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ARGONNENATIONALLABORATORY 970 0 SouthCas s Avenue , Argonne , Illinoi s 6043 9

DRAF T —D O NOT CIT E ESTIMATINGTH ERISKS O F LEAD-INDUCE D HEALT H EFFECT S

b y Thoma s S . Wallsten * an dRonal dG . Whitfiel d Energ y an dEnvironmenta l System s Division Decisio nan dSyste mScience s

Januar y 198 6

wor k sponsore db y U.S . ENVIRONMENTALPROTECTIO NAGENC Y Offic e of Ai r Qualit y Plannin g an dStandard s 

## 2T- £ 

## ~$~ 

## tr

*L.L . Thurston e Psychometri c Laboratory , Universit y of Nort hCarolina , Chape l Hil lP. 3

CONTENT S ABSTRAC T 1 1 INTRODUCTIO N 1 1. 1 Overvie w 2 1. 2 Motivatio n 3 1. 3 Judgmenta l Probabilit y Encodin g 7 1. 4 Ris k Assessmen t

Strateg y 9 1. 5 Dose-Respons e Uncertaint y 1 0 2 PROBABILISTI C DOSE-RESPONS ERELATIONSHIP S FO RLEAD-INDUCE D ELEVATE

D ERYTHROCYT EPROTOPORPHYRI NLEVEL S 1 1 3 PROBABILISTI C DOSE-RESPONS EFUNCTION S FO RLEAD-INDUCE D HEMOGLOBI

N DECREMENT S 1 7 3. 1 Protoco l Developmen t 1 8 3. 2 Protoco l Outlin e 1 8 3. 3 Conduc t

of th e Session s • 2 0 3. 4 Encodin g th e Judgment s 2 1 3. 5 Representin g th e Judgment s 24 3. 6 Th e Expert s 2 6 3. 7 Result s 2 8 3.7. 1 Hemoglobi n Level s < 1 1 g/dL , Age s 0- 3 Year s 2 8 3.7. 2 Hemoblobi n Level s < 1 1 g/dL , Age s 4- 6 Year s 3 2 3.7. 3 Hemoglobi n Level s < 9. 5 g/dL , Age s 0- 3 Year s 3 5 3.7. 4 Hemoglobi n Level s <

_9. 5 g/dL , Age s 4- 6 Year s 3 8 3. 8 Discussio n 3 8 4 PROBABILISTI C DOSE-EFFEC T AN D DOSE-RESPONS ERELATIONSHIP S FO R LEAD-INDUCE D I Q DECREMENT S 4 2 4. 1 Protoco l Developmen t 4 6 4. 2 Protoco l Outlin e 47 4. 3 Conduc t

of th e Session s 4 8 4. 4 Encodin g th e Judgment s 4 9 4. 5 Representin g th e Judgment s 5 0 4. 6 Th e Expert s 5 2 4. 7 Result s 5 2 4.7. 1 Contro l Grou p Mea nI Q 5 3 4.7. 2 Within-Grou p I Q Standar dDeviatio n5 5 4.7. 3 Mean IQ Decrement s fo r th e Low SE S Grou p 5 5 4.7. 4 Mean I Q Decrement s fo r th e Hig hSE S Grou p 60 4.7. 5 Chang e in Percentag e of Lo w SE S Grou p wit hIQ s < 8 5 60 4.7. 6 Chang e in Percentag e of Hig hSE S Grou p wit hIQ s < 8 5 6 3 4. 8 Discussio n 6 6

t nCONTENT S (Cont'd )

5 ESTIMATE

D RISK S O FADVERS EHEALT H EFFECT S UNDERALTERNATIVE AIR-LEA D SCENARIO S 67 5. 1 Exposur e Estimate s 67 5. 2 Ris k Result s fo r

EP7 3 5. 3 Ris k Result s fo r

Hemoglobi n7 8 5. 4 Ris k Result s fo r

I Q 8 4 5.4. 1 Expecte dIQ . Decremen t 8 5 5.4. 2 Increase dProbabilit y o f Lead-Induce dI Q Level s Bein g < IQ * 8 8 REFERENCE S 9 5 APPENDI X A : Fittin g Function s t o Dat ao nLead-Induce dElevate d

Erythrocyt e Protoporphyri nLevel s 9 6 APPENDI X B : Hemoglobi n 9 9 APPENDIX C : Intelligenc e Quotien t 15 0 APPENDIX D : Ris k

Estimate s 20 5

TABLE S 1. 1 Illustrativ e Ris k

Outpu t fo r aSpecifie dHealt hEffec t Give nFul l Informatio n 6 1. 2 Illustrativ e Ris k

Outpu t fo r aSpecifie dHealt hEffec t Give nIncomplet e Informatio n 8 2. 1 Sampl e Size s Base do n Blood-Lea dLeve l fo r Piomelli' s Dat a1 4 3. 1 Consultant s fo r

th e Hemoglobi nProtoco l 1 9 3. 2 Expert s Wh

o Participate di n th e Hemoglobi nEncoding s 2 7 4. 1 Consultant s fo r

th e I Q Protoco l 4 4 4. 2 Expert s Wh

o Participate din th e I Q Encoding s 4 5 5. 1 198 0 Populatio n Dat afo r Selecte dU.S . Poin t

Source s o f

Lea d Emission s 6 9 5. 2 Comparativ e Ai r

Qualit y a t

Censu s Trac t

Centroid s Surroundin g Modele dPoin t

Source s 7 0 5. 3 Geometri c Mean Blood-Lea dLevel s fo r 84-Mont hCohort s 7 4

I VTABLES (Cont'd )

A. l Probabilit y Distribution s an dParameter s fo r Piomelli' s Dat ao n Erythrocyt e Protoporphyri n Level s amon g New Yor k Cit y Childre n 9 8 B. l Summar y of

Variable s Pertainin g t o th e Normal-On-Log-Odd s Functio n11 7 B. 2 Encode dProbabilit y Judgment s o f Expert s Regardin g Lead-Induce d Hemoglobi n Decrement s 120 B. 3 Summar y of

Function s Fi t

t o th e Probabilisti c Judgment s of Expert s Regardin g Lead-Induce dHemoglobi nDecrement s 12 4 B. 4 Summar y an dCompariso n of Judgment s an dFitte dFunction s Concernin g Lead-Induce dHemoglobi nDecrement s 12 9 C l Encode dJudgement s abou t th e MeanI Q of

Childre nSheltere dfro m Lea dExposur e 16 9 C. 2 Encode dJudgement s abou t Populatio nStandar dDeviatio n17 0 C. 3 Encode dJudgement s abou t MeanI Q Decrement s of Childre nExpose d t o Lea d17 1 C. 4 Parameter s of

Function s Fi t

t o th e Probabilisti c Judgment s of Expert s Regardin g Mean I Q Level s amon g Childre nSheltere dfro m Lea dExposur e 17 7 C. 5 Summar y o f

Function s Fi t

t o th e Probabilisti c Judgment s o f Expert s Regardin g Populatio n Standar dDeviatio nfo r IQ Level s 17 8 C. 6 Summar y of

Functio n Fi t

t o th e Probabilisti c Judgment s of Expert s Regardin g Mean IQ Decrement s amon g Childre nExpose dt o Lea d17 9 C. 7 Summar y an dCompariso n of Judgment s an dFitte dFunction s Concernin g Lead-Induce dI Q Effect s 18 2 D. l Upper

- an dLower-Boun dEstimate s of th e Geometri c MeanBlood-Lea dLevel s Childre nLivin g aroun dSelecte dU.S . Source s of Lea dEmission s 20 6 D. 2 Specificatio n of

Distribution s fo r

th e Risk s of

Elevate dEPLevel s amon g Childre n Age s 0- 6 Year s 20 8 D. 3 Summar y of

Hemoglobi n Ris k

Distribution s fo r

Childre nAge d0- 3 Year s 21 0 D. 4 Summar y of

Distribution s fo r

Expecte dI Q Decremen t a t Ag e 7 fo r Lowe r SE S Population s of

Childre n22 2 D. 5 Summar y o f

Distribution s fo r

Increase dProbabilit y of IQ^IQ * a t

Ag e 7 fo r Lowe r SE S Population s of

Childre n22 7P. 6

FIGURE S 2. 1 Mea

n Respons e Rat e vs . Dos e fo r E PLevel s >_3 3 yg/d Lan d5 3 yg/d L1 3 2. 2 Median Respons e Rat e an d90 % Credibl e Interva l vs . Dos e fo r EP= 3 3 yg/d L1 5 2. 3 Median Respons e Rat e an d90 % Credibl e Interva l vs . Dos e fo r E P= 3 5 yg/d L1 6 3. 1 Dose-Respons e Functions , Hemoglobi nLeve l ±1 1 g/dL , Ages 0- 3 Year s 2 9 3. 2 Compariso n of

Judgments , Hb 5 1 1 g/dL , Age s 0- 3 Year s 3 1 3. 3 Dose-Respons e Functions , Hemoglobi nLeve l <_1 1 g/dL , Age s 4- 6 Year s 3 3 3. 4 Compariso n of

Judgments , Hb <_1 1 g/dL , Age s 4- 6 Year s 3 4 3. 5 Dose-Respons e Functions , Hemoglobi nLeve l <_9, 5 g/dL , Age s 0- 3 Year s 3 6 3. 6 Compariso n of

Judgments , Hb < 9.5 , Age s 0- 3 Year s 3 7 3. 7 Dose-Respons e Functions , Hemoglobi nLeve l <_9. 5 g/dL , Ages 4- 6 Year s 3 9 3. 8 Compariso n of

Judgments , H

b < 9.5 , Age s 4- 6 Year s 4 0 4. 1 Judgment s abou t

Contro l Grou p MeanI Q 5 4 4. 2 Judgment s abou t

O, Q 5 6 4. 3 Judgment s abou t

A

—fo r aLowe r SE S Populatio n5 7 4. 4 Compariso n of

Judgment s abou t

A

—fo r aLowe r SE S Populatio n5 9 4. 5 Judgment s abou t

A

—fo r aHighe r

SE S Populatio n6 1 4. 6 Comparison s o f

Judgment s abou t

A

—fo r aHighe r

SE S Populatio n6 2 4. 7 Increase dProbabilit y of Havin g I Q < 8 5 fo r

aLowe r SE S Populatio n6 4 4. 8 Blood-Lea dLeve l Compariso no f Increase dProbabilitie s o f Havin g I Q < 8 5 fo r

aLowe r SE S Populatio n, 6 5 5. 1 Respons e Rate , % , wit hE P> 3 3 yg/d L7 6 5. 2 Respons e Rate , % , wit hEP> 5 3 yg/d L7 7 5. 3 Poin t

Sourc e 5 , wit hHb < 1 1 yg/d L7 9 V IP. 7

FIGURES (Cont'd ) 5. 4 Poin t

Sourc e 5 , wit hHb < 9. 5 yg/d L8 0 5. 5 Poin t

Sourc e 2 , wit hHb < 1 1 yg/d L8 1 5. 6 Poin t

Sourc e 2 , wit hH b < 9. 5 yg/d L8 2 5. 7 Expecte dIQ Decremen t fo r Lowe r SE S Childre nLivin g aroun d Sourc e 5 8 6 5. 8 Expecte dI Q Decremen t fo r Lowe r SE S Childre nLivin g aroun d Sourc e 2 8 7 5. 9 Increase dProbabilit y o f Childre nLivin g aroun dSourc e 5 Havin g I Q Level s £7 0 9 0 5.1 0 Increase dProbabilit y o f Childre nLivin g aroun dSourc e 5 Havin g I Q Level s < 8 5 9 1 5.1 1 Increase dProbabilit y of Childre nLivin g aroun dSourc e 2 Havin g I Q Level s < 7 0 9 2 5.1 2 Increase dProbabilit y of Childre nLivin g aroun dSourc e 2 Havin g IQ Level s < 8 5 9 3

V l lP. 8

ESTIMATIN

G TH E RISK S OF LEAD-INDUCED HEALT H EFFECT S b y Thoma s S . Wallste nan dRonal dG . Whitfiel d

ABSTRAC T

to be completed. 1 INTRODUCTION Th e Clea n Ai r

Ac t charge s th e U.S . Environmenta l Protectio nAgenc y (EPA ) wit h settin g an dreviewin g bot hprimar y an dsecondar y Nationa l Ambien t Ai r Qualit y Standard s (NAAQS ) fo r

selecte dpollutants
. Eac hprimar y standar dmus t b e se t a t aleve l sufficien t t o protec t

publi c healt hwit ha nadequat e margi nof safety
. Thi s repor t present s th e result s of

aris k assessmen t

performe dt o assis t

inth e revie w o f

th e primary
. NAAQ S fo r

lead
. Fo r eac hreview , th e scientifi c basi s fo r revisin g th e primar y lea dNAAQ S i s presente din a n update ddocumen t entitle dAir

Quality Criteria for

Lead, hereafte r referre dt o a s th e criteri adocumen t (CD) . I t

summarize s an devaluate s availabl e scientifi c evidenc e abou t th e advers e healt heffect s of lead
. A

nEPA staf

f pape r i s the n written , whic hconsider s th e informatio ninth e C D inspecifyin g th e element s EPA staf f member s believ e t o b e critica l i n revisin g th e lea dNAAQS . Th e staf f pape r i s intende d t o bridg e th e ga p betwee n th e scienc e presente dinth e C D an dth e informatio nneede db y th e EPA Administrato r i n settin g ane w ambien t standar dfo r

lead
. Particula r

attentio n i s pai dt o thos e area s wher e judgment s mus t b e base do ncarefu l interpretatio n of imperfec t

evidence
. Indeed , t o provid e th e require dadequat e margi nof safety , uncertaint y mus t

b e take n int o consideratio na t eac hste p o f

th e process .P. 9

Scientifi c uncertaint y wa s handle di nahighl y simplifie dmanne r whe nth e 197 8 air-lea dstandar dwa s set . Instea dof quantifyin g uncertainty , deterministi c assumption s wer e mad e tha t

wer e considere dconservativ e give nqualitativ e assessment s of th e uncertaint y associate dwit havailabl e evidence
. Calculation s base do nthes e assumption s resulte dinaprimar y lea dNAAQ S o f 1. 5 y g Pb/m ° o f

air
. Soo n thereafte r

EPA' s Offic e o f

Ai r Qualit y Plannin g an dStandard s (OAQPS ) bega n explorin g method s of ris k assessmen t

tha t incorporate duncertaint y i n th e standard-settin g proces s in aformal , defensible , an dope nmanner . Thi s repor t present s th e outcom e of

forma l ris k

assessment s regardin g thre e advers e healt heffect s of lea dt o ai dth e EPA Administrato r i n determinin g a nadequat e margi nof safet y fo r

th e curren t revie w of

th e primar y lea dNAAQS . Thi s wor k wa s funde db y EP A unde r anInteragenc y Agreemen t

betwee n EPA an dth e U.S . Departmen t of Energy . O f th e man y potentia l advers e healt heffect s associate dwit hexposur e t o lead , EPA' s OAQP S selecte dthre e fo r inclusio ni nthi s ris k assessment : hemoglobi n decrement , elevate derythrocyt e protoporphyri n(EP ) levels , an dintelligenc e quotien t (IQ ) decrement
. I t

was decide dt o limi t

th e populatio na t

ris k fo r thi s ris k assessmen t

t o al l U.S . childre n fro mbirt hthroug hthei r sevent hbirthdays
. Pregnan t wome n(fetus) , wh o ar e particularl y sensitiv e t o lead , ar e no t explicitl y include dinthi s analysis
. 1. 1 OVERVIE

W T o th e exten t

possible , detail s o f

th e method s an dresult s o f th e ris k assessment s ar e presente di n appendixe s rathe r tha ninth e bod y of

thi s report . Nevertheless , reader s wil l obtai nagoo dunderstandin g of th e ris k assessment s fro mth e mai ntext . Sectio n 1. 2 present s th e motivatio n fo r th e particula r

for mof th e ris k assessment s tha t

wer e carrie d out . Sectio n 1. 3 discusse s th e rol e of judgmenta l probabilit y encodin g i nth e ris k assessment . Sectio n 1. 4 summarize s th e overal l ris k assessmen t

strategy , whil e Sec . 1. 5 discusse s dose-respons e uncertainty
.P.1 0

Sectio n 2 treat s th e dose-respons e uncertaint y fo r lead-induce delevate dE P levels
. Becaus e relativel y complet e dat aar e available , judgmenta l probabilit y encodin g wa s unnecessar y i n considerin g lead-induce dchange s inEPlevel
. Section s 3 an d4 focu s o n dose-respons e uncertaint y fo r lead-induce dhemoglobi nan dI Q decrements , respectively
. Judgmenta l probabilit y encodin g wa s require dinthes e cases ; th e encodin g procedure s ar e describe din th e respectiv e section s prio r t o th e summarie s of

th e results
. Sectio n 5 discusse s possibl e blood-lead * (PbB ) distribution s an dthei r level s o f uncertaint y unde r

alternativ e NAAQS . Th e uncertaint y fo r eac hhealt heffec t

i s the n combine dwit htha t

fo r eac halternativ e Pb B distributio nt o yiel dderive dris k estimates
. Th e repor t

conclude s wit hfou r

appendixes
. 1. 2 MOTIVATION Th e purpos e of

aris k assessmen t

fo r lea dhealt heffect s i s t o estimat e probabilit y distribution s ove r fraction s of

th e populatio na t

ris k tha t woul dsuffe r specific , well-define dhealt heffect s unde r alternativ e primar y NAAQ S fo r lead
. Th e probabilitie s mus t

b e estimate di naformal , defensibl e manne r tha t i s ope nt o publi c scrutiny
. The y wil l generall y reflec t tw o source s of

uncertainty , on e derivin g fro mth e characteristic s o f

th e dat aan dth e othe r fro malac k

of knowledge
. Th e forme r typ e of uncertaint y reflect s measuremen t an dsamplin g error , an dprobabilitie s ar e generall y calculate db y mean s of standar dstatistica l procedures
. Althoug hthi s typ e of uncertaint y ca n b e altere db y mean s of experimenta l manipulations , i t canno t b e eliminate dcompletel y in an y finit e study
. Th e latte r

typ e of uncertaint y reflect s th e paucity , incompleteness , an dindirec t natur e of

muc hof

th e availabl e data
. Fo r example , i t

i s frequentl y necessar y t o dra w inference s abou t

ahealt heffec t

i naspecifi c populatio no nth e basi s of epidemiologica l
•Bloo dlea di s generall y use da s th e inde x of lea dexposur e i nhealt hstudie s an di s use di n thi s way inthi s assessment .o r

clinica l dat ao n differen t population s unde r

varyin g o r

differen t

exposur e conditions , o r fro mlaborator y dat ao n othe r specie s o r

o nin vitro preparations
. Thi s typ e of uncertaint y i s judgmental , an dn o statistica l technique s exis t fo r quantifyin g it
. I t

can , however , b e quantifie dusin g appropriat e procedure s t o encod e subjectiv e probabilities
. Differen t expert s wil l asses s th e uncertaint y differently , dependin g o nthei r fait hi n th e implici t o r explici t theorie s require dfo r

extrapolatio nfro mth e dat at o th e effec t i n questio nan do n thei r

perceptio n o f

th e distanc e ove r

whic hth e extrapolatio nmus t b e made
. Therefore , i t

i s necessar y tha t

th e procedure s accommodat e an drepresen t a possibl e divergenc e of

judgments
. Th e leve l of thi s typ e of

uncertainty , a s wel l a s th e degre e of

divergenc e amon g experts , ca nb e reduced , an dconceivabl y eve neliminated , b y increasin g th e amoun t of availabl e knowledge
. Conductin g aris k

assessmen t

i nwhic hthes e tw o type s of uncertaint y ar e distinguishe dprovide s on e mean s fo r respondin g t o achalleng e issue db y William Ruckleshau s i n aspeec hgive n a t Princeto nUniversit y whe nh e wa s EP A Administrator
. H e stated : I f I amgoin g t o propos e control s tha t ma y hav e seriou s economi c an d socia l effects , I nee dt o hav e som e ide ao f ho w muc hconfidenc e shoul d b e place di n th e estimate s o f ris k tha t prompte dthos e control s (Ruckleshaus , 1984 , p . 158)
. I n th e sam e talk , h e wen t o n t o propos e som e principle s fo r reasonabl e discussion s abou t risk : First , w e mus t insis t o nris k

