Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Estimating Hazardous Concentrations for Environmental Risk Assessment with Ecotoxicological Effect Data Graeme Hickey1 Peter Craig1 Andy Hart2 Ben Kefford3 Jason Dunlop4 1Department of Mathematical Sciences, Durham University, UK 2Central Science Laboratories, York, UK 3School of Applied Sciences, RMIT, Victoria, Australia 4Department of Natural Resources and Water, Queensland, Australia RSS AGM Meeting, 2008
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Outline of presentation: 1 Background of the risk assessment. 2 A lower-tier risk assessment problem. 3 A higher-tier risk assessment problem: an example.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Background Background I will focus on aquatic Risk Assessment (RA) to chemicals.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Background Background I will focus on aquatic Risk Assessment (RA) to chemicals. Governing bodies (e.g. EU, US-EPA) want to estimate the hazardous concentration (HC), i.e. the maximum permissible/safe concentration, for a toxicant.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Background Background I will focus on aquatic Risk Assessment (RA) to chemicals. Governing bodies (e.g. EU, US-EPA) want to estimate the hazardous concentration (HC), i.e. the maximum permissible/safe concentration, for a toxicant. The substance might be a discharged chemical (e.g. pesticide in a river) or an environmental change (e.g. rising salinity toxicity due to land clearing).
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Background Background I will focus on aquatic Risk Assessment (RA) to chemicals. Governing bodies (e.g. EU, US-EPA) want to estimate the hazardous concentration (HC), i.e. the maximum permissible/safe concentration, for a toxicant. The substance might be a discharged chemical (e.g. pesticide in a river) or an environmental change (e.g. rising salinity toxicity due to land clearing). For lower-tier RA; if HC < Predicted Environmental Concentration then the risk is high. Immediate action required or a more refined assessment.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Toxicity Data Current (EU) Practice 0.0 0.4 0.8 Species 1 Response x1 0.0 0.4 0.8 Species 2 Response x2 and so on... 0.0 0.4 0.8 Species n Response xn Toxicity tolerance data for n distinct species is provided: x1, x2, . . . , xn (n is very small!). Each xi is independently derived (estimated) from a species dose-response curve, which is expensive. Experimental error assumed negligible, so not propogated.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Current Methods Current (EU) Deterministic Approach HC def = min{x1,x2,...,xn} AF
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Current Methods Current (EU) Deterministic Approach HC def = min{x1,x2,...,xn} AF The Assessment Factor (AF) is an arbitrary value (> 1; typically 10, 100, or 1000) used to account for uncertainty and variability (although not made clear which uncertainties!). Concept of risk measurement is replaced with perceived conservatism.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Current Methods Current Probabilistic Approaches Assume y1 = log(x1 ), y2 = log(x2 ), . . . , yn = log(xn ) are realisations from the same distribution – the Species Sensitivity Distribution (SSD). N(µ, σ2) is the typical choice.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Current Methods Current Probabilistic Approaches Assume y1 = log(x1 ), y2 = log(x2 ), . . . , yn = log(xn ) are realisations from the same distribution – the Species Sensitivity Distribution (SSD). N(µ, σ2) is the typical choice. The SSD is defined to be the probability that a randomly selected species drawn from the ecological assemblage has its toxicological endpoint violated at a specified (log-) environmental concentration.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Current Methods Current Probabilistic Approaches Assume y1 = log(x1 ), y2 = log(x2 ), . . . , yn = log(xn ) are realisations from the same distribution – the Species Sensitivity Distribution (SSD). N(µ, σ2) is the typical choice. The SSD is defined to be the probability that a randomly selected species drawn from the ecological assemblage has its toxicological endpoint violated at a specified (log-) environmental concentration. The HC is often defined to be the p-th percentile of the SSD (HCp ); typically p = 5 based on experience (e.g. Dutch government)
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Current Methods Current Probabilistic Approaches Assume y1 = log(x1 ), y2 = log(x2 ), . . . , yn = log(xn ) are realisations from the same distribution – the Species Sensitivity Distribution (SSD). N(µ, σ2) is the typical choice. The SSD is defined to be the probability that a randomly selected species drawn from the ecological assemblage has its toxicological endpoint violated at a specified (log-) environmental concentration. The HC is often defined to be the p-th percentile of the SSD (HCp ); typically p = 5 based on experience (e.g. Dutch government) The ‘Gold Standard’ is Aldenberg & Jaworska’s (2000) 50% and lower 5% confidence limit estimate of the sampling distn 5th percentile – estimators are closed form (non-central t). Extrapolates whilst accounting for inter-species variability and accounts for sampling uncertainty. Ignores other uncertainties!
