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1 Probabilistic Risk Assessment in 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: Biostatistics DuPont Applied Statistics Group

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2 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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4 Deterministic Probabilistic Toxicity Exposure TER

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5 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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6 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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7 Ecosystem level assessment Current 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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8 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 assessment Probabilistic Approach

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10 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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11 How Many Species? Newmans method: 40 to 60 species –Snowballs 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 in some non-target plant studies

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12 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 2 nd slide following: uniform [0,1] generated Various distributions fit –Actual laboratory data suggests yes

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13 Power to Detect non-Lognormality Exponential Distribution Generated SWKSADCMSample Size

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14 Does it Matter? Q05 Simulations: True value =0.05 Uniform [0,1] Generated Distribution3 rd QrtlQ5medianIst QrtlSize Exponential Normal Exponential Lognormal Normal Exponential Lognormal Normal Exponential Lognormal Normal Exponential Lognormal Normal

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15 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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16 Variability and Uncertainty Uncertainty reflects lack of knowledge of the system under study Ex1: what distribution to fit for SSD Ex2: what mathematical model to use to estimate ECx Increased knowledge will reduce uncertainty Variability reflects lack of control inherent variation or noise among individuals. Increased knowledge of the animal or plant species will not reduce variability

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17 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 χ 2 (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

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18 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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19 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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20 Summary Plot for SSD

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21 Putting it All Together Joint 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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22 Calculating Risk The risk is given by Pr[X e >X s ] where X e = exposure, X s =sensitivity or toxicity This is an average probability that exposure will exceed the sensitivity of species exposed Not clear that this captures the right risk Work needed here

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23 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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24 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

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