calculation s bein g expresse da s distribution s of

estimate s an dno t

a s magi c number s tha t ca nb e manipulate dwithou t

regar dt o wha t

the y reall y mean . W

e mus t tr y t o displa y mor e realisti c estimate s of ris k t o sho w arang e of probabilities
. T o hel p d o this , w e nee dne w tool s fo r quantifyin g an d orderin g source s o f

uncertainty , an dfo r

puttin g the mi nperspective
.P.1 2

Second , w e mus t

expos e t o publi c scrutin y th e assumption s tha t underli e ou r

analysi s in managemen t of ris k (Ruckleshaus , 1984 , p . 158)
. I f ther e wer e complet e informatio nrelevan t t o agive nhealt heffec t i n a population , the n th e statistica l uncertaint y coul db e represente db y asingl e probabilit y distributio nfo r

eac halternativ e NAAQ S unde r consideration
. A hypothetica l exampl e of aris k assessmen t

outpu t of thi s typ e i s give ninTabl e 1.1. * Fo r example , in thi s hypothetica l situation , th e probabilit y i s 0.0 1 tha t fewe r tha n0.5 % of

th e populatio n wil l suffe r th e healt heffect , th e probabilit y i s 0.0 5 tha t fewe r tha n1 % o f

th e populatio n wil l suffe r it , an ds o forth
. (Equivalently , th e probabilit y i s 0.9 9 tha t mor e tha n99.5 % of

th e populatio n wil l no t

suffe r th e healt heffect , 0.9 5 tha t mor e tha n99 % wil l no t suffe r it , etc. ) Alternativ e NAAQ S 4 provide s th e greates t degre e of

protection
. Presumably , outpu t

of thi s sor t

woul db e helpfu l t o th e EP A Administrato r in selectin g astandar dtha t i n hi s o r

he r judgmen t

woul dprotec t

th e publi c healt hwit ha n adequat e margi n of

safety
. Fo r

example , i

f h e o r sh e determine dtha t

th e inten t

of th e Clea n Ai r

Ac t i s me t b y protectin g 99.5 % of th e populatio na t

ris k wit hprobabilit y 0.99 , the n alternativ e 1 woul db e selected
. I f th e inten t

i s me t b y protectin g 99.5 % of th e populatio n wit hprobabilit y 0.95 , the nalternativ e 2 i s th e appropriat e one . O f course , thi s exampl e i s highl y simplifie dbecaus e multipl e healt heffect s wil l generall y b e o f interest , an dpopulation s ca n b e define dinvariou s ways . However , i t illustrate s th e rol e tha t forma l ris k

analysi s ca n pla y inth e standard-settin g process . Generally , th e informatio n relevan t t o aparticula r

healt heffec t

associate dwit h an environmenta l agen t wil l b e indirec t

an dincomplete , an dexpert s wil l diffe r wit h regar dt o th e associate djudgmenta l uncertainty
. Th e exten t o f agreemen t

acros s expert s i s ameasur e of ho w fir mth e probabilit y estimate s are , an di s usefu l informatio n insettin g th e standard
. On e wa y of

representin g th e exten t of agreemen t

i s t o propagat e th e encode d probabilitie s of

eac hexper t

throug hth e entir e analysis , whic hresult s i nafamil y ofP.1 3

TABL E 1. 1 Illustrativ e Ris kOutpu tfo raSpecifie d Healt h Effec tGive n Ful l Informatio n

Respons e

R 0 0.5 % 1.0 Z 1.5 % Rat e Probab i

1
0.0 1 0.0 5 0.4 1 lit

y (Re s pons e Rat e NAAQ S Alternativ

e 2
0.0 6 0.1 1 0.5 3 3

0.1 9 0.2 3 0.6 A 

# ±v

4
0.3 8 0.6 0 0.7 5P.1 4

7 distribution s unde r

eac halternativ e NAAQS . A hypothetica l exampl e inthi s cas e i s show nin Tabl e 1.2 . Unde r alternativ e 1 , fo r

example , ther e i s a0.0 1 t o 0.0 2 probabilit y tha t fewe r tha n 0.5 % o f

th e populatio nwil l suffe r th e healt heffect
. Th e close r togethe r ar e th e distribution s i n afamily , th e mor e fir mar e th e probabilit y estimates
. Insettin g th e NAAQS , th e degre e o f firmnes s i nth e estimate s ca nb e take n int o accoun t i n an y o f

anumbe r

o f ways . Fo r

example , on e criterio nmigh t b e tha t 99.5 % o f th e populatio n b e protecte dwit haprobabilit y whos e lowe r boun di s n o les s tha n0.0 1 o r wit haprobabilit y estimate dt o b e 0.0 2 i na t least , fo r

example , 75 % o f

th e ris k distributions
. Onales s forma l level , th e probabilit y encodin g of eac hexper t

ca n b e accompanie db y adiscussio n of th e relevan t

data
. Summarie s of

thes e discussion s ca n b e a nimportan t

supplemen t

t o th e probabilit y distribution s an dprovid e guidanc e o n thei r use . Th e ris k

assessment s in thi s repor t yiel doutput s simila r

t o thos e i nTabl e 1. 2 plu s associate ddiscussions
. However , whil e endeavorin g t o mak e th e output s full y interpretable , w e d o no t presum e t o sugges t

th e criteri atha t

shoul dgover nthei r

us e in th e standard-settin g process . 1. 3 JUDGMENTAL PROBABILIT Y ENCODING W e wis ht o emphasiz e tha t subjectiv e probabilit y encodin g i s unnecessar y wheneve r adequate , direc t

dat aar e available
. However , mor e ofte ntha nnot , suc hdat a ar e no t available , an dth e onl y alternative s t o encodin g judgmenta l probabilitie s wil l b e t o trea t th e adde duncertaint y qualitatively , whic hcurrentl y canno t b e don e i narigorou s manner , o r

t o ignor e i t

altogether , whic hi s indefensible
. Fo r encode djudgmenta l probabilitie s t o b e useful , the y mus t mee t tw o criteria
. Th e firs t i s subtle , an ditsel f

judgmental , bu t

i s nevertheles s ver y important ; namely , judgment s mus t

b e obtaine dfro mrespecte dexpert s wh o spa nth e rang e of respecte dP.1 5



### TABL E 1. 2 Illustrativ e Ris

kOutpu tfo raSpecified Healt

h Effec tGive

n Incomplet

e Informatio

n

Respons e

R 0 0.5 % 1.0 % 1.5 % Rat e Probabilit y(Re s

1
0.01-0.0 2 0.01-0.0 5 0.29-0.4 1 pons e Rat e <

NAAQ S Alternativ e 2
0.02-0.0 6 0.04-0.1 1 0.40-0.5 3 3

0.11-0.1 9 0.15-0.2 3 0.53-0.6 4 R 0 )

4

0.26-0.3 8 0.49-0.6 0 0.68-0.7 5P.1 6

opinion
. Althoug hi t

woul dappea r

t o b e difficul t

t o establis hwha t

th e rang e of

opinio n i s an dwh o th e appropriat e expert s are , i npractic e th e relevan t issue s ten dt o b e debate d frequentl y an dpublicl y enoug htha t suc hdecision s ar e possible
. Fo r th e presen t

ris k assessments , EPA' s OAQP S selecte dth e expert s whos e judgment s wer e t o b e encoded
. Althoug hthei r name s ar e include dwit hth e assessment , thei r individua l judgment s an ddiscussion s ar e identifie db y cod e lette r only
. Thus , user s of th e ris k assessment s ca n decid e whethe r th e ful l rang e of

opinio ni s represented , an d th e individua l expert s ca n fee l fre e t o giv e thei r bes t response s withou t

worryin g tha t the y ma y involv e themselve s i n endles s argument s o r discussion s wit hother s wh o ma y disagree
. Th e secon dcriterio n i s tha t a nindividual' s encode dprobabilit y judgment s mus t b e stabl e ove r

tim e (barrin g ne w information) , coheren t i nawell-define dway , an d accuratel y represen t

hi s o r he r uncertainty
. Researc hrelatin g t o thes e issue s ha s bee n reviewe db y Wallste n an dBudesc u (1983) , an da nexperimen t specificall y addressin g the m i n th e presen t

contex t wa s performe db y Wallste ne t al
. (1983) . Th e technique s use di n th e presen t

wor k wer e base do n thi s foundatio nbu t als o relie do npilo t

wor k describe din Whitfiel dan dWallste n (1984) . 1. 4 RIS K ASSESSMEN

T STRATEG Y Th e strateg y employe di n thi s analysi s i s mos t easil y understoo db y firs t assumin g tha t n o uncertaint y i s involved
. I nthi s case , on e firs t

specifie s th e dose-respons e curv e fo r eac hselecte dhealt heffec t of lead
. Fo r

awell-define dpopulation , well-define d exposur e conditions , an dawell-define dphysiologica l o r behaviora l effect , adose

respons e curv e plot s th e percentag e of th e populatio nexhibitin g th e effec t a s afunctio n of dos e level
. Thi s functio n i s assume dt o b e unaffecte db y alternativ e air-lea d scenarios
. However , th e alternativ e scenario s d o determin e th e distributio nof dos e level s i nth e population
. Thus , on e ca ncombin e th e dose-respons e functio nfo r ahealt hP.1 7
1 0 effec t wit hth e dos e distributio n unde r eac halternativ e scenari o t o yiel dth e percentag e of th e populatio n tha t

woul dsuffe r

th e effec t

unde r tha t alternativ e scenario
. I nreality , ther e i s uncertaint y a t eac hstep , an di t

mus t b e incorporate dint o th e analysi s in a manne r providin g fina l output s of th e formshow ninTabl e 1. 1 o r 1.2 . 1. 5 DOSE-RESPONS EUNCERTAINT Y I n additio n t o th e tw o type s o f uncertaint y discusse di nSec . 1.2 , ther e i s ambiguit y regardin g th e leve l of a neffec t

tha t shoul db e considere dadvers e an dfo r whic hadose-respons e functio n woul db e of interest
. Thi s issu e wa s deal t wit hin th e presen t wor k b y simpl y selectin g tw o level s of th e relevan t

variabl e fo r

eac hhealt h effec t an destimatin g adose-respons e functio nfo r each
. Th e level s wer e selecte ds o a s t o spa nth e rang e tha t

arguabl y delimit s norma l fro madvers e consequences . I t mus t b e emphasize dtha t

apopulatio ndose-respons e functio nexist s fo r agive n effec t unde r specifie dconditions
. Whe nrelativel y complet e dat aar e availabl e regardin g th e dose-respons e functio n of interest , th e populatio nvalue s ar e stil l uncertai nbecaus e of samplin g an dmeasuremen t error . Becaus e thi s was th e cas e wit helevate dEPlevels , astraightforwar dapplicatio n of th e appropriat e probabilit y distribution s t o th e dat a yielde dth e desire dresult s (se e Sec . 2) . However , whe nth e dat aregardin g th e dose

respons e functio n of

interes t

ar e incomplet e o r

indirect , the nther e i s judgmenta l uncertaint y associate dwit hextrapolatio n(se e Sec . 1.3) . Thi s was th e cas e wit hbot hth e hemoglobi nan dI Q decrements
. Becaus e uniqu e factor s wer e associate dwit heac hof thes e instances , th e procedure s an dmodel s employe dfo r quantifyin g th e uncertaint y wer e different
.P.1 8
1 1 2 PROBABILISTIC DOSE-RESPONS E RELATIONSHIP S FORLEAD-INDUCED ELEVATE

D ERYTHROCYT

E PROTOPORPHYRI

N LEVEL

S Piomell i e t

al
. (1982 ) examine dPb B an dE Plevel s fro m200 4 Ne w Yor k Cit y childre n age s 2 t o 1 2 years , wh o ha dbee nscreene dt o accoun t fo r th e effect s of

iro n deficienc y an dothe r

confoundin g variables
. Empirica l dose-respons e curve s wer e presente dfo r

tw o level s of

EPelevation ; i neac hcase , th e percentag e of th e sampl e wit h EP s abov e th e critica l leve l was plotte da s afunctio nof Pb B level
. Ou r

consultant s fel t tha t th e populatio n fro mwhic hth e sampl e wa s draw nwa s sufficientl y clos e t o th e populatio n of

interes t (childre n up t o thei r

sevent hbirthdays ) tha t extrapolatio nwa s no t necessary . Th e dat awer e use ddirectly. * Becaus e of

th e ver y carefu l procedure s employe db y Piomell i e t al
. (1982) , i t

i s necessar y t o conside r

onl y sampling , an dno t measurement , error . Eac hof th e point s o n adose-respons e functio n i s base do nanumbe r o f observation s (N) , of

whic hX exhibi t th e healt heffec t

an dth e remainde r

( N- X ) do not . Thes e dat aprovid e a nestimat e Pof th e tru e populatio n proportio n Psufferin g th e healt heffec t a t th e Pb B leve l in question
. O

f course , uncertaint y i s associate dwit hth e estimat e becaus e of samplin g error . I n classica l probabilit y theory , thi s uncertaint y i s handle db y usin g th e binomia l distributio nwit hparameter s P, X , an dN t o calculat e confidenc e interval s aroun dPa s a n estimat e of

P , o r mor e generall y t o calculat e aprobabilit y distributio nove r P . Thus , th e outpu t i s aprobabilit y distributio nove r th e percentag e of

th e populatio naffecte da t eac hobserve dPb B level
. Th e Bayesia n approac hi s t o calculat e aposterio r probabilit y distributio nove r P , give n th e dat aan daprio r distributio nove r

P . Whenth e prio r

distributio ni s represente d a s abet adistributio n wit hparameter s aan db , the nth e posterio r distributio ni s als o
•Simila r dat awer e collecte db y Hammon de t al
. (1985 ) o nasampl e fro madifferen t populatio n o f

children
. Th e dose-respons e function s wer e ver y simila r t o thos e obtaine d b y Piomell i e t

al
. (1982) , bu t

certai nnonindependencie s inth e dat adu e t o thei r longitudina l natur e mad e the munsuitabl e fo r th e presen t

purpose .P.1 9
1 2 beta , bu t wit hparameter s a+ X an db + ( N- X) . A conservativ e strateg y i s t o assum e a diffus e prio r

stat e of informatio n characterize db y a= b = 0 (Winkler , 1972) . I nthi s case , th e resultin g probabilit y distributio nove r th e fractio nof

th e populatio naffecte da t a give n Pb B leve l i s ver y clos e t o tha t calculate di nth e classica l manner . Technically , however , th e interpretatio n i s different , an dth e Bayesia napproac huse di s th e on e mos t suitabl e fo r

ou r purposes . Furthe r

detail s ar e provide dbelo w an dinApp . A . Figur e 2. 1 present s th e dose-respons e dat afo r tw o E Plevel s (Piomell i e t

al. , 1982) , an dTabl e 2. 1 present s th e sample-siz e data
. Th e tw o EPlevel s (3 3 yg/d Lan d5 3 yg/dL ) wer e eac hconsidere da s adverse
. Expression s ca nb e determine dfo r th e mea n dose-respons e curve s tha t ar e shown
. Thes e expressions , liste dinApp . A , ar e function s of Pb B leve l an dwha t

Piomell i e t

al
. cal l "natura l frequencies " fo r th e occurrenc e of

EP level s abov e 3 3 yg/d Lan d5 3 yg/dL , an dinvolv e th e norma l probabilit y distributio n function
. A s discusse dabove , th e bet adistributio ni s th e prope r distributio nt o us e t o describ e uncertaint y abou t th e tru e populatio nproportio nsufferin g fro melevate dEP levels
. However , fo r

Pb B level s abov e 5 yg/d Lan dbelo w 5 0 yg/dL , sampl e size s ar e larg e enoug htha t

th e norma l distributio nca nb e use dt o closel y approximat e bet a distribution s fo r

bot hEPlevels
. Tabl e A. l i nApp . A summarize s th e probabilisti c dose

respons e function s tha t wer e derived
. Figure s 2. 2 an d2. 3 sho w media ndose-respons e relationship s an d90 % credibl e interval s fo r

th e 3 3 yg/d Lan d5 3 yg/d LE Plevels , respectively
. Fo r al l case s inwhic ha norma l approximatio n i s adequate , media nan dmea nrespons e rate s ar e identical , an d confidenc e interval s ar e symmetrica l abou t th e media nvalues
. Th e media nvalu e i s tha t respons e rat e a t

whic hi t i s equall y likel y tha t

th e actua l rat e i s abov e o r belo w it
. Ther e i s aprobabilit y of

0.0 5 tha t

th e populatio nrespons e rat e i s belo w th e credibl e interva l rang e an daprobabilit y o f 0.0 5 tha t

i t i s abov e it
.P.2 0
1 3



### c n 99 H 

## I n 95 - <1 > o

* " . 

### wA l Q

_ 0 ) •V ) > 

### 90 H 75 - 

### 50- | 25 ^ 

### ? 10 * > D JZ 

### 5- 4 

### H 1 0 2 0 3 0 4 0



## Blood-Lea d Leve l (yiig/dL ) 5 0

FIGUR E 2. 1 Mea

n Respons e Rat e vs . Dos e fo rE PLevel s > 3 3 yg/d L and 5 3 yg/d L (Source: Adapte d from Piomell i e tal. , 1982 )I I '. » 1 1 II -

p I * JH""*-* - P.2 1

1 4 TABL E 2. 1 Sampl e Size s Base d o n Blood-Lea d Leve l fo rPiomeUi' s Dat a
Pb B (yg/dL )
0-1 0 10-2 0 20-3 0 30-4 0 40-9 8 No . of

Childre n 13 1 117 7 54 4 10 9 4 3 Source : Seaman , persona l communi catio n (1985) .1 5

99 - rj ) 

### ^ . 

### 95 - 

# 2% 90 

# " C§A I tn 75 - C >

^ o > 25 - > D 

### 10 * 

# H 90 % Credibl e Interva l

Media n

1 0 2 0 3 0 4 0 5 0 

## Blood-Lea d Leve l (jug/dL )

FIGUR E 2. 2 Median Respons e Rat e and 90 % Credibl e Interva l vs . Dos e fo r E P= 3 3 yg/d L1 6 P.2 3



