Extending the SSD concept to explore some foundational model limitations: a Bayesian hierarchical approach

Presented at the SETAC Europe 21st Annual Meeting, Milan, Italy (15-19 May 2011)

Transcript

1. Graeme  Hickey1,  Peter  Craig1,  Stuart  Marshall2,  Oliver  Price2,   Mathijs  Smit3,  Andy  Hart4,  Robert  LuCk5,  Peter  Chapman2,reGred,   Dick  de  Zwart5     1Department  of  Mathema/cal  Sciences,  Durham  University,  UK   2Safety  and  Environmental  Assurance  Centre,  Unilever,  Colworth,  UK   3Statoil  ASA,  Trondheim,  Norway   4The  Food  and  Environment  Research  Agency,  York,  UK   5RIVM,  Bilthoven,  The  Netherlands   Extending  the  SSD  Concept  to  Explore   Some  Founda/onal  Model  Limita/ons:     A  Bayesian  Hierarchical  Approach    
2. Species  Sensi/vity  Distribu/ons  (SSDs)   log10 (HC5 ) 0   0.2   0.4   0.6   0.8   1   -­‐2   -­‐1   0   1   2   3   4   %  species  affected   log10 (EC50 )  of  chemical  for  aqua/c  organisms   20 40 60 80 100 0 risk  assessment   standard  se]ng  
3. All  Models  Are  Wrong…   (the  SSD  is  no  excep/on!)…  but  some  are  beaer   than  others.   ASSUMPTION   PRACTICAL  CONSEQUENCE   SSDs  are  independent   Informa/on  gained  about  each  chemical  risk   assessment  will  not  strengthen  learning  of   future  assessments.   Interspecies  varia/on  is  aaributable  to  chemical   effects  only   Observa/on  of  some  species  being  more/less   sensi/ve  not  accounted  for.   Other  sources  of  varia/on  (e.g.  inter-­‐laboratory   and  intra-­‐species  varia/on)  are  ignorable  or   captured  by  an  arbitrary  assessment  factor  (1  ≤   AF  ≤  5)   Confounding  of  the  HC5  interpreta/on  –  should   it  just  represent  interspecies  varia/on?   Representa/ve  of  all  ecosystems   No  account  of  specific  assemblages  and  differing   diversi/es.  
4. Hierarchical  Modelling   = α1   σ1   y1j     log  transformed  toxicity  datum   for  chemical  1  and  species  j   central   tendency     ˿  dispersion   (interspecies   standard  devia/on)   The  standard  SSD  model  can  be  wriaen  as  a  stochas/c  network   +  distribu/on   Chemical  1  
5. Hierarchical  Modelling   α1   σ1   y1j     α2   σ2   y2j     α3   σ3   y3j     αN   σN   yNj     ………...….…..   If  we  have  N  chemical  risk  assessments,  the  usual  SSD  model  is   a  special  (independence)  case  of  a  hierarchical  model.   chemical  1   chemical  2   chemical  3   chemical  N   …………..   ………..  
6. α1   σ1   y1j     α2   σ2   y2j     α3   σ3   y3j     αN   σN   yNj     ……………..   βsp.  j   Model  Assump8on:  Each  toxicity  value  can  be  decomposed  into  a  linear  sum   of  a  chemical  effect,  a  chemical:species  interac/on  effect  and  an  error  term   yij = αi + βjσi + εij εij ∼ N(0, σ2 i ) Normality  is  generally  accepted   by  SSD  prac//oners;  although   can  be  subs/tuted  with   something  more  suitable.     SSD  interspecies  variance  parameters  are   heterogeneous  between  chemicals  i.   Therefore  βj  measures  species  posi/on  as   number  of  standard  devia/ons  from  mean   (log-­‐)toxicity.     βj    <  0  ˰  species  j  typically  sensi/ve   βj    >  0  ˰  species  j  typically  tolerant      
7. α1   σ1   y1j     α2   σ2   y2j     α3   σ3   y3j     αN   σN   yNj     ……………..   βsp.  j   βsp.  1   βsp.  2   βsp.  3   βsp.  M   σβ   Hyper-­‐popula/on  of  species   effects:  βj  ~  N(0,  σβ 2)  
8. α1   σ1   y1j     α2   σ2   y2j     α3   σ3   y3j     αN   σN   yNj     ……………..   βsp.  j   μ,  σα   a,  b   Hyper-­‐popula/on  of   chemical  effects:     αi  ~  N(μ,  σα 2)   Hyper-­‐popula/on  of   interspecies  variances:     σi -­‐2  ~  Γ(a,  b)  
9. Bayesian  Analysis   •  Need  to  ensure  propaga/on  of  >  1st  level   uncertainty.   •  Update  prior  distribu/ons  about  the  hyper-­‐ parameters  using  observed  data  to  retrieve   posterior  distribu/ons.   •  Use  posterior  distribu/ons  to  make  hazard   assessment  inferences  for  retrospecGve  and   prospecGve  chemical  assessments.  