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Connections Relation to Loss Functions The choice of the lower 5% estimator is prescribed to err on the side of caution. But, it has no ecological relevance.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Connections Relation to Loss Functions The choice of the lower 5% estimator is prescribed to err on the side of caution. But, it has no ecological relevance. It can be shown that the estimator(s) are Bayes rules w.r.t. the class of Generalised Absolute Loss (GAL) functions using Jeffreys’ prior: π(µ, σ2) ∝ σ−2 for µ ∈ R, σ2 ∈ R+.; i.e. δ∗ p (Y) = arg min δ(Y) Eµ,σ2|YL ψp(µ, σ2), δ(Y) where δ(Y) is an estimator, and ψp(µ, σ2) is the ‘true’ quantity.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX (Modified-) LINEX Overestimation of the HCp is much more serious than underestimation, hence the lower 5th-percentile choice ⇒ asymmetry is a highly desirable property.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX (Modified-) LINEX Overestimation of the HCp is much more serious than underestimation, hence the lower 5th-percentile choice ⇒ asymmetry is a highly desirable property. Assuming that a risk manager can specify a loss-benefit portfolio independent of their choice of p; we apply an asymmetric & non-linear loss function: Zieli´ nski’s (Modified-) LINear EXponential (LINEX).
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX (Modified-) LINEX Overestimation of the HCp is much more serious than underestimation, hence the lower 5th-percentile choice ⇒ asymmetry is a highly desirable property. Assuming that a risk manager can specify a loss-benefit portfolio independent of their choice of p; we apply an asymmetric & non-linear loss function: Zieli´ nski’s (Modified-) LINear EXponential (LINEX). Lσ (δp, ψp ) = exp αδp−ψp σ − α δp−ψp σ − 1
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX −4 −2 0 2 4 0 10 20 30 40 ∆ ∆ L(∆ ∆) α α=2 α α=0.5 α α=0 α α=1 Modified-LINEX differs from standard case because ∆ = δp (Y)−ψp (µ, σ2) → ∆/σ. If ∆ was unscaled, the risk assessor must have knowledge of the SSD slope in advance to specify costs/loss (Zieli´ nski, 2005). Scaling allows the risk manager to specify costs on a ‘standardised’ scale.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX A Decision Rule Bayes rules of modified-LINEX and GAL (under Jeffreys’ prior) is ¯ y − κpsy , where κp is called an Assessment Shift-Factor which is independent of the data.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX A Decision Rule Bayes rules of modified-LINEX and GAL (under Jeffreys’ prior) is ¯ y − κpsy , where κp is called an Assessment Shift-Factor which is independent of the data. κp = a percentile of the non-central t-distribution (GAL); scaled parabolic cylinder function (modified-LINEX) Allows for tractable, transparent, and fast risk assessment – appeals to risk managers.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References LINEX A Decision Rule Bayes rules of modified-LINEX and GAL (under Jeffreys’ prior) is ¯ y − κpsy , where κp is called an Assessment Shift-Factor which is independent of the data. κp = a percentile of the non-central t-distribution (GAL); scaled parabolic cylinder function (modified-LINEX) Allows for tractable, transparent, and fast risk assessment – appeals to risk managers. We use Jeffreys’ prior to compare to other proposals (Aldenberg & Jaworska 2000 and EFSA 2005).
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Some Background Effects of Salinity Salinity levels in Australian aquatic environments are increasing, due to poor management practices. A lot of time and resources has been spent on researching agricultural and economic effects.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Some Background It’s Predicted To Get Worse... Year: 2000 Area at Risk = 5,658,000 Ha
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Some Background It’s Predicted To Get Worse... Year: 2000 Area at Risk = 5,658,000 Ha Year: 2050 Area at Risk = 17,000,000 Ha
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Salinity risk assessment is high stakes! This requires a higher level RA.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Salinity risk assessment is high stakes! This requires a higher level RA. In high enough concentrations, it’s toxic to freshwater species.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Salinity risk assessment is high stakes! This requires a higher level RA. In high enough concentrations, it’s toxic to freshwater species. A new and more efficient experimental technique has been proposed by Kefford et al. (2005).
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Salinity risk assessment is high stakes! This requires a higher level RA. In high enough concentrations, it’s toxic to freshwater species. A new and more efficient experimental technique has been proposed by Kefford et al. (2005). We get: (i) more toxicity data; and (ii) in better proportion to ecological structure.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Salinity risk assessment is high stakes! This requires a higher level RA. In high enough concentrations, it’s toxic to freshwater species. A new and more efficient experimental technique has been proposed by Kefford et al. (2005). We get: (i) more toxicity data; and (ii) in better proportion to ecological structure. With more data, we can use more complicated modelling of the SSD; e.g. O’Hagan (2005).