### 99 - 3 . 95 - 

# 2% 90 

# " C?A I • » 75 " 

### c > 

# * i 50 

# - Q)Ll J C C rj ) 25
. • — 

# J 10 - fc* 5 - / 90 % / /) Credibl e Interva l

Media n

1 0 2 0 3 0 4 0 5 0 

### Blood-Lea d Leve l (/xg/6L)

FIGUR E 2. 3 Media

n Respons e Rat e an

d 90 % Credibl e Interva l vs . Dos e fo r E P= 5 3 yg/d LP.2 4

1 7 3 PROBABILISTIC DOSE-RESPONS E FUNCTION S FOR LEAD-INDUCED HEMOGLOBI N DECREMENT S Dat aar e ver y incomplet e regardin g dose-respons e function s fo r lead-induce d hemoglobi n decremen t i n th e ful l populatio nof U.S . childre nprio r

t o th e sevent h birthday
. Therefore , i t wa s necessar y t o encod e experts ' subjectiv e probabilitie s abou t th e populatio n respons e rate s a t eac hof severa l Pb B levels
. Encode dprobabilitie s hav e t o mee t tw o criteria
. On e i s tha t the y b e internall y consisten t b y specifi c criteri atha t wil l b e specifie dshortly
. Th e othe r i s tha t the y ar e satisfactor y t o th e expert s in th e sens e tha t

the y agre e tha t

th e encoding s properl y represen t thei r judgments
. Onl y afinit e numbe r

of Pb B level s ca nb e presente dfo r encoding ; inthi s stud y th e numbe r

wa s abou t

six
. However , i t

i s necessar y t o interpolat e betwee nlevel s t o us e th e judgment s in th e ris k assessments . Suc hinterpolation s ca nb e mad e b y fittin g a suitabl e probabilit y distributio n t o th e encode dvalues
. Th e distributio nmus t fi t th e judgment s b y areasonabl e mathematica l criterion , bu t equall y importantly , th e exper t mus t agre e tha t

th e functio n i s accurate . T o mee t al l thes e requirement s an dt o follo w th e recommendation s develope db y Wallste n e t

al
. (1983) , w e develope daprotoco l fo r th e probabilit y encoding s an dthe n me t wit heac hexper t

o n tw o occasion s separate db y abou t on e month
. Judgment s wer e encode ddurin g th e firs t session , an dfunction s wer e fi t t o the mprio r

t o th e nex t

visit
. Th e judgment s an dfunction s wer e reviewe ddurin g th e secon dsession , an dchange s wer e mad e tha t

wer e deeme dnecessar y b y th e expert . Whenrequired , ther e wa s additiona l follow-u p throug hth e mai l an db y phone
. Sectio n3. 1 describe s th e protoco l development , an dSec . 3. 2 outline s th e protoco l itself
. Th e manne r i nwhic hth e encodin g session s wer e conducted , th e probabilit y encodin g methods , an dth e procedure s fo r fittin g function s t o th e encode d judgment s ar e describe din Sees . 3.3 , 3.4 , an d3.5 , respectively
. Sectio n3. 6 indicate s whos e judgment s wer e encoded , Sec . 3. 7 summarize s th e results , an dSec . 3. 8 provide s som e summar y discussion
.P.2 5
1 8 3. 1 PROTOCOL DEVELOPMEN T Th e consultant s liste din Tabl e 3. 1 aide du s i ndevelopin g th e hemoglobi n probabilit y encodin g protocol
. Thei r assistanc e too k

man y forms , includin g discussin g th e literatur e wit hus , guidin g u s inreadin g ke y studies , an dcarefull y commentin g o n numerou s draft s o f

th e protocol
. Afte r studyin g relevan t

portion s o f

th e C D an ddiscussin g the ma t lengt hwit ha subse t of ou r consultants , wh o fo r

th e mos t

par t wer e th e author s of

thos e portions , w e prepare dafirs t

draft o f th e protocol
. Thi s draf t wa s show nt o thos e expert s a s wel l a s t o other s wh o wer e draw n fro mth e populatio nof peopl e whos e judgment s migh t b e encoded
. W

e worke dwit hthes e experts , structurin g th e proble mi nth e manne r w e woul d i f w e wer e goin g t o encod e thei r judgments , an drevise dth e protoco l accordingly
. In thi s fashion , th e protoco l wen t throug hanumbe r

o f drafts
. I

f al l th e respondent s viewe dth e proble minth e sam e way , thi s way was specifie din th e protocol
. I

f the y differe do r

indicate dtha t

other s migh t

diffe r fro mthem , w e allowe d th e individua l t o individualiz e th e scenario , subjec t onl y t o th e constraint s tha t th e obtaine djudgment s coul dma p int o th e res t of th e mode l an db e comparabl e acros s experts . Th e protoco l wa s ultimatel y structure dsuc htha t th e consultan t

healt hexpert s considere di t

reasonabl e an dindicate dtha t the y woul dfee l comfortabl e providin g th e desire dprobabilisti c judgments
. Th e protoco l wa s teste db y usin g i t t o encod e th e judgmenta l probabilitie s of tw o member s of

th e EPA staf

f familia r

wit hth e effect s of

lead
. Th e tes t

wa s considere d successfu l an di s reporte di n Whitfiel dan dWallste n(1984) . 3. 2 PROTOCOL OUTLIN E Th e ful l protoco l i s presente dinApp . B ; onl y agenera l outlin e i s provide dhere
. Sectio n 1 , th e introduction , indicate s wha t w e wer e attemptin g t o do an dwhy
. Section sP.2 6

1 9
TABL E 3. 1 Consultant s fo r th e Hemoglobi nProtocol

Consultant s Affiliatio n
Dr . Julia nChisol m JohnF . Kennedy Institut e John s Hopkin s Universit y Mr . Jef f Cohe nOAQPS, a U.S . EPA Dr . Anit a Curra nWestcheste r Count y Dept . o f Healt h Mr . Thoma s Feagan s OAQPS , U.S . EPA Dr . Leste r Gran t Environmenta l Criteri a Assessmen t Office , U.S . EPA Mr . JohnHaine s OAQPS , U.S . EPA Dr . Pau l Hammond Dept . o f Environmenta l Healt h Universit y

o f Cincinnat i Mr . Rober t Kellam OAQPS , U.S . EP A Dr . Pau l Musha k Departmen t o f Patholog y Universit y

o f Nort hCarolin a Offic e o f Ai r Qualit y Plannin g an

d Standards .P.2 7
2 0 2- 5 specif

y th e parameter s of

th e problem , s o tha t

th e dose-respons e function s ar e wel l defined
. Sectio n 6 raise s variou s point s inth e literatur e fo r discussion
. Section s 7 an d9 discus s th e proces s o f

probabilit y encoding
. Sectio n8 deal s peripherall y wit hhemoglobi n decremen t

an draise s issue s concernin g possibl e advers e healt heffect s associate dwit h elevate dEPlevels
. More specifically , Sec . 2 define s advers e hemoglobi nlevel s a s 9. 5 g/d Lan d 1 1 g/dL , thereb y bracketin g th e rang e of interest
. Thus , judgment s wer e encode dfo r tw o set s of dose-respons e functions
. Sectio n3 define s th e populatio na t ris k fo r encodin g a s al l Unite dState s childre n fro mconceptio nthroug hthei r sevent hbirthday
. However , th e expert s wer e give n th e optio n of considerin g separatel y th e ag e group s 0- 3 an d4- 6 year s i f the y though t

fo r an y reaso n tha t

th e tw o group s woul dhav e differen t dose-respons e functions
. Therefore , expert s wh o exercise dthi s optio nha dthei r probabilisti c judgment s encode dfo r

fou r dose-respons e relationships
. Sectio n 6 elicit s discussio nfro mth e exper t o nrelevan t

theorie s an ddata
. Thi s ste p helpe densur e tha t th e proble mwas structure dproperly , tha t th e exper t

consciousl y reviewe dhi s o r

he r knowledg e prio r

t o providin g probabilit y judgments , an dtha t a possibl e basi s fo r

understandin g an y discrepan t judgment s was provided
. Section s 7 an d9 , whic hcove r th e probabilit y encoding , wer e derive dfro mou r prio r wor k o n encodin g probabilit y judgment s abou t dose-respons e function s (Wallste n e t al. , 1983) . Sectio n 7 provide s suggestion s o nho w t o minimiz e biase s inprobabilit y encoding , wherea s Sec . 9 discusse s th e intende dprobabilit y encodin g procedure
. 3. 3 CONDUC T OF TH

E SESSIONS Al l session s wer e conducte ddurin g th e winte r of 1984-1985
. Section s 1- 8 of th e protoco l wer e sen t

t o eac hexper t

befor e th e schedule dreview
. Th e protoco l wa s the n use dt o guid e discussio n an dinteractio ndurin g th e sessions
.P.2 8

2 1 Approximatel y on e t o thre e hour s wa s spen t a t th e beginnin g of

th e firs t sessio n discussin g th e materia l in Sees . 2- 6 of th e protocol
. Th e concept s inSec . 7 wer e the n discusse dan dillustrated , afte r whic hth e probabilit y encodin g began
. (Th e expert s wer e no t require dt o rea dSec . 9 of th e protocol ; i t

simpl y constitute darecor dof wha t w e wer e doing. ) Th e actua l encodin g too k abou t fou r t o si x hours
. Th e secon dsessio n too k plac e fou r

t o si x week s afte r

th e firs t

sessio nan dlaste d fro mtw o t o fou r

hours
. I t

include darevie w of

th e summarie s of

th e previou s session , whic hha dbee n sen t

inth e mail ; additiona l probabilit y encodin g a s necessary ; an d discussio nof

th e materia l in Sec . 8 of th e protocol
. 3. 4 ENCODIN GTH EJUDGMENT S Probabilit y encodin g bega ninsessio n1 afte r th e relevan t

literatur e an dth e factor s determinin g th e dose-respons e functio nha dbee nthoroughl y discusse dwit hth e expert . Th e intentio n wa s t o encod e probabilit y judgment s fo r possibl e respons e rate s a t Pb B level s of

5 , 15 , 25 , 35 , 45 , an d5 5 yg/dL
. Highe r Pb B level s wer e employe dwit hon e expert . T o determin e usefu l point s inth e dose-respons e spac e fo r encodin g probabilities , eac hexper t

wa s firs t

aske dt o suppl y broa d"99 % confidenc e interval " range s fo r possibl e respons e rate s a t

eac ho f th e Pb B levels
. W

e helpe dth e exper t

determin e thes e range s b y posin g suitabl e questions
. Fo r example , afte r

arang e wa s specified , w e aske dwhethe r th e exper t

coul dconstruc t

aplausibl e explanatio ni f som e da y i t

wer e foun dtha t

th e tru e valu e fel l outsid e tha t

range . Fo r mos t of th e experts , probabilitie s wer e encode dusin g aprobabilit y wheel
. Fo r thi s purpose , th e rang e of possibl e respons e rate s fo r eac hPb B leve l was divide dint o fiv e equa l interval s fo r

detaile dencodin g a t

si x points
. Fo r

example , i

f th e response-rat e rang e a t aparticula r

Pb B leve l was 0.2-0.7 , subsequen t encoding s wer e recorde da t 0.2 ,P.2 9
2 2 0.3 , 0.4 , 0.5 , 0.6 , an d0.7 . I f durin g th e encodin g proces s i t becam e apparen t

tha t othe r point s eithe r

insid e o r

outsid e th e rang e wer e important , the y wer e incorporated
. Blood-lea dlevel s wer e presente dfo r encodin g inarando morder ; fo r aparticula r Pb B level , respons e rate s wer e als o presente di narando msequence . Probabilitie s wer e encode dfo r

al l respons e rate s a t

agive nPb B leve l befor e movin g o nt o th e nex t Pb B level
. Th e probabilit y whee l use dfo r th e encodin g i s radiall y divide dint o tw o sector s of adjustabl e relativ e area s —on e orang e an don e blue
. Th e whee l ca nb e spu ns o tha t i t randoml y stop s wit heithe r secto r unde r apointer
. Fo r

aparticula r

respons e rat e Ra t

a give nPb B leve l L , th e whee l wa s se t a t som e relativ e are ao f blue , an dth e exper t

wa s aske dt o conside r

th e followin g question : I s i t mor e probabl e tha t

th e tru e respons e rat e a t blood-lea dleve l Li s les s tha n R , o r

tha t arando mspi nth e whee l woul dsto p wit hth e pointe r o n blue ? Thus , th e exper t

was aske dt o weig htw o probabilitie s an ddecid e whic hwa s greater . Th e expert' s answe r

determine dwhethe r

th e proportio nof

blu e wa s increase do r decreased , an dth e questio n was pose dagain
. Thi s procedur e was continue dunti l th e whee l wa s se t suc htha t th e exper t

considere di t

equall y likel y tha t

th e whee l woul drandoml y lan do n blu e a s tha t

th e tru e respons e rat e wa s les s tha nRfo r Pb B leve l L . Th e relativ e are aof blu e was the n provisionall y take na s th e judge dcumulativ e probabilit y F(R|L) . Th e procedur e wa s repeate dfo r th e require drespons e rate s unti l a nentir e cumulativ e probabilit y distributio n ove r Rfo r 0 < R< 1. 0 ha dbee nencode dfo r aPb B of

L . I f afte r aperio dof

tim e th e exper t

di dno t becom e comfortabl e wit hth e probabilit y wheel , a n encodin g metho dbase do nsuccessiv e interval s an dhypothetica l bet s wa s used
. I

n thi s case , acumulativ e subjectiv e probabilit y of F(R|L ) = 0.5 0 wa s firs t encode db y havin g th e exper t specif y apopulatio nrespons e rat e Rfo r th e Pb B leve l unde r consideratio n suc htha t i f abe t wer e mad e suc htha t th e payof

f depende do nP.3 0

2 3 whethe r th e tru e respons e rat e turne dou t t o b e abov e o r

belo w R , th e exper t

woul db e indifferen t

a s t o whic hbe t

h e held
. I

nothe r words , th e exper t

specifie darespons e rat e suc htha t i nhi s o r

he r judgmen t

i t wa s equall y likel y tha t th e tru e rat e i s abov e a s belo w it
. Frequently , i t

turne dou t

tha t th e exper t

was no t indifferen t

betwee nth e tw o side s of th e be t an dtha t wit halittl e mor e effor t i t wa s possibl e t o fin darespons e rat e a t whic h h e o r sh e was . Havin g determine dth e respons e rat e correspondin g t o asubjectiv e probabilit y of 0.50 , th e exper t

wa s the n aske dt o imagin e tha t infac t th e necessar y researc hha dbee n done , tha t

th e tru e respons e rat e wa s now known , an dtha t i t wa s greate r

tha nth e valu e h e ha djus t

indicated
. (On hal f

th e occasion s a t

thi s point , h e o r

sh e was t o imagin e tha t th e tru e respons e rat e was les s tha ntha t earlie r specified. ) Give ntha t

th e tru e rat e wa s greate r tha n tha t

whic hha dbee n indicated , ane w respons e rat e Rwas t o b e specifie d fo r ane w be t

suc htha t

th e exper t

woul db e indifferen t

a s t o whethe r

hi s payof

f depende do n th e tru e populatio n respons e rat e bein g abov e o r belo w it
. Onc e suc ha valu e wa s determined , thi s corresponde dt o asubjectiv e probabilit y of F(R|L ) = 0.75
. I

n thi s manner , respons e rate s correspondin g t o subjectiv e probabilitie s of 0.25 , 0.50 , an d 0.7 5 wer e encoded
. Respons e rate s correspondin g t o subjectiv e probabilitie s of 0.0 1 an d 0.9 9 wer e als o determine db y imaginin g bet s wit h1:9 9 an d99: 1 odds
. Afte r th e cumulativ e probabilit y distributio nove r respons e rat e wa s encode dfo r agive n Pb B level , regardles s of th e encodin g metho demployed , th e distributio n wa s graphe dan dshow n t o th e exper t fo r discussion
. Any inconsistencie s wer e pointe dou t an dresolved
. Suc hinconsistencie s appeare da s dip s inth e graphs , whic hshoul dris e monotonicall y a s th e respons e rat e goe s fro m0 t o 1 (se e Wallste ne t al. , 1983 , fo r details)
. Th e implication s of th e encode ddistribution s wer e als o discussed
. Fo r example , fo r R , > Rj , F(RJ|L ) = 0.2 5 an dF(R-|L ) = 0.75
. Thes e probabilitie s impl y tha t th e exper t consider s th e tru e respons e rat e equall y likel y t o fal l insid e th e (R- , R- ) interva l a sP.3 1
2 4 outsid e it
. I

f th e exper t

disagree dwit hthi s o r an y of severa l othe r

implications , adjustment s wer e made
. Whe n th e exper t

wa s satisfie dtha t

th e encode ddistributio n represente dhi s probabilisti c judgment , anothe r Pb B leve l was selecte dan dth e proces s wa s repeated
. Whe n distribution s ha dbee nencode dfo r al l selecte dPb B levels , the y wer e plotte do nagrap han ddiscusse dwit hth e expert . I f tw o distribution s crosse da t an y point , thi s inconsistenc y wa s resolve d(se e Wallste ne t al. , 1983 , fo r

details)
. Whe

n th e exper t wa s satisfie dtha t

th e entir e se t

of distribution s represente dhi s o r he r probabilisti c judgments , th e encodin g was finished
. Followin g th e firs t

session , th e encode djudgment s wer e fi t b y distribution s in a manne r describe di n Sec . 3.5
. Summarie s o f thes e fit s an dth e encode djudgments , alon g wit hexplanator y text , wer e sen t t o th e exper t

prio r t o th e secon dvisit
. Durin g th e secon dvisit , al l of

th e material s wer e reviewed , additiona l probabilit y encodin g was carrie dou t

a s necessary , an dth e exper t wa s aske dt o indicat e whethe r th e fitte d distribution s correctl y represente dhi s o r he r judgments
. I

nafe w instances , functio n fittin g was carrie dou t later , an dfurthe r

discussio nwas continue db y lette r an d telephone
. A s see n inApp . C , th e fitte dfunction s wer e ver y clos e t o th e encode d probabilities
. When a n exper t finall y fel t

tha t th e probabilitie s correctl y represente dhi s o r he r judgments , h e o r

sh e fel t tha t th e fitte dfunction s di da s well
. 3. 5 REPRESENTIN GTH EJUDGMENT S Calculatin g ris k

require dfittin g adistributio nt o th e assesse dpoints
. Becaus e th e probabilisti c judgment s abou t th e dose-respons e relationship s ar e generall y "s"

- shape dove r

th e close d[0,1 ] interval , a s demonstrate dinWallste ne t al
. (1983 ) an d Whitfiel dan dWallste n (1984) , i t ca nb e difficul t

t o represen t

the mwit hsimpl e mathematica l functions
. On e particularl y usefu l functio ntha t i s relativel y eas y t o wor kP.3 2
25 wit hi s th e normal-on-log-odd s distributio nfunction , whic hi s obtaine db y fittin g a norma l distributio n t o th e natura l lo g of th e odd s implie db y th e populatio nrespons e rat e R . Thus , th e followin g relationship s ca nb e defined :
X = Y*-

—

, fo r 0 < X < «
Y = ln(X) , fo r

-<" > < Y < =

°
wher e X i s th e odd s variabl e an dY i s th e lo g o f th e odd s variable
. Th e variabl e Y i s assume dt o b e normall y distribute dwit hmea ny an dvarianc e o . I f Y i s normall y distributed , the n X i s log-normall y distributed , an dth e distributio ninduce do nRi s calle d anormal-on-log-odd s distribution
. Althoug hth e normal-on-log-odd s distributio ncanno t b e expresse din aclose dform , al l probabilitie s of interes t ca nb e easil y derive dfro mth e norma l distributio n ove r Y , a s discusse dinApp . B . A separat e normal-on-log-odd s distributio nfunctio nwa s fi t t o th e elicite d cumulativ e distributio n function s (CDFs ) o r th e probabilit y judgment s ove r respons e rat e R , a t eac hPb B leve l L- , wher e j = 1 , ... , m . Thi s fittin g wa s don e b y derivin g least

square s estimate s of

th e parameter s y.

