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Probabilistic Risk Assessmentin Environmental Toxicology

RISK: Perception, Policy & Practice Workshop October 3-4, 2007

SAMSI, Research Triangle Park, NC

John W. Green, Ph.D., Ph.D.Senior Consultant: BiostatisticsDuPont Applied Statistics Group

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Topics Addressed in Environmental Risk Assessment

• Present & proposed regulatory methods– Concerns– Micro- vs macro-assessments

• Variability vs Uncertainty• Exposure and Toxicity

– Exposure models (Monte Carlo, PBA)• extensive literature on exposure

– Toxicity• Species Sensitivity Distributions (Monte Carlo)

– Combining the two for risk assessment

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Deterministic Probabilistic

Toxicity

Exposure

TERTER

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Assessment of Toxicity• Species level assessments

– Laboratory toxicity experiments– Greenhouse studies– Field studies

• Ecosystem level assessment– Most sensitive species– Mesocosm studies– Species Sensitivity Distribution

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Species Level Assessment:NOEC (aka NOAEL) and ECx

• LOEC = lowest tested conc at which a statistically significant adverse effect is observed

• NOEC = highest tested conc < LOEC – LOEC, NOEC depend on experimental

design & statistical test• ECx = conc producing x% effect

– ECx depends on experimental design and model and choice of x

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Ecosystem level assessmentCurrent Method

Determine the NOEC (or EC50) for each species representing an ecosystem

Find the smallest NOEC (or EC50) Divide it by 10, 100, or 1000

(uncertainty factor) Regulate from this value

or argue against it

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• Collect a consistent measure of toxicity from a representative set of species– EC50s or NOECs (not both)

• Fit a distribution (SSD) to these numerical measures

• Estimate concentration, HC5, that protects 95% of species in ecosystem

• Advantages and problems with SSDs

Ecosystem level assessmentProbabilistic Approach

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SSD by Habitat

Visual groupings are not taxonomic classes but defined by habitat , possibly related to mode of action

Selection of Toxicity Data

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How Many Species?• Newman’s method: 40 to 60 species

– Snowball’s chance…– Might reduce this by good choice of

groups to model• Aldenberg-Jaworski: 1 species will do

– If you make enough assumptions,…• 8 is usual target• 5 is common• 20-25 in some non-target plant studies

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Which Distribution to Fit?• Normal, log-normal, log-logistic, Burr

III…?– With 5-8 data points, selecting the “right”

distribution is a challenge• Next slide gives simulation results

• Does it matter?– Recent simulation study suggests yes

• 2nd slide following: uniform [0,1] generated• Various distributions fit

– Actual laboratory data suggests yes

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Power to Detect non-LognormalityExponential Distribution Generated

SW KS AD CM Sample Size

10 11 10 8 4

16 13 16 15 5

24 19 24 23 6

35 26 32 31 8

46 31 43 40 10

68 43 62 58 15

84 60 77 72 20

97 78 93 91 30

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Does it Matter?Q05 Simulations: True value =0.05

Uniform [0,1] Generated

Distribution 3rd Qrtl Q5median Ist Qrtl SizeExponential 0.2341 0.08295 -0.02438 4Normal 0.19371 0.02227 -0.09323 4Exponential 0.19859 0.06788 -0.01593 5Lognormal 0.26667 0.1385 0.064521 5Normal 0.16495 0.02547 -0.08768 5Exponential 0.16714 0.05756 -0.01171 6Lognormal 0.23317 0.13017 0.065593 6Normal 0.13695 0.02157 -0.07665 6Exponential 0.139 0.05249 -0.00116 8Lognormal 0.1993 0.11927 0.063502 8Normal 0.12884 0.02709 -0.05738 8Exponential 0.11034 0.04692 0.004643 10Lognormal 0.17223 0.10481 0.060777 10Normal 0.10975 0.02209 -0.04842 10

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Which Laboratory Species?One EUFRAM case study fits an SSD to the

following

Aquatic toxicologists can comment (and have) on whether these values belong to a meaningful population

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Variability and UncertaintyUncertainty reflects lack of knowledge of thesystem under study

Ex1: what distribution to fit for SSDEx2: what mathematical model to use to

estimate ECxIncreased knowledge will reduce uncertainty

Variability reflects lack of controlinherent variation or noise among individuals.

Increased knowledge of the animal or plant species will not reduce variability

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Variability & Uncertainty• The fitted distribution is assumed log-normal

– Defined by the population mean and variance• Motivated in part by standard relationship shown below

– Randomly sample from the χ2(n-1) distribution.

– Then randomly sample from a normal with the above variance, and mean equal to sample mean

– Note: If formulas below are used, only variability is captured

1)1( n

stx n2

)1(

2

n

ns

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Spaghetti plot Probabilities (vertical variable values) associated with a given value of log(EC50) are themselves distributed

For a given log(EC50) value, the middle 95% of these secondary probabilities defines 95% confidence interval for proportion of species affected at that conc

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For a given proportion (value of y), the values of Log(EC50) (horizontal variable) that might have produced the given y-value are distributed.

For a given y value, the middle 95% of these x-values defines 95% confidence bounds on the distribution of log(ECy) values.

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Summary Plot for SSD

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Putting it All TogetherJoint Probability Curves

Plot exposure and toxicity distributions together to understand the likelihood of the exposure concentration exceeding the toxic threshold of a given percent of the population

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Calculating RiskThe risk is given by

Pr[Xe>Xs]where Xe = exposure, Xs =sensitivity or toxicity

This is an “average” probability that exposurewill exceed the sensitivity of species exposed

Not clear that this captures the right riskWork needed here

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Conclusions

• PRA can bring increased reality to risk management by– communicating uncertainty more realistically– separating uncertainty from variability– clarifying risk of environmental effects

• PRA is only as good as the assumptions and theories on which it rests

• The bad news is that implementation is running ahead of understanding

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Conclusions• SSDs based on tiny datasets unreliable• Need to identify what populations are

appropriate subjects for SSD is vital • 2-D Monte Carlo methods often assume

independent inputs or specific correlations– Not realistic in many cases

• PBA can accommodate dependent inputs– But can lead to wide bounds– Have other limitations restricting use

• MCMC can accommodate correlated inputs– But are mathematically demanding