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


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


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


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


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


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


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


Parallel with point estimatesParallel with point estimates

Assessment of risk from fish consumption

Deterministic(points)

Probabilistic(distributions)

CTE RME MCA PBA


Displaying probabilistic resultsDisplaying probabilistic resultsMean 1.75Median 1.68Variance 0.14Range [0.97, 2.58]95%ile 2.22

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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


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


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


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


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


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


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


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


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)


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


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.


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).


Body weightBody weight

40 60 80 100 1200

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Both Monte Carlo input and the p-box

Mixture of distributions for adult males and females

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Exposure durationExposure duration

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Exposure duration (years)


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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Cooking lossCooking loss

Weighted mixture of losses found in systematic study

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Connecticut

Massachusetts


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


Ingestion rateIngestion rate

100 200 3000

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Ingestion rate (grams fish per meal)

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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]


Correlations for Monte CarloCorrelations for Monte Carlo

Cfish LOSS IR EF ED BWCfish

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Dependencies for PBADependencies for PBA

Cfish LOSS IR EF ED BWCfish

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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


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


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


Projected riskProjected riskMCA and PBA,Rising Pond,total PCB,cancer,microexposure,independent

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Projected riskProjected riskMCA and PBA,Rising Pond,total PCB,non-cancer,adult,microexposure,independent

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Projected riskProjected riskMCA and PBA,Rising Pond,total PCB,cancer,one-dimensional,independent

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14Cancer risk (unitless)

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Projected riskProjected riskMCA, PBA, DBARising Pond,total PCB,cancer,microexposure,unknown dependence

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Sensitivity for MCASensitivity for MCA

Correlation analysis

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input value


Sensitivity for PBASensitivity for PBA

Pinch each p-box in turn to the MCA distribution

Compare breadth of output before and after pinching


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


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


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


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

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