- an do: , denote db y y ; an dOJ , fo r th e norma l distributio n applie dt o th e log-odd s transforme dvariabl e Y , a s describe di nApp . B . Thes e distributions , eac hwit hseparat e least-square s estimate s fo r y - an do: , ar e referre d

2 t o a s th e best-fittin g normal-on-log-odd s distributions
. Th e standar dregressio n r statistic , whic hcompare s actua l judgment s t o thos e predicte db y th e fitte dfunction , assesse s ho w wel l th e derive ddistributio nrepresent s th e probabilit y judgment s a t agive n Pb B level
. A s presente dfull y in App . B , th e normal-on-log-odd s distributio ndescribe dth e 1 2 encode djudgment s ver y well , wit hr value s generall y exceedin g 0.95
. (A nr valu e of 1. 0 indicate s aperfec t fit. ) Nevertheless , goodnes s of fi t was sacrifice dt o asmal lP.3 3 2 6 degre e b y fittin g a n expert' s probabilit y judgment s wit hafamil y of equal-varianc e normal-on-log-odd s distributions
. Suc haprocedur e ensure s tha t th e derive ddistribution s a t tw o differen t

lea dlevel s neve r

cros s on e another , no t eve na t th e extremes . Crossin g woul dimpl y tha t

exceedin g aspecifie drespons e rat e i s judge dmor e probabl e a t blood

lea dleve l L , tha n a t

Ln , wher e L« i s greate r tha nLj
. Equal-varianc e normal-on-log-odd s distribution s wer e derive db y (1 ) obtainin g a least-square s estimat e of th e standar ddeviatio npoole dove r lea dlevels , o' , (2 ) settin g al l th e a', equa l t o o ' , an d(3 ) findin g ne w least-square s estimate s o f th e means , y ' (se e J PJ App . B) . Th e resul t

i s ase t of normal-on-log-odd s distributions , on e fo r eac hblood-lea d leve l LJ , tha t

hav e acommo n varianc e an ddiffe r onl y i nth e mean . Thei r goodnes s of

fi t ca n als o b e assesse db y calculatin g r betwee nobserve dan dpredicte djudgments
. Becaus e fo r

eac hPb B leve l L; , probabilit y judgment s wer e elicite dove r virtuall y th e entir e [0,1 ] interval , an dthes e judgment s exhibite dn o inconsistencie s (i.e. , crossings) , th e fi t

of th e equal-varianc e normal-on-log-odd s distribution s wa s generall y clos e t o tha t

of th e best-fittin g normal-on-log-odd s distributions
. Becaus e th e equal

varianc e distribution s canno t giv e ris e t o inconsistencies , thes e representation s of a n expert' s judgment s ar e preferre dfo r estimatin g risk
. The y wer e infac t accepte db y eac h expert , wit hasligh t

adjustmen t

require dfo r

Exper t D . 3. 6 TH EEXPERT S Th e individual s liste di nTabl e 3. 2 wer e selecte dinth e fal l of 198 4 b y EPA/OAQP S fo r

participatio n in th e stud y a s experts . Al l o f the magree dt o participate , wit hth e understandin g tha t thei r judgment s woul db e kep t anonymous . Result s ar e therefor e presente dfo r Expert s A throug hE , th e code s bein g randoml y assigne dt o th e name s liste din Tabl e 3.2 .27 TABLE 3. 2 Experts Wh o Participate d i n th e Hemoglobi n Encoding s P.3 4

Exper t Affiliatio n
Dr . Julia n Chisol m
Dr . Bernard Davido w Dr . Pau l Hammon

d
Dr . Sergi o Piomell i

Dr . Joh n Rose n Joh

n F . Kenned

yInstitut e John s Hopkin s Universit y Ne wYor k Cit yBoard o f Healt h Dept . o f Environmenta l Healt h Universit yo f Cincinnat i Columbi a Universit y Ne wYor k Cit yLead Poisoning Preventio n Progra

m Montefior e Hospita l an d Medica l Cente rP.3 5
2 8 3. 7 RESULT S Th e qualitativ e discussion s abou t th e effect s o f

lea dar e summarize di nApp . B . Th e detaile dquantitativ e results , includin g th e encode djudgments , paramete r value s fo r th e fitte dfunctions , an dgoodness-of-fi t measure s ar e als o give ninApp . B . Thi s sectio n use s th e function s fi t

t o eac hindividual' s probabilisti c judgment s t o summariz e th e quantitativ e results
. Th e function s accuratel y represen t th e underlyin g encode dvalues , bot hbecaus e goodnes s of fi t wa s excellen t

an dbecaus e eac hexper t endorse dth e outpu t of th e respectiv e function s a s representin g hi s judgments
. Recal l tha t

probabilisti c judgment s wer e encode dabou t dose-respons e function s fo r lead-induce dhemoglobi n decrement s amon g U.S . childre nage d0- 6 years . Hemoglobi n level s o f

9. 5 g/d Lan dIL O g/d Lwer e considered , an dth e expert s wer e give n th e optio n of

dividin g th e populatio nof childre nint o ag e group s of 0- 3 an d4- 6 years . Result s ar e presente dseparatel y fo r th e fou r

condition s obtaine db y crossin g th e tw o hemoglobi nlevel s wit hth e tw o ag e groups . ' Expert s A , D , an dEbeliev e tha t dose-respons e relationship s ar e differen t fo r th e tw o ag e group s an dtherefor e provide dfou r distinc t set s of probabilisti c judgments
. Exper t C believe s tha t

asingl e dose-respons e functio napplie s t o childre ninth e 0- 6 ag e rang e an dtherefor e provide dasingl e se t o f probabilisti c judgment s fo r eac hhemoglobi n level
. Exper t

B fel t uncomfortabl e wit hth e notio nof judgmenta l probabilit y encodin g an dtherefor e di dno t

suppl y an y judgments
. Hi s qualitativ e comment s ar e presente di n Sec . B. 4 of

App . B . 3.7. 1 Hemoglobi n Level s < 1 1 g/dL , Age s 0- 3 Year s Figur e 3. 1 summarize s th e judgment s of Expert s A , C , D , an dEregardin g th e dose-respons e functio n fo r hemoglobi nlevel s les s tha no r equa l t o 11. 0 g/d Lin U . S . childre nag e 0- 3 years . (Wit hExper t C s concurrence , hi s judgment s fo r ag e 0- 6 ar e reproduce din bot hth e 0- 3 an d4- 6 ag e groups. ) Eac hperson' s judgment s ar e show n in a separat e panel
.M



## o a pi P J d o c o I r e c n 

### " 8 n

o 

### S *•*• • n B 

## fi I-*- * o c r < n *—. | A o q 

### a 

## r ( V u o I w "- d n 

# 5 P r(H b 

### < 1 1 g/dL ) 

### P r(H b 

### < 1 1 g/dL )



### P r(H b 

### < 1 1 g/dL ) 

### P r(H b 

### < 1 1 g/dL )
o -_ ^

_ * O l " K l t n 0 4 m

** . U l w U l 1 r _M

O O 1 , 1 \ .V" . • » 1 - A • . N 

### » A - x

# •-AYx 

# * *'\ - % * • » •\ • . % \ \ \ \ N V ' •X' • V \ \ \ •. \ * ' •\ W

O 1

\ N \
* \ * . m X T 3 C D

- 1 -* - o

V \ % K >P.3 7
3 0 Th e graph s ar e analogou s t o th e usua l dose-respons e function s foun din th e literature , except , of

course , tha t

the y ar e base do nprobabilisti c judgment s rathe r tha n o ndirec t data
. Th e dark , centra l curv e ineac hpane l show s th e media njudge ddose

respons e curv e fo r

eac hexpert . I

nothe r words , fo r

agive npanel , accordin g t o tha t expert , a t

eac hbloo dlea dleve l ther e i s a0.5 0 probabilit y tha t th e tru e respons e rat e i s abov e th e indicate dvalu e an da0.5 0 probabilit y tha t th e tru e respons e rat e i s belo w it
. Th e tw o lighte r

line s o n eithe r

sid e of th e media ncurv e contai nth e centra l 50 % credibl e interval
. Thus , accordin g t o th e exper t i naparticula r

panel , a t

eac hbloo dlea d leve l ther e i s a0.2 5 probabilit y tha t th e tru e respons e rat e i s belo w th e lowe r ligh t curve , a0.5 0 probabilit y tha t i t i s betwee nth e tw o ligh t curves , an da0.2 5 probabilit y tha t i t i s abov e th e uppe r

one . I n asimila r

manner , th e dashe dan ddotte dpair s o f curve s contai n centra l 90 % an d98 % credibl e intervals , respectively
. Th e mor e tightl y packe dth e famil y o f function s ar e i napanel , th e les s uncertaint y a n exper t

indicate s inhi s judgments
. Thus , Figur e 3. 1 give s arathe r complet e representatio n of eac hexpert' s probabilisti c judgments
. Figur e 3. 2 i s les s complete , bu t provide s aconvenien t mean s of

comparin g judgment s acros s experts . Th e axe s ar e th e sam e a s inFigur e 3.1 . Th e vertica l bar s a t eac hlea dleve l represen t eac hexpert' s centra l 90 % credibl e interva l fo r respons e rate , an dth e do t

withi n eac hba r

indicate s th e media njudgmen t a t tha t lea dlevel
. Not e firs t

tha t ther e i s substantia l overla p i nth e judgment s of expert s C , D , an d E . Thi s i s tru e despit e th e fac t tha t exper t C s judgment s ar e fo r th e ful l 0 t o 6 ag e range , whil e thos e of

th e other s ar e restricte dt o ag e 0-3 . Th e judgment s of exper t A ten dt o diffe r

fro mthos e o f

C , D , an dE . Considerin g th e overlappin g judgment s of C , D , an dEfirst , not e tha t non e suggest s athreshold
. Accordin g t o thei r media njudgments , th e bes t estimat e of respons e rat e i s betwee n 4 % an d9 % a t Pb B = 5 yg/dL , risin g t o betwee n22 % an d28 % a t Pb B = 5 5 yg/dL
.5 0

4 0

V I J D 30 H

J D o O 1 0 

# T
•? T 

# i T T

TT 

# T 

# t i t H 

# I i t 

# T

* I

I 

# 1 

# 1 1 • 

# i i 

# l t o 

# i :T i 

# ? ]

i i i— i I •1 1 •—— i 1 i i— i 1 r—i— i 1 i i— i 1 1 r-—" i 1—i—i— i 1 i' i III I 1— i • ACD E ACD E ACD E ACO E A C D t ACO E ACD E ACD C 5 fig/d L 1 5 fig/d L 2 5 fiq/dl 3 5 /xg/d L 4

5 fiq/dl 5 5 /*g/d L 65 i*g/d L 7 5 fiq/dl 

### Blood-Lea d Leve l

FIGUR E 3. 2 Compariso n o f

Judgments , H

b < 1 1 g/dL , Age s 0- 3 Year sP.3 9 32 Exper t C expresse s th e leas t uncertaint y i nhi s judgmen t abou t dose-respons e function , an dExper t

Eexpresse s th e most , althoug hi nal l cases , varianc e i n th e judgment s increase s wit hPb B withi nth e rang e considere d(cf
. th e 90 % credibl e interval s represente db y th e vertica l bar s inFigur e 3.2) . Thus , considerin g th e 90 % credibl e interval s fo r

expert s C , D , an dE , respons e rat e i s greate r tha navalu e betwee n12 % an d 28 % a t Pb B = 5 yg/dL , wit hprobabilit y 0.05
. Respons e rat e the nrises , an dexceed s a valu e betwee n 40 % an d62 % a t Pb B = 5 5 yg/dL , als o wit hprobabilit y 0.05
. Exper t A' s judgment s diffe r

fro mthos e o f

Expert s C , D , an dE . Accordin g t o hi s judgments , bloo dlead s les s tha n abou t 4 5 yg/d Ld o no t

caus e hemoglobi nlevel s t o di p belo w 1 1 g/d Lin thi s ag e group . A t Pb B = 4 5 yg/dL , th e mos t likel y respons e rat e i s 3% , an dthi s rise s t o amos t likel y rat e of

16 % a t Pb B = 7 5 yg/dL
. Furthermore , wit h probabilit y 0.05 , th e respons e rat e a t Pb B = 4 5 yg/d Li s greate r tha n15% , an dwit hth e sam e probabilit y i t

i s greate r

tha n50 % a t

Pb B = 7 5 yg/dL
. Althoug hou r primar y interes t i s i n bloo dlead s les s tha n o r equa l t o 5 5 yg/dL , w e inquire dabou t th e highe r

level s her e t o provid e afulle r

pictur e of

Exper t A' s judgments
. 3.7. 2 Hemoglobi n Level s < 1 1 g/dL , Age s 4- 6 Year s Figure s 3. 3 an d3. 4 displa y th e judgment s regardin g dose

- respons e function s fo r hemoglobi n level s les s tha n o r equa l t o 1 1 g/d Lfo r

childre nag e 4- 6 years . The y ar e rea d i n exactl y th e sam e way a s ar e Figure s 3. 1 an d3.2 . A s before , th e judgment s of expert s C , D , an dEoverla p considerably , an ddiffe r fro mthos e of

A . Accordin g t o C , D , an dE , ther e i s n o threshold ; th e mos t likel y respons e rate s ar e betwee n 2 % an d7 % a t Pb B = 5 yg/dL , risin g t o betwee n14 % an d26 % a t Pb B = 5 5 yg/dL
. I n thi s case , exper t

D expresse s th e leas t

uncertainty , whil e exper t Econtinue s t o expres s th e greates t

uncertainty
. Wit

hprobabilit y 0.05 , respons e rat e exceed s avalu e betwee n 6 % an d19 % a t Pb B = 5 yg/dL , an dwit hth e sam e probabilit y i t exceed s avalu e betwee n 19 % an d46 % a t Pb B = 5 5 yg/dL
.P.4 0
3 3

t Exper t A .-•0.9 5 •*•* •~ 

### f Exper t C

Exper t D

o > V ! 3 0 - 20 - JD 1 0 Exper t E

i i i i i 5 1 5 2 5 3 5 4 5 5 5 -* L

FIGUR E 3. 3 Dose-Respons e Functions , Hemoglobi n Leve l < 1 1 g/dL , Age s 4- 6 Year s4 0 -

C T30 - D> V I J D X
J D d J D O 2 0 -

10 - 

# * i V I

mt -**•*• - 

# T 

# 1 II i

i i 

# i l 

# ?I i

x

### I 

# i l 

# i i i l 

# I ! i l 

# I l u >

- i 1 1 i i 1 I— I r I i i r— i III I 1 i i 1 1 1 r— i III I 1 1 1 1 r - ACO E ACD E ACD E ACD E ACD E ACD E ACD E ACD E 5 tig/d L 1 5 /xg/d L 2 5 /xg/d L 3 5 /xg/d l 4 5 /xg/d L 5 5 /xg/d L 6 5 xxg/d L 75 xtg/d L 

### Blood-Lea d Leve l

FIGUR E 3. 4 Compariso n o f

Judgments , H

b < 1 1 g/dL , Age s 4- 6 Year s

T J J* .P.4 2

3 5 A s before , exper t

A' s vie w i s tha t

ther e ar e extremel y lo w probabilitie s of lead

induce dhemoglobi n effect s a t th e exposur e level s considered
. Inhi s judgment , blood

lea dlevel s les s tha n abou t 5 5 yg/d Ld o no t

caus e hemoglobi nlevel s t o g o belo w 1 1 g/d L i n thi s ag e group . Th e mos t likel y respons e rat e a t 5 5 yg/d Li s 2% , whil e a t 7 5 yg/d Li t

i s 11% . Wit

hprobabilit y 0.05 , respons e rat e exceed s 9 % a t 5 5 yg/dL , an dwit hth e sam e probabilit y i t

exceed s 34 % a t

7 5 yg/dL
. 3.7. 3 Hemoglobi n Level s < 9. 5 g/dL , Age s 0- 3 Year s Figure s 3. 5 an d3. 6 displa y th e judgment s regardin g dose-respons e function s fo r hemoglobi n level s les s tha n o r equa l t o 9. 5 g/d Lfo r childre nag e 0- 3 years . The y ar e rea di nth e sam e manne r a s ar e th e previou s pair s o f figures
. I nexper t A' s judgment , n o amoun t of lea dwithi nth e rang e of interes t (belo w 5 5 yg/dL ) wil l caus e hemoglobi n level s t o dro p a s lo w a s 9. 5 g/dL , an dtherefor e n o result s ar e show n fo r

him
. Also , althoug hth e judgment s fo r C , D , an dEten dt o overlap , the y d o no t

displa y th e sam e degre e o f similarit y tha t

the y d o a t

th e highe r

hemoglobi n level
. I nparticular , lookin g a t th e media njudgments , C an dEagre e inestimatin g th e mos t likel y respons e rat e a t 2% , whil e D i s certai ntha t th e respons e rat e i s 0% , a t Pb B = 5 yg/dL
. Then , exper t C s media nrespons e rat e judgmen t increase s relativel y slowl y wit hbloo dlead , whil e tha t of exper t D increase s relativel y quickly
. A s aresult , a t Pb B = 5 5 yg/d LD an dEagre e tha t th e mos t

likel y respons e rat e i s 20% , whil e C consider s i t t o b e 7% . Not e furthe r

tha t exper t Eexpresse s considerabl e uncertaint y i nhi s judgments , whil e C an dD expres s muc hless
. Thus , dependin g o nth e expert , a t Pb B = 5 yg/d L respons e rat e exceed s 3 % o r 18 % wit hprobabilit y 0.0 5 (recal l tha t accordin g t o exper t

D i t i s definitel y 0%) . A t Pb B = 5 5 yg/dL , i t

exceed s avalu e fro m13 % t o 70 % wit h probabilit y 0.05
.P.4 3 36

/•*""• . - J ^ O ) • o > V I JD

* w a. t ExDer

t C 10 - 8 - 6 - 4 - 2 - 0 - •0.9 5 * * * * ...0.7 5 ..•• •^0. 5
, ' ...••'^^^...0.2 5
' y'^y^.-"

„-0.0 5

1 1 1 1 1 * 5 1 5 2 5 3 5 4 5 5 5
t Expert D 30- | | Expert E 50- I 

## c r ^ 4 0 

### u. *\ 3 0 c n V I 20 * JD X 1 0 L .

- i 1 1 1 r -

1 5 2 5 3 5 4 5 5 5 •> L

FIGUR E 3. 5 Dose-Respons e Functions , Hemoglobi n Leve l < 9. 5 g/dL , Age s 0- 3 Year s5 0

40-\


### m o i 3 0 V I J D

^ 2 0 J D O J D O i
_ O L 1 0 

# T

- i r 

# T I i T 

# i A 

# li 

# 1
Tr 1 r - i 1 1 - r - i 1 1 r - i r 

# u 1

' •: 

# i i 1

i r C D E 5 ixg/d L C D E

1 5 /ug/d L C D E

2 5 /xg/d L C D E

3 5 /Lxg/d L C D E

4 5 /xg/d L C D E

5 5 Axg/d L 

### Blood-Lea d Leve l OJ ^ 1

FIGUR E 3. 6 Compariso n o f Judgments , li b < 9.5 , Age s 0- 3 Year s3 8

3.7. 4 Hemoglobi n Level s < 9. 5 g/dL , Age s 4- 6 Year s Figure s 3. 7 an d3. 8 displa y th e judgment s regardin g dose/respons e function s fo r hemoglobi n level s les s tha n o r equa l t o 9. 5 g/d Lfo r childre nag e 4- 6 years . The y ar e rea din th e sam e manne r a s ar e th e previou s pair s of figures
. Th e patter nof judgment s i s ver y simila r

t o tha t see n fo r

th e younge r

ag e group , bu t

th e respons e rat e value s ar e lower
. Exper t

A judge dtha t

bloo dlea da t

th e level s unde r

consideratio nwoul dno t reduc e hemoglobi n t o 9. 5 g/dL , an dexper t D judge dtha t

i t woul dtak e a t

leas t 2 5 yg/d L of bloo dlea dt o do so . Th e media njudgment s of expert s C an dEar e consistentl y similar , whil e thos e of

exper t D joi nthe ma t

Pb B = 3 5 yg/d Lan dhigher
. Fo r expert s C , D , an dE , th e media n judgment s a t Pb B = 5 yg/d Lar e 0 % an d2% ; a t Pb B = 5 5 yg/dL , the y rang e fro m7 % t o 13% . Again , exper t

Eexpresse s th e greates t degre e of

uncertainty
. Fo r

C an dE , a t Pb B = 5 yg/dL , respons e rat e exceed s 3 % an d9% , respectively , wit hprobabilit y 0.05
. Fo r C , D , an dE , a t

Pb B = 5 5 yg/dL , wit hprobabilit y 0.05 , respons e rat e exceed s 8 % t o 50%
. 3. 8 DISCUSSIO

N I t mus t b e born e in min dtha t thes e judgment s ar e wit hrespec t t o lead-induce d respons e rat e ove r

an dabov e an y bas e respons e rat e du e t o iro ndeficienc y an dothe r factors
. Thus , level s of uncertainty , a s wel l a s difference s o r similaritie s of

opinio n reflecte dhere , ar e limite dsolel y t o th e effect s of lea do nhemoglohi n level
. Althoug hthe y diffe r

in detail , i t

i s notabl e tha t

th e judgment s of

expert s C , D , an dEhav e overridin g similarities
. O f particula r

interest , C s judgment s fo r th e 0- 6 year s ag e grou p ten dt o b e jus t belo w thos e o f

D an dEfo r

age s 0- 3 years , an djus t abov e thei r judgment s fo r

age s 4- 6 years . Collectively , th e judgment s of C , D , an dEdiffe r fro mthos e o f

A , wh o consider s tha t

blood-lea dlevel s considere dhav e littl e o r n o effec t o nhemoglobi n levels
.3 9 P.4 6

t Expert C

t Expert D Expert E

FIGUR E 3. 7 Dose-Respons e Functions , Hemoglobi n Leve l < 9. 5 g/d L Age s 4- 6 Year s4 0 P.4 7



### r o I o- H

I---0- H U J - Q

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### (-|p/ 6 g« 6 > qH ) XijuqDqoj d >

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A l I n al l cases , uncertaint y (indicate db y variance ) increase s wit hbloo dlead , a s on e woul dexpec t

o n rationa l grounds
. Thi s increas e i s rationa l becaus e statistica l uncertaint y abou t

abinomia l paramete r (respons e rate , i nthi s case ) increase s a s th e estimate dvalu e move s towar dth e cente r o f th e rang e fo r

tha t parameter . Ther e i s als o les s informatio navailabl e a t th e lowe r

hemoglobi nleve l tha na t th e highe r one , if fo r n o othe r

reaso ntha ntha t

i t occur s les s frequently
. A s aresult , judgment s depen do n agreate r extrapolatio nfro mavailabl e data , an dgreate r disagreemen t

amon g expert s i s t o b e expected
. Thi s i s precisel y wha t happened
. I t

i s interesting , however , tha t expert s A , C , an dD exhibi t mor e certaint y a t