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Salinity risk assessment is high stakes! This requires a higher level RA. In high enough concentrations, it’s toxic to freshwater species. A new and more efficient experimental technique has been proposed by Kefford et al. (2005). We get: (i) more toxicity data; and (ii) in better proportion to ecological structure. With more data, we can use more complicated modelling of the SSD; e.g. O’Hagan (2005). We are interested in the Victorian environment.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Model 1: Bayesian Extension of Aldenberg & Jaworska (2000) yi ∼ N(µ, σ2) ⇒ FSSD (y) = Φ y−µ σ
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Model 1: Bayesian Extension of Aldenberg & Jaworska (2000) yi ∼ N(µ, σ2) ⇒ FSSD (y) = Φ y−µ σ Model 2: A Version of O’Hagan et al. yi ∼ N(µti , σ2) where ti = taxonomic order of species i. ⇒ FSSD (y) = N t=1 ωt Φ y−µt σ where ωt are the ‘estimated’ (or otherwise) taxonomic order weights.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Remodelling Beginning of a New Model Model 1: Bayesian Extension of Aldenberg & Jaworska (2000) yi ∼ N(µ, σ2) ⇒ FSSD (y) = Φ y−µ σ Model 2: A Version of O’Hagan et al. yi ∼ N(µti , σ2) where ti = taxonomic order of species i. ⇒ FSSD (y) = N t=1 ωt Φ y−µt σ where ωt are the ‘estimated’ (or otherwise) taxonomic order weights. Prior Distributions Expert elicitations for µt ’s. All other parameters – applied posterior distributions updated with (training data) Queensland data.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Discussion & Conclusions Current probabilistic proposals for estimating the HC and risk are based on arbitrary or unsatisfactory principles, as demonstrated by reducing them to loss functions.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Discussion & Conclusions Current probabilistic proposals for estimating the HC and risk are based on arbitrary or unsatisfactory principles, as demonstrated by reducing them to loss functions. EU Technical Guidance Document allows for probabilistic application of SSD based estimators (although not clear how) – so there is motivation for development.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Discussion & Conclusions Current probabilistic proposals for estimating the HC and risk are based on arbitrary or unsatisfactory principles, as demonstrated by reducing them to loss functions. EU Technical Guidance Document allows for probabilistic application of SSD based estimators (although not clear how) – so there is motivation for development. The extrapolation methods discussed [here] only account for natural species variability and sampling uncertainty. There are other uncertainties – lots of them! Does over-conservatism allow us to mask these additional uncertainties? Answer: We don’t know (yet!).
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Discussion & Conclusions Current probabilistic proposals for estimating the HC and risk are based on arbitrary or unsatisfactory principles, as demonstrated by reducing them to loss functions. EU Technical Guidance Document allows for probabilistic application of SSD based estimators (although not clear how) – so there is motivation for development. The extrapolation methods discussed [here] only account for natural species variability and sampling uncertainty. There are other uncertainties – lots of them! Does over-conservatism allow us to mask these additional uncertainties? Answer: We don’t know (yet!). Restrictions to data impoverishment should be addressed; c.f. Kefford et al.’s technique.
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References Discussion & Conclusions Current probabilistic proposals for estimating the HC and risk are based on arbitrary or unsatisfactory principles, as demonstrated by reducing them to loss functions. EU Technical Guidance Document allows for probabilistic application of SSD based estimators (although not clear how) – so there is motivation for development. The extrapolation methods discussed [here] only account for natural species variability and sampling uncertainty. There are other uncertainties – lots of them! Does over-conservatism allow us to mask these additional uncertainties? Answer: We don’t know (yet!). Restrictions to data impoverishment should be addressed; c.f. Kefford et al.’s technique. We can invert the risk assessment problem to answer: How do we prioritise clean-up operations with finite resources?
Outline CRA: Haz. Concs. Loss Functions Salinity SSDs Closing Remarks References References Aldenberg, T. and Jaworska, J. S. (2000). Uncertainty of the Hazardous Concentration and Fraction Affected for Normal Species Sensitivity Distributions. Ecotoxicol. Environ. Saf. 46, 1–18. European Food Safety Authority Panel on Plant Health, Plant Protection Products and their Residues (2005). Question No. EFSA-Q-2005-042. The EFSA Journal. 301, 1–45. Hickey, G. L., Kefford, B. J., Dunlop, J. E. and Craig, P. S. (2008). Making Species Salinity Sensitivity Distributions Reflective of Naturally Occurring Communities: Using Rapid Testing and Bayesian Statistics. Environ. Toxicol. Chem. 27, No. 11, pp. 2403–2411. Hickey, G. L., Craig, P. S. and Hart, A. (2009). On The Application of Loss Functions in Determining Assessment Factors for Ecological Risk. Ecotoxicol. Environ. Saf. 72, No. 2, pp. 293–300. O’Hagan, A., Crane, M., Grist, E. P. M. and Whitehouse, P. (2005). Estimating Species Sensitivity Distributions With the Aid of Expert Judgements. Unpublished. http://www.tonyohagan.co.uk/academic/pdf/SSD-stat.pdf Zieli´ nski, R. (2005). Estimating Quantiles With Linex Loss Function. Applications to VaR Estimation. Applicationes Mathematicae. 32: 367–373.
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