope factor (kilogram days/milligram),Cfish = concentration of PCB in fish tissue (milligrams/kilogram),LOSS = cooking loss (unitless),CF = conversion factor (1 kilogram / 1000 grams),a = age index (child, adult),EF = exposure frequency (meals/year),ED = exposure duration (age 1-6 for children, age 7-70 for adults),IR = ingestion rate of fish tissue by humans (grams/meal),BW = body weight of humans (kilograms), andAT = averaging time (days) = 70 years × 365 days/year.
Housatonic River Project pg 22
Non-cancer riskNon-cancer risk
Riska = Cfish·(1−LOSS)·CF·EFa·IRa / (AT·RfD·BWa)
Riska = non-cancer risk at age a (unitless),a = age index (child, adult),Cfish = concentration of PCB in fish tissue (milligrams/kilogram),LOSS = cooking loss (unitless),CF = conversion factor (1 kilogram / 1000 grams),EF = exposure frequency (meals/year),IR = ingestion rate of fish tissue by humans (grams/meal),AT = averaging time (365 days),RfD = reference dose (milligrams/kilogram/day), andBW = body weight of humans (kilograms).
Housatonic River Project pg 23
Body weightBody weight
40 60 80 100 1200
0.5
Body mass (kilograms)
Both Monte Carlo input and the p-box
Mixture of distributions for adult males and females
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Housatonic River Project pg 24
Exposure durationExposure duration
0 10 20 30 40 50 600
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Children
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70
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Exposure duration (years)
Housatonic River Project pg 25
Exposure frequencyExposure frequency
Exposure frequency (meals/year)0 200 400 600 800 1000
Adults and children
Empirical distribution based on n > 1000
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Housatonic River Project pg 26
Cooking lossCooking loss
Weighted mixture of losses found in systematic study
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Connecticut
Massachusetts
Housatonic River Project pg 27
AnnualizationAnnualization
DeterministicIR = 32 grams/day EF = 365 days/year
ProbabilisticIR = 227 grams/meal EF = (uncertain) meals/year
DeterministicIR = 32 grams/day EF = 365 days/year
ProbabilisticIR = 227 grams/meal EF = (uncertain) meals/year
Housatonic River Project pg 28
Ingestion rateIngestion rate
100 200 3000
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Ingestion rate (grams fish per meal)
1
Housatonic River Project pg 29
Concentration in fish tissueConcentration in fish tissue
EPA guidance requires using the EPC
MCACfish = same as EPC in point estimate
PBACfish = [sample average concentration, EPC]
EPA guidance requires using the EPC
MCACfish = same as EPC in point estimate
PBACfish = [sample average concentration, EPC]
Housatonic River Project pg 30
Correlations for Monte CarloCorrelations for Monte Carlo
Cfish LOSS IR EF ED BWCfish
LOSS
IR
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BW
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Housatonic River Project pg 31
Dependencies for PBADependencies for PBA
Cfish LOSS IR EF ED BWCfish
LOSS
IR
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BW
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?
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Housatonic River Project pg 32
Monte Carlo assumptionsMonte Carlo assumptions
• Exposure only through fish ingestion• Exposures strictly additive• Red distributions are correctly specified• All variables are mutually independent• Body masses constant through time• Precise weights for cooking methods
• Exposure only through fish ingestion• Exposures strictly additive• Red distributions are correctly specified• All variables are mutually independent• Body masses constant through time• Precise weights for cooking methods
Housatonic River Project pg 33
Probability bounds assumptionsProbability bounds assumptions
• Exposure only through fish ingestion• Exposures additive• Body masses constant through time• Relaxed perfect distribution assumptions• Relaxed independence assumptions• Precise weightings for cooking methods
• Exposure only through fish ingestion• Exposures additive• Body masses constant through time• Relaxed perfect distribution assumptions• Relaxed independence assumptions• Precise weightings for cooking methods
Housatonic River Project pg 34
Some of the resultsSome of the results
• There were hundreds of probabilistic (distributional) calculations
• We look at the results for four of these, just to get a flavor
• Also peek at part of the sensitivity studies
• There were hundreds of probabilistic (distributional) calculations
• We look at the results for four of these, just to get a flavor
• Also peek at part of the sensitivity studies
Housatonic River Project pg 35
Projected riskProjected riskMCA and PBA,Rising Pond,total PCB,cancer,microexposure,independent
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Exc
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Pro
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Housatonic River Project pg 36
Projected riskProjected riskMCA and PBA,Rising Pond,total PCB,non-cancer,adult,microexposure,independent
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0 500 1000 1500 2000Hazard quotient (unitless)
Exc
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Pro
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Housatonic River Project pg 37
Projected riskProjected riskMCA and PBA,Rising Pond,total PCB,cancer,one-dimensional,independent
0
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14Cancer risk (unitless)
Exc
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Pro
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Housatonic River Project pg 38
Projected riskProjected riskMCA, PBA, DBARising Pond,total PCB,cancer,microexposure,unknown dependence
0
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0 0.01 0.02 0.03 0.04 0.05 0.06Cancer risk (unitless)
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Housatonic River Project pg 39
Sensitivity for MCASensitivity for MCA
Correlation analysis
outp
ut v
alue
input value
Housatonic River Project pg 40
Sensitivity for PBASensitivity for PBA
Pinch each p-box in turn to the MCA distribution
Compare breadth of output before and after pinching
Housatonic River Project pg 41
Sensitivity for PBASensitivity for PBA
Pinch each p-box in turn to the MCA distributionPinch each p-box in turn to a point estimate
Compare breadth of output before and after pinching
Housatonic River Project pg 42
Sensitivity studiesSensitivity studies
correlation pinch uncertainty pinch bothMonte Carlo Probability bounds analysis
Cfish 6.7IRadult 26.0 26.0IRchild 13.0 13.0BWadult 13.0 5.3BWchild 0.1 0.5EDadult 74.0 25.0 57.0EDchild 2.1 8.6 22.0EFadult 5.5 6.9 8.1EFchild 5.5 30.0 40.0LOSS 0.6 0.0 0.0
Housatonic River Project pg 43
HHRA documentationHHRA documentation
• See volume I, §5.6 for synopsis
• See volume IV, §6 for details
• See volume IV, §8 for import
• See volume I, Attachment 5 for intro to PBA
• See volume I, §5.6 for synopsis
• See volume IV, §6 for details
• See volume IV, §8 for import
• See volume I, Attachment 5 for intro to PBA
Housatonic River Project pg 44
Attachment 5 (PBA introduction)Attachment 5 (PBA introduction)
• Addressed to Monte Carlo users
• Deriving p-boxes from limited information• Algorithms for arithmetic computations• Numerical examples• PBA as a method of sensitivity analysis• Sensitivity analyses on top of a PBA• PBA within EPA’s tiered approach
• Addressed to Monte Carlo users
• Deriving p-boxes from limited information• Algorithms for arithmetic computations• Numerical examples• PBA as a method of sensitivity analysis• Sensitivity analyses on top of a PBA• PBA within EPA’s tiered approach