9. 5 g/d Ltha n a t 11. 0 g/dL , despit e th e greate r extrapolation
. Indeed , exper t A i s positiv e tha t

ther e i s n o effec t here
. Apparently , A , C , an dD' s understandin g of th e effect s of

lea do n hemoglobi n leve l ar e suc htha t eac hfeel s mor e confiden t abou t respons e rate s a t

th e lowe r hemoglobi n level
. Th e revers e i s tru e fo r exper t E . Finally , i t

shoul db e recalle dtha t th e expert s wer e selecte dt o represen t th e rang e of respecte dopinion
. Th e fac t tha t nevertheless , ther e i s considerabl e similarit y inth e patter n o

f judgment s illustrate s som e of th e benefit s of

th e probabilit y encodin g procedure
. Th e difference s of opinio ntha t

hav e appeare dinth e literatur e an dindebat e hav e bee ndu e t o ami x of disagreement s abou t

definitions , abou t

interpretation s of

an d extrapolation s fro mdata , an dabou t wha t constitute s prope r

publi c healt hpolicy
. However , i t

i s clea r tha t th e expert s exhibi t

muc hles s disagreemen t whe nthe y ar e require dt o focu s o n th e scientifi c issue s an dt o conside r carefull y thei r

uncertaint y abou t thes e matters . Th e judgment s represente dher e ar e of interes t i nthei r ow nright
. However , i n Chapte r 5 the y wil l b e combine dwit hestimate dbloo dlea ddistribution s unde r alternativ e NAAQ S t o obtai n derive dris k distributions
.P.4 9
4 2 4 PROBABILISTI C DOSE-EFFEC T AND DOSE-RESPONS E RELATIONSHIP S FORLEAD-INDUCED I Q DECREMENT S A s wit hhemoglobin , ther e ar e incomplet e dat aregardin g IQ effect s of lea din th e populatio n o f

U.S . childre n prio r

t o thei r sevent hbirthdays
. Indeed , i t i s fai r t o sa y tha t th e availabl e dat aar e themselve s ver y controversial , makin g i t doubl y necessar y t o encod e experts ' subjectiv e probabilities
. A nexac t paralle l t o th e hemoglobi nsituatio nwoul dhav e entaile ddefinin g dose

respons e function s in term s of percentag e of

th e populatio nwit hlead-induce dI Q decrement s exceedin g agive n amount , an dthe nencodin g subjectiv e probabilitie s abou t suc hfunctions
. Thi s prove dt o b e infeasible , however , becaus e i t di dno t fram e th e issu e inth e way tha t

researcher s in th e are athin k abou t it , no r interm s of

event s tha t

wer e in principl e observable
. Inference s abou t th e effect s o f

lea do nIQ requir e comple x statistic s o n grou p data , becaus e IQ depend s o nmultiple , correlate dfactor s actin g ove r lon g period s of

time
. Thus , i t

i s impossibl e t o observ e a nI Q decremen t ina nindividua l an dt o attribut e tha t

decremen t

t o aparticula r

cause . I n orde r t o pos e question s abou t outcome s tha t

th e expert s commonl y thin k abou t an dt o elici t

probabilisti c judgment s tha t ar e suitabl e fo r

us e inth e ris k

assessment , a hypothetica l experimen t wa s created
. I

nthi s hypothetica l study , ver y larg e number s o f childre n ar e randoml y assigne da t conceptio neithe r

t o acontro l grou p o r t o on e of severa l lea dexposur e groups . Exposur e level s remai napproximatel y fixe da t th e specifie dleve l unti l th e children' s sevent hbirthdays , a t whic htim e th e WIS C I Q tes t i s administered
. Bloo dlea di s measure da t th e thir dbirthday
. Th e ver y larg e number s of subject s pe r

grou p eliminat e th e nee dt o thin k abou t samplin g error , an dth e rando m assignmen t

of subject s t o condition s eliminate s th e nee dt o thin k abou t comple x analyse s of covariance ; group s diffe r onl y in term s of

exposur e t o lead
. Th e expert s wer e aske dt o conside r thi s experimen t

an dt o provid e subjectiv e probabilitie s abou t expecte dmea n I Q difference s betwee n th e contro l grou p an deac hof th e exposur e groups .P.5 0

43 O f course , suc hastud y canno t an dshoul dno t

b e done , bu t

i t i s inprincipl e doable
. Furthermore , th e hypothetica l dat aar e identica l i nformt o dat aactuall y collected , bu t

withou t th e troublesom e features
. Indeed , th e poin t of th e necessar y comple x statistic s o n th e rea l dat ai s t o attemp t t o dra w inference s abou t wha t th e I Q differenc e woul db e betwee n alead-expose dan danonexpose dgrou p if th e confoundin g variable s wer e no t

present . Thus , researcher s thin k abou t thi s issue , an di t

i s precisel y abou t i t tha t th e expert s wer e aske dt o mak e probabilisti c judgments
. I n orde r t o calculat e subjectiv e probabilitie s abou t IQ dose-respons e function s fro mjudgment s abou t

mea n IQ differences , i t wa s necessar y t o obtai njudgment s abou t othe r matter s a s well
. Thus , probabilisti c judgment s wer e encode dabou t th e mea n I Q of th e unexpose dcontro l group , a s wel l a s abou t th e I Q standar ddeviatio nwithi nexposur e groups . Th e I Q measur e i s constructe ds o tha t i t i s approximatel y normall y distribute d withi n th e population
. Th e expert s wer e aske dwhethe r the y fel t

tha t th e norma l distributio nwa s reasonabl y applie dt o I Q score s withi neac hof th e exposur e groups . Subsequently , subjectiv e probabilitie s abou t dose-respons e function s of interes t coul db e calculate dusin g norma l distributio ntheor y inconjunctio nwit hth e probabilisti c judgment s abou t

mea n IQ decrement , mea nIQ of th e contro l group , an dwithin-grou p standar ddeviation
. Sectio n4. 1 describe s th e protoco l development , inwhic hi t i s mad e clea r

ho w thi s hypothetica l experimen t wa s arrive dat ; th e protoco l i s outline di nSec . 4.2 . Section s 4.3-4. 5 discus s th e conduc t of th e encodin g sessions , th e method s of probabilit y encoding , an dth e mathematica l representatio nof th e judgments , respectively
. Sectio n 4. 6 indicate s whos e judgment s wer e encoded , Sec . 4. 7 summarize s th e results , an dSe c 4. 8 provide s som e discussion
.P.5 1
4 4 TABL E 4. 1 Consultant s fo rth e I Q Protoco l

Consultant s Affiliatio n

Dr . Verno nBenignu s Dr . Rober t Bornshei n Mr . Jef f Cohe n Dr . Anit a Curra n

Dr . Gerr i Dawso n Dr . Ki m

Dietric h

Dr . Clair e Ernhar t

Dr . Leste r Gran t Dr . Lloy

dHumphrey s Dr . Lyle Jone s Dr . Herber t Needlema n Dr . Davi dOtt o Dr . Steve nSchroede r Dr . Bernar d Weis s HERL , U.S . EPA Universit y

o f Cincinnat i OAQPS , U.S . EPA Westcheste r Count y Departmen t o f Healt h Universit y

o f Nort hCarolin a Universit y

o f Cincinnat i
Clevelan d Metropolita n Genera l Hospita l ECAO , U.S . EPA Universit y

o f Illinoi s Universit y

o f Nort hCarolin a Universit y

o f Pittsburg h HERL , U.S . EPA Universit y

o f Nort hCarolin a Universit y

o f Rocheste rP.5 2

4 5 TABL E 4. 2 Expert s Wh

o Participate d i n th e I

Q Encoding s

Exper t Affiliatio n
Dr . Ki m

Dietric h Dr . Clair e Ernhar t

Dr . Herber t Needlema n
Dr . Michae l Rutte r
Dr . Gerhar d Winneke

Dr . Willia

m Yul e Universit y o f Cincinnat i Cleveland Metropolita n Genera l Hospita l Universit y

o f Pittsburg h Institut e o f Psychiatr y London , U.K . Universit y

o f Dusseldor f Dusseldorf , F.R.G . Institut e o f Psychiatr y London , U.K .P.5 3
46 4. 1 PROTOCO

L DEVELOPMEN

T A larg e numbe r

of people , liste di nTabl e 4.1 , serve da s consultant s in th e developmen t

of thi s protocol
. A s alread y indicated , ou r origina l intentio nwa s t o develo p aprotoco l analogou s t o th e on e fo r hemoglobi ndecrement , accordin g t o whic hw e woul d encod e experts ' probabilisti c judgment s abou t dose-respons e function s fo r lead-induce d I Q decrements
. I

n preparation , w e rea drelevan t portion s of

th e C D an dconsulte dwit h Drs . Verno n Benignus , Rober t Bornshein , Ki

mDietrich , Davi dOtto , an dStephe n Schroeder
. A firs t draf t of aprotoco l wa s developed , designe dt o elici t probabilisti c judgment s abou t

dose-respons e curve s fo r advers e effect s define dinterm s of IQ decrements
. Thi s draf

t was discusse dwit hmos t of th e peopl e mentione dabov e a s wel l a s wit hDrs . Clair e Ernhart , Leste r Grant , Lloy dHumphries , Lyl e Jones , Herber t Needleman , an dBernar dWeiss
. Tw o factor s becam e clea r inth e discussions
. First , althoug hth e concep t of adose-respons e curv e i s wel l define din thi s context , i t

i s no t commonl y used , fo r

reason s alread y introduce dinSectio n4.1 . Th e secon dfacto r

wa s tha t

i n attemptin g t o respon dt o th e questions , th e expert s wer e envisionin g hypothetica l experiments , considerin g wha t th e outcome s migh t

be , an dthe n extrapolatin g fro mtha t t o th e dose-respons e function s of interest
. Thus , i t appeare dtha t

i t woul db e fa r

mor e consisten t

wit hth e expert s usua l way o f thinkin g an db e easie r fo r the mt o respon dif

thei r probabilisti c judgment s abou t outcome s of

suitabl e hypothetica l experiment s wer e encode ddirectly
. I naddition , b y properl y designin g thes e hypothetica l experiments , i t woul db e possibl e t o eliminat e th e nee dt o worr y abou t

som e of

th e complexitie s tha t aris e i nactua l research
. Th e extrapolation s tha t

the y wer e tryin g t o d o mentall y coul dthe nb e don e mathematically
. Accordingly , ane w versio n of th e protoco l was develope dt o elici t probabilisti c judgment s abou t

th e outcome s o f

idea l hypothetica l experiments
. Thi s protoco l als o indicate dhow th e judgment s woul db e use dan dth e assumption s tha t woul db eP.5 4
47 incorporate din workin g wit hthem
. Th e ne w draf t was discusse dwit hDrs . Verno n Benignus , Anit aCurran , Clair e Ernhart , Lloy dHumphries , Lyl e Jones , Herber t Needleman , Davi dOtto , an dStephe nSchroeder
. The y foun di t muc heasie r

an dmor e natura l t o respon dt o thi s versio n tha nt o th e previou s one . However , variou s comment s lea dt o athir ddraf

t o f th e protoco l incorporatin g a nimprove didea l hypothetica l experimenta l design
. Thi s draf t was discusse dwit hmos t of th e peopl e wh o ha dsee n th e previou s one , an dsom e ver y mino r change s wer e made
. Th e protoco l was the n use dwit htw o pilo t subjects , on e a nEPA environmenta l healt hscientis t

an dth e othe r

apsycholog y graduat e studen t doin g arelate d dissertation
. Th e judgmenta l probabilit y encoding s wen t ver y well
. However , in analyzin g th e judgment s an ddiscussin g thes e analyse s wit hDr . Lyl e Jones , i t becam e apparen t tha t mino r change s wer e stil l necessary . Thus , afina l versio n of th e protoco l was created
. I t was discusse dwit hanumbe r of th e peopl e wh o ha dsee n th e previou s drafts , an dwas considere dsuitabl e fo r subsequen t

use . 4. 2 PROTOCO

L OUTLIN

E Th e ful l protoco l i s provide dinApp . C . Onl y anoutlin e i s give nhere
. Sectio n 1 i s a n introduction , describin g th e ris k assessmen t

projec t an dth e purpos e of

th e probabilit y encoding
. Sectio n2 describe s th e idea l hypothetica l experiment , in whic hlarg e number s of childre nar e randoml y assigne da t conceptio n t o on e o f si x exposur e group s o r t o acontro l grou p sheltere dfro mlead
. Environmenta l lea d exposur e i s roughl y constan t a t th e appropriat e leve l fo r eac hchild , suc htha t

whe nhi s o r he r bloo dlea di s measure do n th e thir dbirthday , i t i s a t th e designate dlevel
. Th e sam e environmenta l exposur e continue s unti l th e sevent hbirthday , whe nth e WISC- RI Q tes t i s administered
. Thus , eac hexper t was t o conside r

th e tim e cours e of

lea dinth e children' sP.5 5 4 8 system s accordin g t o hi s o r he r ow ntheoretica l understanding , subjec t t o th e constrain t tha t bloo dlea dwas a t

th e designate dleve l o nth e thir dbirthday
. I t was explaine din thi s sectio ntha t probabilisti c judgment s woul db e encode d regardin g th e mea n I Q decremen t fo r eac hexposur e grou p relativ e t o th e contro l group , th e mea nI Q of

th e contro l group , an dwithi nth e grou p I Q standar ddeviation
. Further , ther e wa s discussio n regardin g th e shap e of th e withi ngrou p I Q distribution
. However , i f a nexper t

considere dth e I Q effect s of lea dt o b e differen t

fo r lowe r socioeconomi c statu s (SES ) tha n fo r

middl e an duppe r

SE S subpopulations , the njudgment s woul db e encode dseparatel y fo r

th e tw o groups . Fo r

thi s purpose , lo w SE S childre nwer e define d a s thos e comin g fro mhousehold s wit hincome s belo w th e fifteent hpercentile
. Sectio n3 define dth e populatio na t ris k a s childre nup t o thei r sevent hbirthday , thereb y indicatin g why th e IQ measur e i s take na t tha t time
. Section s 4 an d5 specifie d exposure , physiological , an denvironmenta l condition s t o assum e fo r th e hypothetica l experiment
. A s wit hth e hemoglobi n protocol , Sectio n6 focuse do nissue s inth e literatur e t o elici t discussio n prio r

t o th e probabilit y encoding
. Th e purpose s wer e t o insur e tha t th e proble mwas structure dproperl y fo r th e expert , t o caus e hi mo r he r t o consciousl y revie w hi s o r

he r knowledg e prio r

t o providin g probabilisti c judgments , an dt o provid e a possibl e basi s fo r

understandin g discrepan t judgments , shoul dthe y occur . Sectio n 7 discusse dfactor s t o b e awar e of whe nencodin g probabilities , an dSectio n8 documente d th e encodin g procedure
. 4. 3 CONDUC T OF TH

E SESSION

S Th e session s wer e conducte dinth e Sprin g of 1985 , an dwit hon e exceptio nwer e carrie dou t

in a n analogou s fashio nt o thos e fo r hemoglobin
. I

nlie u of providin g th e detail s again , th e reade r i s referre dt o Sec . 3.3 .P.5 6
4 9 Th e singl e exceptio n was tha t informatio nwas brough t alon g t o ai dth e expert , shoul dth e perso n hav e wante dit , inencodin g probabilitie s abou t contro l grou p mea n IQ an dwithi ngrou p I Q standar ddeviation
. Th e informatio nconcerne dWISC- RI Q mean s an dstandar ddeviation s fo r subpopulation s stratifie db y variou s demographi c variables , a s compile db y Kaufman an dDoppel t (1976 ) an dsubsequentl y summarize db y Sattle r (1982). *
4. 4 ENCODING TH

E JUDGMENT S Probabilit y encodin g bega n inth e firs t sessio nafte r

th e relevan t

literatur e an d th e factor s affectin g lea deffect s o nI Q ha dbee nthoroughl y discusse dwit hth e expert . Th e intentio nwas t o encod e probabilit y judgment s fo r possibl e mea nIQ decrement s in si x lea dexposur e group s relativ e t o th e contro l group . Th e exposure s wer e suc htha t a t thei r thir dbirthdays , member s of respectiv e group s ha dblood-lea dlevel s of 5 , 15 , 25 , 35 , 45 , an d5 5 yg/dL
. However , highe r level s wer e specifie dfo r afe w of th e experts . T o determin e usefu l point s inth e spac e of mea nIQ decrement s fo r encodin g probabilities , eac hexper t wa s firs t

aske dt o suppl y broa d"99 % confidenc e interval " range s fo r

possibl e mea n IQ difference s betwee nth e contro l an deac hof th e exposur e groups . W

e helpe dth e exper t

determin e thes e range s b y posin g suitabl e question s (e.g. , afte r arang e wa s specified , w e aske dwhethe r th e exper t

coul dconstruc t

aplausibl e explanatio n if

someda y i t

wer e foun dtha t

th e tru e mea ndifferenc e wa s outsid e tha t range) . I

n asimila r

manner , "99 % confidenc e intervals " wer e obtaine dfo r th e mea n I Q of th e contro l grou p an dth e withi ngrou p standar ddeviation
. A t thi s point , al l of

th e expert s agree dtha t

withi n SE S leve l th e sam e standar ddeviatio njudgment s applie dt o al l *I t shoul db e pointe dou t tha t thes e normativ e dat acoul dno t b e use dinplac e of