10. Example   •  Ecotoxicity  database  extracted  from  the  U.S.   EPA  Web-­‐ICE  database.  1600  E(L)C50  values   (lethality  or  immobility)  spanning  201   chemicals  (each  with  ni  ≥  5)  and  77  species.     hap://www.epa.gov/ceampubl/fchain/webice/   •  Prior  distribu/ons  chosen  to  closely  represent   ‘ignorance’  (so-­‐called  ‘non-­‐informaGve’).    
11. density 0 1 2 3 4 5 !! 0.6 0.7 0.8 0.9 1.0 1.1 !! 1.2 1.3 1.4 1.5 Hyper-­‐parameter  Posterior   Distribu/ons   median  (+  95%  credible  interval)   σβ :  0.81  (0.65,  1.01)   σα :  1.33  (1.21,  1.48)     ˰  more  varia/on  between  chemicals   density 0 2 4 6 a 1.0 1.2 1.4 1.6 1.8 2.0 2.2 b 0.2 0.3 0.4 0.5 Es/mates  consistent  with  European   Food  Safety  Authority  (2005,  EFSA  J.   301,  pp.  1-­‐45)  report.     Equivalent  to  ≈  3  addi/onal   measurements    →  stabilizes   interspecies  variance  es/mate.   species  :  σβ   chemical  :  σβ   a   b  
12. Posterior distribution summaries of !j −2 −1 0 1 2 Paratanytarsus dissimilis Asellus aquaticus Oreochromis mossambicus Cypris subglobosa Atherix variegata Asterias forbesi Poecilia reticulata Oryzias latipes Ameiurus melas Planorbella trivolvis Carassius auratus Neanthes virens Paratanytarsus parthenogeneticus Lumbriculus variegatus Ictalurus punctatus Ptychocheilus lucius Cyprinus carpio Crangonyx pseudogracilis Pimephales promelas Catostomus commersonii Dugesia tigrina Allorchestes compressa Cyprinodon variegatus Gasterosteus aculeatus Rana sphenocephala Lepomis cyanellus Caecidotea intermedia Cyprinodon bovinus Poeciliopsis occidentalis Lepomis macrochirus Lepomis microlophus Chironomus tentans Gambusia affinis Gila elegans Oncorhynchus clarkii Salvelinus fontinalis Oncorhynchus kisutch Xyrauchen texanus Bufo boreas Sander vitreus Notropis mekistocholas Micropterus salmoides Pomoxis nigromaculatus Caecidotea brevicauda Oncorhynchus mykiss Etheostoma lepidum Salmo salar Farfantepenaeus duorarum Etheostoma fonticola Salvelinus namaycush Perca flavescens Menidia beryllina Salmo trutta Ischnura verticalis Oncorhynchus tshawytscha Erimonax monachus Menidia menidia Oncorhynchus gilae Gammarus fasciatus Chironomus plumosus Ceriodaphnia dubia Esox lucius Daphnia magna Crassostrea virginica Acipenser brevirostrum Hyalella azteca Pteronarcys californica Gammarus pseudolimnaeus Salvelinus confluentus Lagodon rhomboides Daphnia pulex Pteronarcella badia Orconectes nais Gammarus lacustris Americamysis bahia Simocephalus serrulatus Claassenia sabulosa ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2   1   0   -­‐1   -­‐2   Evidence  that  some  species  are  more  sensi/ve  than  others   βj   Posterior  summaries  of  βj  
13. The  Role  of  Taxonomy   genus family order class phylum kingdom 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 |median(!S1 ! !S2 )| The  more  taxonomically   spread  species  are  in  an   SSD,  the  larger  the   interspecies  variance  will   be.  
14. Posterior  HC5  Distribu/ons   Isofenphos !p Density 0.0 0.2 0.4 0.6 0.8 1.0 1.2 -4 -2 0 2 Pentachlorophenol !p Density 0.0 0.5 1.0 1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Model [Default] [H: Q = !] [H: Q = {!}] n  =  5   n  =  24   log10 (HC5 )   log10 (HC5 )   Status  quo   Extrapolate   Interpolate   Model  Assump/on   Status  quo  =  REACH  Technical  Guidance  Document  with  log-­‐normal  SSD   Extrapolate  =  ecosystem  is  an  infinitely  large  collec/on  of  species   Interpolate  =  ecosystem  comprised  of  77  species  listed  in  database   hierarchical   models   Aldenberg  &   Jaworska  (2000);   EES  
15. Conclusions   •  The  SSD  concept  is  not  defunct!     •  Hierarchical  modelling  and  Bayesian  sta/s/cs   open  up  the  op/on  for  ‘beaer’  modelling  with   transparent  uncertainty  propaga/on.   •  Useable  for  mul/ple-­‐hypothesis  tes/ng  and   risk  management.  
16. Acknowledgements   [DATA]  Sandy  Raimondo  and  Mace  Barron  (U.S.   EPA,  Gulf  Ecology  Division)   [DISCUSSION]  Mick  Hamer  (Syngenta)  and   Malyka  Galay-­‐Burgos  (ECETOC)    
17. Exis/ng  Hierarchical  Approaches   •  Lu]k  &  Aldenberg  (1997),  ET&C   •  European  Food  Safety  Authority  (2005)   •  Jager  et  al.  (2007),  EES   •  Morton  (2008),  Environmetrics   •  U.S.  EPA  Web-­‐ICE  Program(?)   Common  theme:  use  data  from  mul/ple  chemicals  to   improve  future  risk  assessments