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
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.
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.
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).
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.
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.
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.
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.
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.
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)
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!
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.
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.
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.
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).
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
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.
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.
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.
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).
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.
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.
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).
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.
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).
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.
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.
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.
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.
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.
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!).
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.
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?
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.