Th e experts ' judgment s regardin g contro l grou p mea nIQ an dwithi ngrou p IQ standar d deviation , becaus e the y wer e base do nchildre nwit hvaryin g amount s o f lea din thei r systems . Thus , eac hexper t ha dt o adjus t

thes e value s a s h e o r

sh e though t

appropriat e give n hi s o r

vie w o n Th e IQ effect s of lead
. Eac hperso nha dth e option , o f course , o f takin g th e tabulate dvalue s a s poin t estimates
.P.5 7
50 exposur e groups , an dtha t i t wa s reasonabl e t o assum e norma l I Q distribution s withi n subgroups
. Function s wer e fi t

t o th e judgment s followin g th e firs t session
. Summarie s of th e fit s plu s descriptiv e informatio nwer e sen t t o thos e expert s inth e U . S . fo r thei r revie w prio r

t o th e secon dvisi t

wit hthem
. Du e t o tim e an dfinancia l constraints , thi s was no t possibl e t o provid e th e Europea nexpert s wit ha nopportunit y t o revie w th e sam e material s prio r

t o th e secon dmeeting
. Instead , the y wer e brough t t o th e secon dsessio n an dexplaine dthere
. Durin g th e secon dvisi t wit hbot hth e Europea nan dth e U.S . experts , th e material s wer e reviewed , additiona l probabilit y encodin g wa s don e a s necessary , an deac hperso n indicate dwhethe r th e fitte ddistributio ncorrectl y represente dhi s o r

he r judgments
. I

nafe w instances , subsequen t functio nfittin g was carrie dout , an dfurthe r discussio nwas continue db y mai l an dtelephone
. Fortuitously , tw o of th e European s wer e i n th e Unite dState s shortl y afte r th e secon dsession , an di t was possibl e t o hav e ashor t thir dsessio nwit heac hone . A s wil l b e see n in App . D , th e fitte dfunction s wer e infac t ver y clos e t o th e encode dprobabilities
. Whe n w e reache dth e poin t tha t a nexper t

fel t tha t th e probabilitie s correctl y represente dhi s o r he r judgments , tha t

perso nfel t

tha t th e fitte d functio ndi da s well
. 4. 5 REPRESENTING TH E JUDGMENTS A s wit hhemoglobin , i t

wa s necessar y t o fi t

distribution s t o th e assesse dpoint s t o calculat e risk
. Th e natur e of th e variable s bein g judge dwer e differen t tha n wit h hemoglobin , bu t

a s before , th e judgment s wer e generall y S-shaped
. Judge dmea n I Q differenc e wa s bounde dfro mbelo w b y 0 (theoretically , thi s nee dno t hav e bee nth e case , bu t non e of th e expert s gav e an y credenc e t o th e possibilit y of lea denhancin g IQ) . Judgment s abou t

mea n contro l grou p I Q an dwithin-grou p I Q standar ddeviatio nwer e s o fa r fro man y limit s tha t

fo r practica l purpose s the y coul db e treate da s unbounded
. Thus , differen t distribution s wer e require dher e tha nwit hhemoglobin
.P.5 8
5 1 Fo r al l th e experts , judgment s abou t mea ncontro l grou p IQ an dwithin-grou p IQ standar ddeviatio n wer e fi t wel l b y norma l o r

lognorma l distributions
. Th e goodnes s of fi t measur e here , a s befor e an di n wha t follows , wa s th e r-squar e statisti c comparin g actua l judgment s t o thos e predicte db y th e fitte dfunction
. Wit hregar dt o mea n I Q differences , som e expert s gav e judgment s fo r eac hlea d leve l tha t

wer e roughl y symmetri c aroun daparticula r value , an dother s gav e judgment s tha t wer e positivel y skewed , i.e. , attribute dsmal l probabilitie s t o ver y larg e differences
. Generally , th e forme r judgment s wer e bette r fi t wit hnorma l distribution s an dth e latte r

wit hlognorma l distributions , i.e. , distribution s ove r lo g I Q difference
. Specifically , fou r

familie s of

distribution s wer e fi t

t o eac hexpert' s judgment s abou t mea n IQ differences
. On e was th e norma l distributio nallowin g aseparat e mea n an dvarianc e fo r

eac hlea dlevel , anothe r wa s th e lognorma l allowin g aseparat e mea n an dvarianc e fo r

eac hlea dlevel , an dth e remainin g tw o wer e equa l varianc e norma l an d lognorma l distributions
. I n th e latte r

tw o cases , norma l an dlognorma l distribution s wer e fi t respectivel y usin g asingl e poole dvarianc e estimat e fo r each , bu t

allowin g separat e mea nvalue s a t

eac hlea dlevel
. Generally , th e norma l functio nfi t bette r tha nth e equal-varianc e norma l function , an dth e lognorma l functio nfi t bette r tha nth e equal-varianc e lognorma l function
. However , eac hse t of judgment s wer e distinctl y bette r fi t b y eithe r

th e norma l o r th e lognorma l distributions , an donl y th e bette r of th e tw o type s of

distribution s wa s considere dfurthe r

fo r tha t set . A s argue din Sec . 3.5 , th e equal-varianc e distribution s hav e th e virtu e of neve r crossin g an dtherefor e neve r leadin g t o inconsistencies
. However , th e equa l varianc e fit s wer e s o poo r

fo r al l expert s bu t

one , tha t

ther e wa s n o poin t

inpursuin g the minthos e cases . I

norde r fo r th e equal-varianc e fit s t o b e acceptable , th e slope s of th e transforme djudgment s mus t b e abou t

th e same . Tha t

generall y was no t

th e situatio n fo r th e cas e of

I Q decrements , makin g i t undesirabl e t o utiliz e equal-varianc e fits
. Althoug hP.5 9
5 2 thi s cause s th e curve s t o cros s a t som e point , th e distribution s ar e space dsufficientl y fa r apart , tha t

th e crossing s occu r

in th e ver y extrem e tails
. Thi s i s asmal l cos t fo r representin g th e judgment s accuratel y withi nth e range s of interest
. 4. 6 TH E EXPERT S I n Marc hof

198 5 th e individual s liste dinTabl e 4. 2 wer e selecte db y EPA/OAQP S staf f fo r participatio n i n th e study
. Al l agreed , agai nwit hth e understandin g tha t thei r judgment s woul db e anonymous . Th e judgment s presente dher e ar e attribute dt o Expert s Fthroug hK, wit hthes e lette r designation s havin g bee nrandoml y assigned
. W e ar e gratefu l t o thes e peopl e fo r thei r har dwor

k an dth e man y hour s the y spen t wit hus . 4. 7 RESULTS Thi s sectio n utilize s th e function s fi t t o eac hindividual' s probabilisti c judgment s t o presen t

asummar y of

th e quantitativ e results
. Th e function s provid e a naccurat e representatio n of

th e underlyin g encode dvalues , bot hbecaus e goodnes s of fi t was excellen t an dbecaus e eac hexper t endorse dth e outpu t

of th e respectiv e function s a s representin g hi s o r

he r judgments
. Summarie s of

th e qualitativ e discussion s abou t th e IQ an dbehaviora l effect s of lea dar e i n Sec . C. 4 o f App . C . Detaile dquantitativ e results , includin g th e encode d judgments , paramete r

value s fo r

th e fitte dfunctions , goodnes s of fi t measures , an d derive dsubjectiv e probabilitie s abou t dose-respons e functions , ar e liste di nAppendi x C . Recal l tha t

th e expert s wer e give nth e optio nof makin g separat e judgment s fo r lowe r an dhighe r

SE S children
. Th e lowe r SE S grou p wa s define da s thos e childre nwhos e famil y income s do no t

excee dth e fifteent hpercentile ; th e remainin g childre nwer e t o b e considere din th e highe r SE S group . Al l th e expert s excep t Fbeliev e tha t

a t th e dose s unde r consideration , lea dinteract s wit hvariable s tha t contribut e t o SE S level
. Therefore , al l excep t

Felecte dt o provid e separat e judgment s fo r th e tw o SE S levels
.P.6 0
53 I t i s convenien t

t o presen t

simultaneousl y th e judgment s abou t th e lowe r

an d highe r SES contro l grou p mea n I Q values , an dt o d o th e sam e wit hth e judgment s abou t th e within-grou p standar ddeviations
. However , th e judgment s abou t th e mea n I Q decrement s ar e mos t

easil y comprehende dif the y ar e show nseparatel y fo r th e tw o SE S levels
. F' s judgment s wil l b e repeate dinth e case s fo r purpose s of

comparison
. 4.7. 1 Contro l Grou

p Mea n I Q Exper t I fel t unabl e t o provid e judgment s abou t th e mea nI Q o f

agrou p o f childre n sheltere dfro mlea dexposure . Th e othe r experts ' judgment s ar e show ninFigur e 4.1 , categorize db y SE S level
. Th e to p fou r bar s represen t

th e lo w SE S judgment s of G , H , J , an dK ; th e centra l ba r represent s th e singl e overal l judgmen t of F ; an dth e lowe r fou r bar s represen t

th e hig hSES judgment s of G , H , J , an dK . Th e symbo l withi n eac hba r i s th e media njudge dmea nI Q value
. I nothe r words , fo r agive n bar , accordin g t o tha t expert , ther e i s a0.5 0 probabilit y tha t th e contro l grou p meanIQ woul db e abov e th e valu e indicate db y th e symbo l an da0.5 0 probabilit y tha t i t woul db e belo w th e indicate dvalue
. Th e bracket s immediatel y t o th e lef t an d righ t of th e symbo l denot e eac hexpert' s centra l 50 % credibl e interval , i.e. , th e interva l suc htha t ther e i s a0.2 5 probabilit y of th e mea nI Q fallin g belo w it , a0.5 0 probabilit y of th e mea nIQ fallin g withi n it , an da0.2 5 probabilit y of th e mea nI Q fallin g abov e it
. Th e othe r pai r of bracket s denote s th e centra l 90 % credibl e interval
. Expert s G , H , an dJ sho w considerabl e agreemen t i nthei r judgment s regardin g th e lo w SES group . Thei r media n judgment s abou t th e mea nI Q rang e fro m9 5 t o 9 7 points , an d(fro mthei r 90 % credibl e intervals) , wit hprobabilit y 0.05 , th e mea n I Q exceed s avalu e tha t

i s betwee n 9 8 an d10 3 points
. Exper t K' s media njudgmen t

i s 8 5 points , an daccordin g t o hi mo r her , th e mea nIQ exceed s 9 2 point s wit hprobabilit y 0.05
. Th e judgment s o f

al l fou r expert s overla p considerabl y regardin g th e hig hSE S group . Thei r

media n judgment s rang e onl y fro m104 t o abou t 10 6 points
. Th e uppe r limit s of th e 90 % credibl e interval s rang e fro m10 8 t o 11 2 points
.54 P.6 1

1 \o


### 110 - 105 - 

## I Q 0 

## 100 -
9 5 -
9 0 -
8 5 - T

• J -

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### <

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1 

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• • 0 

# 1

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# 1 1 i A 

# 1 

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## F G H J K 

## Lowe rSE S F G H J K



## Highe rSE S

FIGUR E 4. 1 Judgment s abou tContro l Grou p Mea n I QP.6 2

5 5 Exper t Fdisplay s th e leas t

uncertainty
. Hi s o r

he r judgment s abou t

th e entir e populatio nfal l betwee n thos e of th e othe r

expert s fo r

th e lo w an dhig hSE S levels , a s the y should
. Th e media n judgmen t i s 10 1 points ; wit hprobabilit y 0.05 , th e mea n I Q exceed s 10 2 points
. 4.7. 2 Within-Group I

Q Standard Deviatio n Exper t I fel t unabl e t o provid e judgment s abou t thi s variable , a s well
. Th e judgment s of

th e remainin g expert s ar e show ninFig
. 4.2 , arrange daccordin g t o th e sam e forma t a s Fig
. 4.1 . Exper t Fwas certai n tha t

th e within-grou p IQ standar ddeviatio nwoul db e identica l t o thatnorme dfo r th e populatio na s awhole , 1 5 points
. Exper t G , considerin g eac ho f th e tw o SE S group s t o b e somewha t mor e homogeneou s tha nth e overal l population , was certai n tha t th e within-grou p I Q standar ddeviatio nwoul db e 1 4 point s in eac hcase . Th e judgment s of

expert s H , J , an dK

wer e relativel y similar
. The y though t tha t th e IQ s of

th e lo w SE S grou p woul db e mor e homogeneou s tha nthos e of th e hig hSE S group , an dtherefor e estimate dlowe r standar ddeviations
. Th e media njudge dstandar d deviatio n fo r

th e lowe r

SES leve l rang e fro m12. 4 t o 1 3 points ; uppe r limit s of

th e 90 % credibl e interval s rang e fro m1 4 t o 1 5 points
. Exper t J wa s certai ntha t

th e standar d deviatio n woul db e 1 4 point s fo r th e uppe r

SE S level , whil e H an dK hav e media n estimate s of

13. 5 an d14. 3 points , respectively
. Th e uppe r limit s o f thei r 90 % credibl e interval s ar e 15. 6 an d15. 1 points , respectively
. 4.7. 3 Mea

n I Q Decrement s fo rth e Lo wSES Grou

p Figur e 4. 3 summarize s th e judgment s of al l si x expert s regardin g mea n IQ decrement s fo r

th e lo w SES group . Eac hperson' s judgment s ar e show ninaseparat e panel
. Bloo dlea di s o n th e absciss aan dmea nIQ decremen t (mea ncontro l grou p IQ minu s mea n expose dgrou p IQ) i s o nth e ordinate
.56 P.6 3



# a I Q I D


### 15 -
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13 -
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## F G H J K 

## Lowe rSE S F G H J K



## Highe rSE S

FIGUR E 4. 2 Judgment s abou to I QP.6 4

5 7

2 5 3 5 4 5 5 5 6 5 5 1 5 2 5 3 5 4 5 5 5

A ' Q | Exper t H 15 H
10 H

• * L 5 1 5 2 5 3 5 4 5 5 5 A,-** A • Q i Exper t J

1 5 2 5 3 5 4 5 5 5 6 5

FIGUR E 4. 3 Judgment s abou tA

—fo raLowe rSES Populatio nP.6 5
5 8 Th e dark , centra l curv e i n eac hpane l show s th e media njudge dI Q decremen t fo r eac hlea dlevel
. I

n othe r words , fo r

agive npanel , accordin g t o tha t exper t ther e i s a 0.5 0 probabilit y tha t

th e actua l mea nI Q decremen t woul db e greate r

tha nth e indicate d value , an da0.5 0 probabilit y tha t i t woul db e less
. Th e successivel y lighte r pair s o f curve s tha t

bracke t th e media n curv e represen t centra l 50% , an d90 % credibl e intervals
. Figur e 4. 4 allow s acompariso nof judgment s acros s th e experts . Th e axe s ar e th e sam e a s in Figur e 4.3 . Th e vertica l bar s a t eac hlea dleve l represen t eac hexpert' s centra l 90 % credibl e interval , an dth e symbol s ar e hi s o r he r media njudgments
. Exper t Fconsistentl y judge s th e IQ effect s of lea dt o b e les s tha nd o th e othe r experts , an devidence s considerabl y les s uncertaint y abou t th e magnitud e of

thes e effect s tha n do th e others
. Exper t Fi s certai ntha t

ther e i s n o IQ effec t

of lea dup t o a t leas t 1 5 yg/dL
. A t

2 5 yg/dL , th e media njudge dIQ decremen t i s abou t 0. 5 point , an dthi s increase s t o amedia n judge dI Q decremen t of jus t unde r 2 point s a t

6 5 yg/dL
. Accordin g t o F , a t 2 5 yg/dL , th e I Q decremen t exceed s approximatel y 1 poin t wit hprobabilit y 0.05 , whil e a t 6 5 yg/dL , i t

exceed s 5 point s wit hth e sam e probability
. Ther e ar e overridin g similaritie s inth e judgment s of th e othe r

experts , althoug h ther e ar e als o small , consisten t difference s amon g them
. Thus , onl y G , H , an dJ giv e an y credibilit y t o ther e bein g IQ effect s a s lo w a s 5 yg/dL , whil e I doe s s o a t 1 5 yg/dL , an dK doe s a t 2 5 yg/dL
. Th e judgment s of H an dJ ar e consistentl y ver y close , a s ar e thos e of G , I , an dK

, whic ha s agrou p ar e somewha t lowe r tha nthos e of

H an dJ . Considerin g th e fiv e set s of

judgments , th e media njudge dIQ decremen t a t 5 yg/d Lrange s fro m0 t o 2. 5 points
. Th e media n judge dIQ decremen t a t 5 5 yg/d Li s fro mabou t 7 t o 1 1 points
. Accordin g t o th e judgment s of G , H , an dJ , wit hprobabilit y 0.05 , th e I Q decremen t exceed s 3 t o 5. 5 point s a t 5 yg/dL , whil e accordin g t o al l 5 experts , i t exceed s 1 1 t o 1 7 point s a t 5 5 yg/d Lwit hth e sam e probability
.15 -

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—i—i—i—i—i—i— i 1—i— i 1 1 rr G H I J KF6HIJ K —i—- I ?— ( 1—r r C H I J K —I—1—I—I—•—I—I—I—•—I—I—(—•—I—I—I—I—I—I—I—I—I—I—I—I— I I (fCHlJ K(GHIJ KrCNIJ KFGHIJ K 5 Mg/d L 1 5 fig/dL2 5 A*g/d L 3 5 fzig/dl 4 5 fig/dl

5 5 /ug/d L 

### Blood-Lea d Leve l 6 5 fxg/dL

FIGUR E 4. 4 Compariso n o f

Judgment s abou tAy

^ fo raLowe rSE S Populatio nP.6 7
60 4.7. 4 Mea

n I Q Decrement s fo rth e High SES Grou p Figure s 4. 5 an d4. 6 displa y th e judgment s abou t mea nI Q decremen t

fo r th e hig h SE S group , an dar e rea din th e sam e fashio na s ar e Figs
. 4. 3 an d4.4 , respectively
. A s wit hth e lo w SE S population , Fconsistentl y judge s th e IQ effec t t o b e les s tha nd o th e othe r experts . Fro m2 5 yg/d Lon , th e judgment s of th e other s overlap , with , a s before , thos e o f H an dJ bein g ver y simila r an dsomewha t

greate r tha nthos e of

G , K , an dI , whic hthemselve s ar e similar
. Onl y H give s an y credibilit y t o th e existenc e of a n IQ effec t a t 5 yg/dL , G , I , an dJ d o s o a t 1 5 yg/dL , an dFan dK concu r a t 2 5 yg/dL
. Considerin g al l th e expert s simultaneously , th e media njudge dIQ decremen t a t 1 5 yg/d Lrange s fro m0 t o 2. 5 points ; a t 5 5 yg/dL , i t

range s fro m1. 5 t o 7. 5 points
. Accordin g t o G , H , I , an dJ , wit hprobabilit y 0.0 5 i t exceed s 1 t o 7 point s a t 1 5 yg/dL , whil e accordin g t o al l th e expert s i t exceed s 4 t o 11. 5 point s a t 5 5 yg/d Lwit hprobabilit y 0.05 . 4.7. 5 Chang e i n Percentag e o f Lo wSE S Grou

p with IQs < 8 5 Th e judgment s abou t

contro l grou p mea nIQ , mea nIQ decremen t a t eac h exposur e level , an dwithin-grou p IQ standar ddeviatio nca nb e use dalon g wit hth e assumptio nof

withi n grou p norma l I Q distribution s t o calculat e subjectiv e probabilitie s abou t th e lea dinduce dchang e inpercentag e of th e populatio nwit hIQ' s belo w an y critica l level
. Thes e woul dcorrespon dt o judgment s abou t I Q dose-respons e functions , an dar e th e result s necessar y ultimatel y fo r th e ris k calculations
. Th e mathematica l detail s ar e in Appendi x D . Here , w e illustrat e th e result s fo r acritica l I Q of

8 5 points
. W e poin t out , however , tha t

greate r uncertaint y i s evidence dinthes e dose-respons e function s tha n in th e separat e judgment s show nabove , becaus e uncertaint y abou t thre e parameter s i s bein g combined
. Not e tha t calculation s ar e no t

possibl e fo r

exper t I , becaus e h e o r

sh e decline dt o judg e contro l grou p mea nI Q an dwithin-grou p IQ standar d deviation
.6 1
Expert F

2 5 3 5 4 5 5 5 6 5 A I Q t Expert G 10 - 8 - 6 - 4 - 2 - n *

- ' " .•*• /

U TI I i I 1 5 2 5 35 45 55

Af 7 A
_ l u i txper t J

FIGUR E 4. 5 Judgment s abou tA

—fo raHighe rSE S Populatio n10 -

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1 I I III I 1 1 1 1 1 1 1 1 1 1 1 1 l— l 1 r— I l— l 1 1 1 1 1 1 •1 1 1 1 1 I I 1 1 IIIIIII — rGHIJ KFGHIJ KFGHIJ Kf GH I J * FGHIJ KFGHIJ KFGHIJ K 5 /ug/d L 1 5 fig/dl

2 5 /xg/d L 3 5 /xg/d L 4 5 fig/dL5 5 fig/dL6 5 /ug/d L 

### Blood-Lea d Leve l

FIGUR E 4. 6 Comparison s o f

Judgment s abou tAy

^ fo raHighe rSE S Populatio nP.7 0

6 3 Figure s 4. 7 an d4. 8 sho w th e calculate dsubjectiv e probabilitie s abou t th e dose

respons e functio n fo r

increas e in percentag e of IQ' s les s tha no r

equa l t o 8 5 point s in th e lo w SES population
. Th e absciss ai nbot hcase s i s bloo dlead , th e ordinat e i s populatio n respons e rat e (i.e. , lea dinduce dincreas e i npercentag e belo w 8 5 points) , an dth e curve s ar e analogou s t o thos e i n th e precedin g figures
. A s woul db e expected , F' s judgment s sugges t muc hlowe r

dose-respons e function s tha n do thos e of

th e others
. Th e result s fro mG , H , J , an dK overla p considerably , wit h thos e fro mH an dJ bein g ver y simila r an dslightl y greate r

tha nthos e fro mGan dK, whic hthemselve s ar e similar
. Accordin g t o F , th e media njudge drespons e rat e i s les s tha n1 % a t 2 5 yg/dL , risin g t o 4 % a t

6 5 yg/dL
. Wit

hprobabilit y 0.05 , i t

exceed s 1 % a t

2 5 yg/dL , an dwit hth e sam e probability , i t

exceed s 7 % a t

6 5 yg/dL
. Fo r

G , H , an dJ , th e media nrespons e rat e i s fro m2.5 % t o 6 % a t 5 yg/dL , whil e includin g K , i t i s betwee n21 % an d32 % a t 5 5 yg/dL
. Fo r

th e sam e experts , th e respons e rat e exceed s abou t 4 % t o 11 % a t

5 yg/dL , 14 % t o 26 % a t

2 5 yg/dL , an d29 % t o 45 % a t 5 5 yg/dL , eac hwit hprobabilit y 0.05
. 4.7. 6 Chang e in Percentag e o f Hig h SES Grou

p with IQ

s < 8 5 Th e patter n of

similaritie s an ddifference s acros s expert s i s th e sam e her e a s i t wa s above , s o correspondin g figure s ar e no t shown
. Generally , highe r SE S childre n ar e les s a t ris k tha n lowe r

SE S children
. Th e result s fo r Far e th e sam e a s thos e show n previously , becaus e the y ar e base do nth e sam e judgments
. Accordin g t o G , H , an dJ , th e media n judge drespons e rat e i s fro mabou t 0.5 % t o 3 % a t

1 5 yg/dL , whil e accordin g t o G , H , J , an dK , i t

i s fro mabou t

5 % t o 12 % a t

5 5 yg/dL
. Accordin g t o th e sam e experts , th e media n respons e rat e exceed s 2 % t o 7.5 % a t 1 5 yg/dL , 4 % t o 11 % a t 2 5 yg/dL , an d9.5 % t o 18 % a t

5 5 yg/dL , al l wit hprobabilit y equa l t o 0.05
.*i 1— 4 Cm 

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### Blood-Lea d Leve l

FIGUR E 4. 8 Blood-Lea d Leve l Compariso n o f Increase d Probabilitie s o f Havin g I

Q < 8 5 fo raLowerSES Populatio nP.7 3
6 6 4. 8 DISCUSSION Considerin g th e extensiv e debat e concernin g th e IQ effect s of lead , th e degre e of consensu s reflecte din th e presen t result s i s notable
. Thi s i s particularl y so , sinc e th e expert s wer e selecte ds o a s t o spa nth e ful l rang e of opinion
. A s occurre dwit hth e hemoglobi nresults , askin g th e expert s t o encod e thei r subjectiv e probabilitie s abou t specific , well-define dscientifi c outcome s eliminate ddisagreement s abou t definitions , policy , an dothe r

matters . Th e remainin g disagreements , evidence dinth e precedin g results , ar e du e t o differin g interpretation s of , an dextrapolation s from , evidence
. Generally , Expert s H an dJ provide dsimila r judgments , a s di dExpert s G , I , an d K . Furthermore , thes e tw o set s of judgment s overlappe dt o agrea t extent . Exper t

F consistentl y estimate dsmalle r effect s tha ndi danyon e else , an dindicate dles s uncertaint y abou t

them
. Uncertaint y (a s indicate db y variance ) generall y increase dwit hbloo dlea dwithi n th e rang e of

interest , a s woul db e expected
. I naddition , individua l subjectiv e probabilitie s cove r

broade r range s fo r

th e lo w SE S tha nfo r

th e hig hSE S group . Thi s resul t may reflec t

mor e dat aa t

th e hig hSE S level , o r mor e uncertaint y abou t th e influenc e of

th e covariate s a t

th e lo w SE S level
. Th e judgment s regardin g bot hmea nIQ decrement s an ddose-respons e function s ar e of interes t in thei r

ow n right
. However , inSec . 5 the y wil l b e combine dwit h exposur e estimate s t o yiel dris k distributions
.P.7 4

6 7 5 ESTIMATE

D RISK S OF ADVERSE HEALT H EFFECT S UNDERALTERNATIV

E AIR-LEA D SCENARIO S Risk s of advers e healt heffect s unde r alternativ e air-lea dstandard s ca n b e estimate db y combinin g dose-respons e function s wit hblood-lea ddistribution s appropriat e t o th e alternativ e standards
. Th e estimate s mus t incorporat e th e uncertaint y associate d wit hdose-respons e function s a s wel l a s tha t associate dwit hblood-lea ddistributions
. Th e forme r

ha s bee n discusse din Sees . 2- 4 fo r EP , hemoglobin , an dIQ , respectively ; th e latte r wil l b e covere din thi s section
. Th e mai nfocu s of

thi s sectio ni s t o estimat e th e risk s o f advers e healt heffect s unde r alternativ e air-lea dscenario s fo r youn g childre ninth e vicinit y of severa l poin t source s o f

lea dlocate din th e U.S . Result s wer e obtaine db y mathematicall y combinin g th e Pb B an ddose-respons e informatio nint o aris k model
. Th e exposur e informatio n(i.e. , Pb B level s fo r

alternativ e air-lea dscenarios ) was develope db y PEI Associates , Inc. , unde r contrac t

t o EPA , usin g th e integrate dlead-uptake / biokineti c mode l presente din th e EPA staf

f paper . Sinc e methodologica l developmen t i s no t complete , thes e result s ar e preliminary
. Thi s sectio ni s organize dint o fiv e mai nsubsections
. Th e firs t cover s alternativ e air-lea dscenario s an destimate dresultan t Pb B distribution s amon g childre nresidin g in th e vicinit y of

selecte dpoin t

source s o f

lead
. Th e nex t

thre e subsection s presen t estimate s of

th e risk s of

advers e healt heffect s involvin g EP , hemoglobin , an dIQ , respectively
. 5. 1 EXPOSUR

E ESTIMATE

S EPA' s OAQP S use da n integrate dlead-uptake/biokineti c mode l t o estimat e th e relationship s betwee n ai r qualit y an dblood-lea dlevel s amon g U.S . childre nresidin g in th e vicinit y of

poin t source s of

lea demissions
. Th e mode l incorporate s abiokinetic

metaboli c model develope da t New Yor

k University , whic htake s int o accoun t th eP.7 5
6 8 absorptio nof

lea dint o th e bloodstrea mthroug hinhalatio nan dingestion , an dit s subsequen t

movemen t

amon g body compartment s (i.e. , blood , bone , an dsof t tissue)
. Bloo dlea di s th e inde x of lea dexposur e generate db y th e mode l fo r presen t purposes . Estimate s o f

exposur e tak e int o accoun t change s i nactivit y patterns , physiology , an d metabolis mo f

childre n throug hvariou s stage s i nthei r development
. Fo r

example , childre n si x month s an dsi x year s of ag e diffe r

i nterm s of

numerou s physiologica l indicators , a s wel l a s concentratio nof lea dinth e immediat e environment , degre e of hand-to-mout hactivity , tim e spen t outdoor s vs . indoors , difference s inlea dabsorptio n in th e gastro-intestina l trac t a t differen t

ages , etc . Fo r

thi s analysis , onl y childre n tha t liv e in housin g tha t

i s fre e of

lead-base dpain t

hazard , an dwh o ar e no t expose dindirectl y t o occupationa l source s of lea dfro mhousehol dmembers , wer e modeled
. Blood-lea dlevel s fo r

childre nlivin g i nth e vicinit y o f fiv e U.S . poin t

source s of lea demission s wer e include din ou r analysis
. Fo r

th e are asurroundin g thes e poin t sources , whic hwil l remai n nameles s a t thi s time , th e tota l numbe r of childre n (0- 6 years) , th e numbe r

of childre n inth e 84-mont hcohort , an dth e percentag e of thos e childre nlivin g in household s havin g income s belo w povert y leve l ar e liste dinTabl e 5.1
. Thi s leve l approximatel y correspond s t o th e lowe r SES leve l (th e lowes t

15% , base do n famil y income ) use din th e IQ encodings
. Seve n alternativ e air-lea dscenario s wer e considere dfo r eac hof

th e poin t sources . Thes e ar e groupe din thre e categories : baseline , precontrol , an dpostcontrol
. Fo r illustrativ e purposes , air-qualit y estimate s base dondispersio nmodelin g use din th e exposur e analysi s ar e presente dinTabl e 5. 2 fo r area s surroundin g th e fiv e poin t source s unde r differen t

air-lea dscenarios
. I t i s importan t

t o not e tha t

thes e air-lea dvalue s represen t estimate s a t

th e geographi c center s of th e censu s tract s surroundin g th e 9 differen t poin t sources . Air-lea dconcentration s a t othe r recepto r

site s close r

t o th e poin t source s ar e generall y highe r tha nth e range s shown
. Th e baselin e scenari o represent s modele dai r qualit y a s i t

existe daroun dth e particula r poin t sourc e fo r

th eP.7 6


### 69
TABL E 5. 1 198 0 Populatio nData a fo

r SelectedU.S . Point Source s o f Lea d Emission s

Poin t Sourc e 1 2 3 4 5 Typ e SecondarySmelte r SecondarySmelte r BatteryPlan t BatteryPlan t PrimarySmelte r Tota l Numbe r o f Childre n Age d 0- 6 Year s " 15,83 5 4,61 4 23,42 2 12,95 6 12,57 6 Numbe r o f

Childre n i n 84-Mont h Cohort 5 2,27 3 67 1 3,30 5 1,99 4 1,71 8 Percen t belo w

Povert yLevel 0
1 4 2 4 1 9 1 1 6

aNumber s calculate d based o n 198 0 U.S . Burea u o f Censu s dat a an d aggregate d acros s censu s tract s aroun d eac h poin t source . Populatio n dat a represen t the numbe r o f childre n livin g i n housing fre e o f lead-base d pain t hazard s an d exposur e t o occupationa l source s o f lead . I n thi s case , the 84-mont h cohor t i s a grou p o f childre n born i n January 197 4 an d alread

y7 year s ol d a t the en d o f the exposur e period .
c Dat a ar e fro

mFerd o (1986) .P.7 7
7 0 TABLE 5. 2 Comparativ e Ai rQuality a tCensu s Trac tCentroid s Surrounding Modele d Poin tSource s

Rang e o f Monthl y Air-Lea dConcentrations 3 Poin t 1990-199 6 1990-199 6 Source s 1974-198 0 1983-198 9 (0.2 5 pg/m 3 ) b (1. 5 yg/m 3 ) b 1 0.53-1.8 3 0.01-0.9 2 0.01-0.0 3 0.01-0.1 3 2 0.54-1.8 3 0.02-0.9 2 0.01-0.0 3 0.01-0.1 3 3 0.53-1.8 3 0.01-0.9 2 0.01-0.0 3 0.01-0.1 3 4 0.53-1.8 3 0.01-0.9 2 0.01-0.0 3 0.01-0.1 3 5 0.01-1.2 7 0-0.6 4 0-0.0 4 0-0.2 3

a Monthl y

air-lea d concentration s expresse d i nmicrogram s pe r cubi c mete r an

d rounde d t o tw

o significan t digit s wer e esti mate d b

y anothe r contracto r fo r EP A usin g IS C dispersion mode l an

d gasoline-lead-consumptio ndat a (base d onprevious , current , o r futur e emissio nrates ) a t geographi c centroid s o f censu s tract s surroundin g eac hpoin t sourc e unde r differen t scenario s (Johnso nan d Paul , 1986) . Range s reflec t spatia l variabilit y around poin t source s (decreasin g air-lea d level s wit hincrease d distances ) an d tempora l trend s (reduc tioni ngasolin e lead emission s sinc e the 1970s) . Th e 1990-199 6 scenario s assume tha t the modele d poin t sourc e i s i ncomplianc e wit hwhateve r lead NAAQ S i s bein g analyzed . Fo r example , th e highes t air-lea d concentratio nprojecte d a t a nai r qualit y

recepto r unde r th e 0.2 5 yg/ m lead NAAQ S i s no highe r tha n0.2 5 pg/ m , wit hal l othe r recepto r point s jus t a t o r below

tha t level . Ai r qualit y value s a t geographi c centroid s ar e considerabl y below othe r recepto r value s becaus e o f distanc e fro

m th e poin t sourc e an d a nassumptio ntha t air leadlevel s i na nare a declin e linearl y wit hreduction s i n emissio nrates .P.7 8

7 1 1974-198 0 tim e period
. Similarly , th e precontro l perio dcover s th e year s 1983-89 . Blood-lea dlevel s ar e estimate dt o b e lowe r inth e precontro l vs . baselin e period s primaril y becaus e of

th e beginnin g of

th e gasolin e lea dphasedown , th e implementatio n of th e ambien t

ai r qualit y standar dfo r

lead , an dreduction s of lea dlevel s incanne dfoods
. Lea dexposur e i n th e U.S . als o decline di nthi s er adu e t o additiona l factor s suc ha s increase dawarenes s of lead-base dpain t

hazard s an dth e gradua l reductio ninth e old , lead-base dpainte dhousin g stock
. Th e postcontro l perio dspan s 1990-96 , an dinclude s fiv e alternativ e air-lead-leve l scenario s (lea dNAAQ S of 0.25 , 0.5 , 0.75 , 1 , an d 1. 5 yg/m 3 ) . Fo r eac halternativ e air-lea dscenari o considere dinth e postcontro l period , i t i s assume dtha t

th e poin t

sourc e i s inattainmen t wit hwhateve r

standar di s analyzed
. I n othe r words , th e highes t

air-qualit y recepto r

sit e woul db e a t

o r belo w whateve r

standar d leve l i s considered
. I

f th e dispersio nmodelin g indicate dtha t astandar dleve l woul db e exceede din th e postcontro l scenario , th e highes t recepto r

sit e was adjuste ddow nt o th e standar dlevel , wit hal l othe r recepto r

site s reduce dproportionately
. Th e reade r i s referre dt o alea dexposur e repor t (Johnso nan dPaul , 1986 ) tha t detail s th e metho duse d t o mode l ai r

qualit y fo r

eac hscenario
. Blood-lea dlevel s inth e postcontro l perio dar e estimate dt o b e furthe r reduce dprimaril y becaus e of th e continue dreduction s in lea d level s incanne dfood s an ddrinkin g water . Fo r eac hair-lea dscenario , uppe r an dlowe r

boun destimate s of

th e geometri c mea nbloo dlead s wer e calculate db y th e exposur e model
. Thes e bound s wer e obtaine db y considerin g arang e of

"high " an d"low " setting s o f paramete r

value s tha t

significantl y affec t fina l Pb B estimates
. Many o f th e alternativ e postcontro l scenario s resulte din mea nPb B level s tha t

wer e essentiall y equivalen t an drelativel y lo w (

< 5 yg/dL)
. Thi s suggest s tha t

th e smal l incrementa l change s inambien t ai r qualit y level s unde r

th e alternativ e NAAQ S analyze dma y no t b e sufficien t

t o significantl y influenc e Pb B distribution s amon g population s of childre ninth e future
. Th e resul t ma y b e misleading ,P.7 9

7 2 however , becaus e majo r air-qualit y impact s ar e confine dprincipall y t o th e immediat e vicinit y ( < 1 km ) of

th e poin t

sources , whil e th e modele dbloo dlead s wer e obtaine db y averagin g ove r

relativel y larg e area s aroun dth e poin t source s (resultin g i nair-lea dlevel s dow n t o urba n o r

rura l backgroun dconcentration s a t th e boundarie s of

th e poin t

sourc e impac t areas) . A complet e tabulatio nof th e scenario s use dinth e ris k calculation s i s provide di n App . D . Eac hscenari o contain s upper - an dlower-boun destimate s of th e geometri c mean s of modele dbloo dlead s fo r th e 84-mont hcohor t

fo r fou r ag e periods : 0- 3 years , 4- 6 years , 0- 6 years , an dth e 36t hmont hof life
. Estimate s fo r

th e firs t

tw o period s ar e neede din orde r

t o combin e exper t

judgment s abou t

hemoglobi ndecrements , whic hwer e obtaine dfo r

subpopulation s of

childre nof

thos e ages . Th e thir di s neede dt o estimat e th e risk s of

elevate dEPlevels , an dth e las t i s neede dt o estimat e th e ris k of I Q effects
. Al l ris k estimate s presente dar e fo r th e 84-mont hcohort s modele dineac hair

lea dscenario
. Th e 84-mont hcohor t i s th e cohor t

of childre nbor ninth e beginnin g of eac hexposur e period , an dwh o reac hthei r sevent hbirthday s a t

th e en dof

th e exposur e period
. Th e 84-mont hcohort s constitut e onl y asmal l fractio nof th e tota l numbe r

o r childre n age d0- 6 year s surroundin g eac hpoin t sourc e modeled
. I

naddition , ris k estimate s fo r

lead-induce dIQ effect s ar e presente dsolel y fo r childre nfro mfamilie s of childre n fro mlowe r

SE S status . Thi s grou p of childre nconstitute s 6-24 % of th e tota l poulatio nof

childre n aroun deac hof th e fiv e poin t

source s (Tabl e 5.1)
. A s aresult , an y headcoun t

ris k number s tha t

woul db e calculate dbase do nthes e ris k estimate s woul d underestimat e th e tota l ris k i n th e populatio no f

youn g childre nmodeled
. A t thi s time , headcoun t

ris k estimate s ar e no t

presented
. I t i s assume dtha t

bloo dlead s ar e describe db y lognorma l distribution s wit hth e geometri c mea n (GM) value s tabulated , an dasingl e geometri c standar ddeviatio n(GSD ) of 1.42 . Propertie s of

th e lognorma l distributio nar e describe di nApp . B . Th e geometri c mea n (GM) bloo dlead s fo r al l 84-mont hcohort s fo r th e thre e scenario s tha t ar eP.8 0

7 3 significantl y differen t

fro mon e anothe r

(fo r Source s 2 an d5 ) ar e liste dinTabl e 5.3
. Al l of th e postcontro l scenario s resul t inPb B level s tha t

ar e nearl y identical , s o onl y on e postcontro l scenari o (havin g uppe r an dlowe r

G M Pb B values ) i s listed
. Geometri c mea n blood-lea dvalue s ar e lowes t aroun dSourc e 5 , whic hi s locate dinarura l area , an d highes t aroun dSourc e 2 , a n urba n area . Th e other s (als o urba nareas ) ar e slightl y les s tha n thos e fo r

Sourc e 2 . T o illustrate , th e upper-boun destimat e of G M = 27 yg/d Lfo r th e baselin e exposur e scenari o fo r Sourc e 2 mean s tha t

55 % of th e populatio nwoul dhav e ha dPb B level s abov e th e curren t Center s fo r

Diseas e Contro l definitio no f a nelevate d Pb B leve l of

2 5 yg/dL
. Th e correspondin g lowe r boun dof

G M = 19. 4 yg/d Lmean s tha t 33 % of th e populatio n woul dhav e exceede dtha t level
. A s apoin t

of reference , ove r

th e year s 1976-80 , th e secon dNationa l Healt han d Nutritio nSurve y (NHANE S II) (Annes t e t al. , 1982 ) wa s conducted
. I t include drepre sentativ e examinee s fro murba n an drura l population s age dsi x month s t o fiv e years . Urba n examinee s ha daG M Pb B leve l of

approximatel y 1 7 yg/dL
. Thi s valu e i s abou t 0. 2 yg/d Llowe r

tha n th e lowe r

boun dG M Pb B estimat e fo r

childre nage d0- 6 year s a t Sourc e 2 . Rura l childre n ha da n averag e Pb B leve l of 13. 9 yg/dL , whic hi s abou t 0. 5 yg/d L highe r tha nth e uppe r

boun dfo r

Sourc e 5 fo r

th e baselin e scenario
. 5. 2 RIS K RESULT S FO RE P A complet e listin g of

result s an ddescription s of th e model s use dt o estimat e th e ris k ar e provide din App . D . A n overvie w i s presente dhere
. A s discusse di nSec . 2 an d App . A , E Pdose-respons e uncertaint y was calculate dfro mth e dat apublishe db y Piomell i e t al
. (1982) . Recal l tha t tw o level s of

E Pwer e considere dt o b e advers e healt heffects , 3 3 yg/d Lan d5 3 yg/dL , whic har e on e an dtw o standar ddeviation s abov e th e "reference " EPleve l (21. 7 yg/dL ) determine dfo r th e grou p o f

childre nhavin g th e lowes t Pb B levels
. Th e probabilisti c dose-respons e function s wer e combine dwit hth e Pb B distribution s (fo r

childre n age d0- 6 years ) describe di nSec . 5. 1 t o produc e th e overal l ris kP.8 1 

### 74
TABL E 5. 3 Geometri c Mea nBlood-Lea d Level s (yg/dL ) fo

r 84-Mont hCohorts *

Sourc e 5 Sourc e 2 b Ag e Grou

p Lowe r Uppe r Lowe r Uppe r Baselin e Scenari o (1974-80 ) 0- 3 Year s 4- 6 Year s 0- 6 Year s 36t h Mont h 8. 6

6. 4 7. 7 7. 7 13. 9 11. 5 13. 4 12. 9 19. 4

14. 3 17. 2 19. 2 27. 0

21. 2 24. 5 27. 1 Precontro l Scenari o (1983-89 ) 0- 3 Year s 4- 6 Year s 0- 6 Year s 36t h Mont h 3. 3

2, 0 2. 7 2. 9 6. 7

5. 5 6. 2 6. 5 5. 2

2. 4 4. 0 4. 4 9. 9

5. 9 8. 2 9. 7 Postcontro l Scenario s (1990-96 ) 0- 3 Year s 1. 4 3. 7 1. 4 3. 6 4- 6 Year s 1. 1 3. 6 1. 1 3. 4 0- 6 Year s 1. 3 3. 7 1. 3 3. 7 36t h Mont h 1. 3 3. 7 1. 3 3. 7

a Estimate d Pb

B level s ar e average s base d o n air-qualit yestimate s fo r geographi c center s o f al l censu s tract s withi n the impac t are a surrounding a give n poin t source . Value s fo r othe r source s ar e abou t 5-10 % lowe r tha

n thos e fo r Sourc e 2 .P.8 2

7 5 result s fo r

EP . Thes e result s ar e summarize dinFigs
. 5. 1 an d5. 2 fo r th e 33-yg/d Lan d 53-yg/d LE Plevels , respectively
. Eac hfigur e show s result s fo r si x air-lea dscenario s (lower

- an dupper-boun dG M value s fo r

baseline , precontrol , an dpostcontro l tim e periods ) fo r

Source s 2 , ^ an d5
. Th e ful l ris k estimat e fo r

eac hscenari o i s aprobabilit y distributio n ove r

anumbe r

o r fractio nof

th e population , bu t

onl y th e media nan d90 % credibl e interval s ar e shown
. Th e media ni s indicate db y anX , an dth e 90 % credibl e interva l i s indicate db y bar s extendin g bot habov e an dbelo w th e media nvalue
. Fo r th e precontro l an dpostcontro l scenario s fo r area s surroundin g al l source s bu t Sourc e 5 , EPris k

estimate s ar e approximatel y a t backgroun dlevels
. Specifically , th e media n value s ar e abou t 10.7 % fo r

th e 33-yg/d LEPlevel , an d2.1 % fo r th e 53-yg/d LEP level
. Th e 90 % credibl e interval s aroun dthes e media nvalue s ar e abou t 6-15 % (fo r 3 3 yg/dL ) an d0.1-5 % (fo r 5 3 yg/dL)
. Fo r th e baselin e scenario s an dSource s 1-4 , th e media nrespons e rate s ar e abou t 21 % (fo r 3 3 yg/dL ) an d8 % (fo r 5 3 yg/dL ) fo r

th e lower-boun dG

M Pb B value s an dar e abou t twic e thos e rate s fo r

th e upper-boun dG

M Pb B values
. Th e uncertaint y abou t thes e value s i s quit e small , indicate db y 90 % credibl e interval s tha t ar e abou t

equa l t o th e media n value s plu s o r

minu s 1-2% . Th e narro w 90 % credibl e interval s ar e du e t o th e larg e number s of

childre n in th e highe r Pb B group s examine db y Piomell i e t al
. (1982) , whic hdominat e th e ris k calculation s fo r

th e baselin e scenario s fo r Source s 1-4 .P.8 3 7 6

5 0



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Pr e L U

Pos t Sourc e 5 Sourc e 2

FIGUR E 5. 2 Respons e Rate , % , wit h E P> 5 3 yg/d LP.8 5 7 8
5. 3 RISE RESULT S FORHEMOGLOBI N Recal l fro mSec . 3 tha t th e probabilisti c judgment s of fou r expert s regardin g dose-respons e function s fo r lead-induce dhemoglobi ndecrement s wer e obtaine dfo r tw o hemoglobi n level s considere dt o b e belo w norma l (9. 5 g/d Lan d1 1 g/dL)
. I nafashio n exactl y th e sam e a s tha t fo r calculatin g th e risk s o f advers e EPeffects , function s tha t th e expert s agree drepresente dthei r judgment s (cf
. Sec . 3 ) wer e combine dwit hth e variou s Pb B distribution s describe di nSec . 5.1 , t o produc e estimate s o f overal l risk
. Th e result s of

th e calculation s (App . D) ar e summarize dinFigs
. 5.3-5.6
. Result s ar e show n onl y fo r

childre n age d0- 3 years , wh o ar e mor e sensitiv e t o lea dexposur e tha n childre n age d4- 6 years . Medianris k estimate s fo r

childre nage d4- 6 year s an dfo r childre nage d0- 6 year s ar e jus t slightl y lowe r

tha nthos e fo r

age s 0- 3 years . Th e uppe r end s of th e credibl e interval s fo r age s 0- 3 year s ar e abou t 25 % highe r

tha nthos e fo r

age s 0- 6 years . Figure s 5. 3 an d5. 4 ar e fo r Sourc e 5 , fo r

th e 11-g/d Lan d9.5-g/d Lhemoglobi n levels , respectively
. Figure s 5. 5 an d5. 6 ar e analogou s an dfo r Sourc e 2 . I

nthes e figures , media nvalue s of

th e ris k distribution s an d90 % credibl e interval s aroun dthos e value s ar e indicate dfo r

eac hair-lea dscenario , base do nth e function s fi t t o th e judgment s of Expert s A , C , D , an dE . Th e media ni s indicate db y a nX , an dth e 90 % credibl e interva l i s indicate db y bar s extendin g bot habov e an dbelo w th e media nvalue
. Th e bar s ar e of variou s texture s t o hel p on e t o visuall y discriminat e result s fo r th e individua l experts .2 5

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83 Figur e 5. 3 (fo r

th e 11-g/d Lhemoglobi nlevel ) indicate s tha t th e Exper t

A ris k estimates * ar e essentiall y zer o fo r al l case s an dtha t

th e 90 % credibl e interval s fo r Expert s D an dEris k

estimate s overla p t o som e degree
. Th e difference s betwee nth e ris k estimate s base do n th e lowe r an dth e uppe r

G M Pb B value s ar e respons e rate s o f abou t 2 % fo r Expert s C- Ei n th e baselin e scenario s an d1 % fo r Expert s C an dEan d2 % fo r Exper t D fo r in th e precontro l scenarios
. Uppe r an dlowe r

G M Pb B value s ar e equa l in al l postcontro l scenarios
. I n th e precontro l scenario , th e media nrespons e rate s fo r Exper t C ris k estimate s ar e abou t

twic e thos e fo r

Exper t D an dabou t

15 % les s tha nthos e fo r Exper t E . Th e Exper t D an dEris k

estimate s demonstrat e th e larges t amount s of

uncertainty , havin g uppe r 90 % credibl e interva l (CI ) value s abou t twic e th e media nvalues , an dlowe r 90 % CI value s abou t

hal f th e media n values
. Fo r Exper t C , thes e difference s ar e abou t 25-75 % an d50-75% , respectively
. Thi s differenc e i s eviden t fro mth e wide r

90 % credibl e interval s indicate din Fig
. 5. 3 fo r th e Exper t

D an dEris k

estimates
. Th e highes t

ris k estimate s ar e obtaine dfor.th e baseline , upper-boun dscenario , fo r whic hth e ag e 0- 3 G

M bloo dlea di s 13. 9 yg/dL ; th e lowes t ris k estimate s ar e obtaine d fo r th e precontro l an dpostcontro l (lowe r G M scenarios ) fo r

whic hth e ag e 0- 3 G

M bloo d lea di s 1. 4 yg/dL
. Th e .ratio s of th e highes t

an dlowes t

media nris k

estimate s ar e abou t 1.3 , 1.9 , an d1. 5 fo r

Expert s C , D , an dE , respectively
. Thus , a norde r o f magnitud e reductio n in bloo dlea dresult s ina t mos t a50 % reductio ninth e media nvalu e of estimate drisk
. Similarly , th e larges t uppe r bound s an dth e smalles t lowe r bound s o

f th e 90 % credibl e interval s o n ris k d o no t chang e muc hingoin g fro mth e highes t Pb B scenari o t o th e lowes t

Pb B scenario
. Thus , th e rang e of estimate drisk s tha t

ar e plausibl e i s no t ver y sensitiv e t o th e mea n Pb B level s associate dwit hth e scenario s considere di nthi s study
. •Whe n w e us e th e phras e "exper t A ris k estimates, " w e mea nalonge r statement , namely , "ris k

estimate s base do n th e judgment s of Exper t A. "P.9 1 8 4 I n nearl y al l of

th e scenario s fo r

Sourc e 5 , ther e i s virtuall y n o chanc e tha t an y childre n wil l hav e hemoglobi n level s les s tha no r equa l t o 9. 5 g/dL , base do n th e judgment s of

bot hExpert s A an dD . Th e Exper t C an dEris k

estimate s ar e abou t

hal f thos e fo r th e 1 1 g/d Lhemoglobi nlevel
. Th e Exper t C ris k estimate s agai nsho w th e smalles t degre e of

uncertainty
. A s fo r

th e 1 1 g/d Lhemoglobi nlevel , estimate dris k varie s littl e a s G

M bloo dlea di s changed
. Th e conclusio nfo r Sourc e 5 i s tha t

th e probabilit y of

advers e hemoglobi n level s occurrin g decrease s a s ai r lea d(an dhenc e bloo d lead ) decreases , bu t

th e percen t

reductio ninris k

i s considerabl y les s tha nth e percen t reductio n in exposure . Fo r Sourc e 2 , modele dmea nPb B level s ar e abou t doubl e thos e fo r

Sourc e 5 fo r th e baselin e an dprecontro l scenarios , an dabou t th e sam e fo r

th e postcontro l scenarios
. Subsequently , th e risk s (respons e rates ) ar e highe r - - abou t 10-25 % highe r

fo r th e 1 1 g/d L leve l an dabou t

10-100 % highe r

fo r th e 9. 5 g/d Llevel
. I naddition , nonzer o ris k estimate s resul t

fo r Exper t D fo r al l scenario s excep t th e postcontro l 9.5-g/d L hemoglobi n leve l scenario
. Al l of thes e result s ar e consisten t wit hth e observatio n fo r Sourc e 5 tha t

aplo t of ris k vs . G M bloo dlea dwoul db e relativel y flat , especiall y a t th e 1 1 g/d Lhemoglobi n level
. Th e conclusion s fo r

Sourc e 2 ar e that : estimate drisk s ar e highe r tha nthos e fo r Sourc e 5 i n th e baselin e an dprecontro l scenario s (becaus e of highe r estimate dexposur e t o lead) , an dth e sam e fo r th e postcontro l scenarios
. Fo r Sourc e 5 , th e probabilit y of advers e hemoglobi n level s occurrin g decrease s a s ai r lea ddecreases , bu t

th e percen t reductio n in ris k

i s considerabl y les s tha nth e percen t reductio ninexposure . Fo r th e othe r poin t sources , th e G

M Pb B value s ar e abou t 5-10 % les s tha nthos e fo r Sourc e 2 . 5. 4 RIS K

RESULT S FO RI Q Judgment s regardin g I Q effect s wer e obtaine dinamanne r tha t allowe d consideratio n fro mtw o perspective s tha t roughl y correspon dt o dose-effec t an ddose

-P.9 2
8 5 respons e function s of

tw o type s of

healt hendpoints
. Th e firs t of thes e i s expecte dI Q decrement
. Th e secon di s mor e complicated , involvin g th e lead-induce dincreas e in fractio n of

childre n havin g IQ s belo w aspecifie dcritica l leve l denote db y IQ* . W e sho w result s inthi s sectio n fo r IQ * value s of

8 5 an d70 , whic hcorrespon dt o on e an dtw o standar ddeviation s belo w 100 , althoug hothe r value s of

IQ * coul dhav e bee nused
. Furthe r detail s o n calculatin g thes e quantitie s ar e provide dinApp . C . W e discus s th e ris k result s fo r

thes e tw o healt hendpoint s inth e nex t tw o sections
. Bothhealt heffect s requir e combinin g th e judgment s abou t th e dose-respons e function s wit hth e exposur e estimate s fro mSec . 5. 1 t o produc e probabilisti c ris k estimates
. Result s ar e illustrate dher e fo r Source s 2 an d5 , fo r

th e lowe r

SE S grou p (th e mos t sensitiv e population). " Ris k estimate s calculate dfo r Sourc e 5 ar e smalle r

tha nthos e fo r an y othe r

poin t sourc e becaus e th e modele dblood-lea dlevel s ar e lowe r fo r thi s poin t source , an dbecaus e th e percentag e of household s havin g income s belo w povert y leve l i s th e smallest
. Modele dblood-lea dlevel s an dth e percentag e of household s havin g income s belo w th e povert y leve l ar e highes t aroun dSourc e 2 . Fo r

th e remainin g sources , modele d Pb B level s ar e abou t

5-10 % lowe r

tha nthos e fo r

Sourc e 2 . Fo r th e IQ healt heffects , th e bloo dlea dof interes t i s tha t a t th e 36t hmonth
. IQ , a s describe din Sec . 4 , i s measure do nth e sevent hbirthday
. 5.4. 1 Expecte dI Q Decremen t Expecte dI Q decremen t i s calculate db y combinin g th e judgment s abou t I Q decrement s (relativ e t o acontro l grou p of childre nsheltere dfro mlead ) a t eac hblood

lea dleve l wit hablood-lea ddistribution
. Result s ar e show ninFigs
. 5. 7 (fo r Sourc e 5 ) an d5. 8 (fo r

Sourc e 2) . Result s fo r th e othe r

source s ar e slightl y les s tha nthos e fo r Sourc e 2 . I

n thes e figures , media nvalue s of th e expecte dI Q distribution s an d90 % credibl e interval s aroun dthos e value s ar e indicate dfo r baseline , precontrol , an d5 -



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Q Decremen tfo rLowe rSE S Childre n Livin g aroun d Sourc e 5

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FIGUR E 5. 8 Expecte d I Q Decremen tfo rLowe rSE S Childre n Livin g aroun d Sourc e 2P.9 5
88 postcontro l scenario s (upper

- an dlower-boun destimates ; postcontro l scenari o result s ar e essentiall y equivalen t

fo r al l NAAQ S level s analyzed) , base do nth e function s fi t t o th e judgment s of

Expert s Fthroug hK . Th e media ni s indicate db y auniqu e symbo l fo r eac h expert , an dth e 90 % credibl e interva l i s indicate db y bar s extendin g bot habov e an dbelo w th e media n value
. Th e bar s ar e of variou s texture s t o hel p t o visuall y discriminat e result s fo r

th e individua l experts . Fo r Sourc e 5 , th e ris k

estimate s exhibi t

th e followin g patterns . Exper t G , H , an d J ris k estimate s ar e quit e simila r t o on e another , a s ar e Exper t F , I , an dK

ris k estimates
. Th e 90 % credibl e interval s fo r Expert s G , H , an dJ overlap
. Th e distribution s fo r H an dJ ar e nearl y identical , an dthei r media nestimate s ar e abou t doubl e tha t

fo r G . Th e uppe r

end s o f th e 90 % credibl e interval s fo r H an dJ ar e aroun dfou r I Q points
. Th e uppe r

GM , baselin e scenari o ris k estimate s (fo r

al l bu t Exper t F) ar e abou t

on e I Q poin t highe r tha n th e othe r

estimates
. (Thes e media nestimate s of I Q decremen t

ar e abou t 2. 7 fo r H an dJ , 1 fo r

G , an dabou t

0-0. 3 fo r

F , I , an dK. ) Estimate s of IQ decremen t

fo r I an dK ar e essentiall y zer o fo r al l othe r

scenarios
. Fo r Sourc e 2 , th e estimate s of IQ decremen t

ar e abou t

tw o point s highe r

in th e baselin e scenario s fo r

al l expert s excep t

F . (Estimate s of

IQ decremen t

fo r Far e alway s equa l t o zero. ) Thi s i s attributabl e t o th e highe r blood-lea dlevel s estimate daroun d Sourc e 2 . Estimate s fo r th e precontro l an dpostcontro l period s ar e abou t equa l t o thos e fo r Sourc e 5
. A s fo r

EPan dhemoglobin , th e genera l patter nfo r estimate s of

I Q decremen t

i s tha t the y d o no t

diffe r substantiall y (withi nanexpert ) inth e precontro l an d postcontro l scenarios
. 5.4. 2 Increase d Probabilit y o f Lead-Induce d I

Q Level s bein g < IQ * T o obtai n function s analogou s t o dose-respons e functions , uncertaint y i nmea n IQ o f childre nsheltere dfro mlead , within-grou p IQ standar ddeviation , an dmea n IQ decremen t

give n differen t

blood-lea dlevel s wer e combine dt o calculat e th e increase dP.9 6

89 probabilit y of

havin g IQ s les s tha n o r equa l t o IQ* , a s afunctio nof Pb B fo r IQ * value s of 7 0 an d85
. Thes e result s wer e the ncombine dwit hth e geometri c mea nbloo dlead s summarize din Tabl e 5. 3 t o calculat e overal l ris k estimates
. Result s ar e show n i n Figs
. 5.9-5.12
. Th e firs t tw o figure s ar e fo r

Sourc e 5 , an d th e nex t tw o ar e fo r

Sourc e 2 . Figur e 5. 9 (fo r IQ * = 70 ) show s tha t th e increase d probabilit y of

havin g IQ level s les s tha no r equa l t o IQ * fo r

thes e modele dpoin t

source s ar e ver y smal l (media n probabilit y value s aroun d0.0 1 t o 0.0 2 fo r Expert s G , H , an dJ ) o r essentiall y zer o (fo r

Expert s Fan dK) . Ther e ar e n o estimate s fo r Exper t I becaus e tha t individua l di dno t

provid e th e neede djudgment s abou t mea nIQ level s fo r

childre n sheltere dfro mlea dexposur e o r abou t IQ standar ddeviations
. Th e larges t

ris k estimate s ar e calculate dinth e uppe r GM , baselin e scenari o (media nestimate s rang e fro m0.014-0.02 4 fo r th e increase dprobabilit y of havin g IQ s _

< 70 , a s on e woul dexpect . Fo r thi s scenario , th e ris k

estimate s base do nth e judgment s of al l expert s bu t

Far e comparable
. Estimate s fo r K of thi s magnitud e resul t

becaus e Exper t K judge s tha t

mea n IQ level s fo r

lowe r SE S childre nsheltere dfro mlea dwil l b e quit e lo w (aroun d85)
. Fo r th e scenario s wit hlowe r blood-lea dlevels , Exper t K ris k estimate s becom e muc hsmalle r relativ e t o th e other s becaus e Exper t K judge s tha t ther e i s athreshol dfo r

lead-induce dIQ effect s aroun d5-1 5 yg/dL
. Fo r IQ * = 85 , th e result s inFig
. 5.1 0 indicat e afive-fol dhighe r degre e of

ris k tha n jus t discussed
. I

n th e precontro l an dpostcontro l scenarios , credibl e interval s fo r Exper t G , H , an dJ ris k

estimate s overla p (media nvalue s of 0.014-0.061 , whil e media n estimate s fo r

Fan dK

ar e zer o an d0.004 , respectively
. Again , th e distribution s fo r H an dJ ar e quit e similar , havin g uppe r 90 % credibl e interva l value s aroun d0.1 . Precontro l an dpostcontro l ris k

estimate s fo r

increase dprobabilit y ar e abou t equal , an dabou t

0.0 1 lowe r inprobabilit y tha n thos e fo r th e lowe r

GM , baselin e scenario
. I nth e baselin e scenario , a60 % decreas e in G M (fro mth e uppe r

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H Lowe r 

# 1 1 1 

# t 1 1

J K G M T

• • 

# I T 

# •i l r i i i 6 i T

— ~ F G H J K Uppe r G M D recontro l -r 1 1 1 O A. F G 

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FIGUR E 5.1 2 Increase d Probability of . Childre n Livin g around Sourc e 2 Havin g I Q Level s < 8 5P. 2 9 4 accompanie db y a25-50 % decreas e inth e ris k estimate s fo r

Expert s G , H , an dJ , an dan 80 % decreas e fo r

Exper t K . Furthe r

decrease s inblood-lea dlevel s d o no t substantiall y lowe r th e ris k estimate s fo r

an y of th e experts . Thus , th e relativ e decreas e i nth e ris k measur e vs . adecreas e i n exposur e depend s o nth e leve l of exposure . Result s fo r

Sourc e 2 ar e show ninFigs
. 5.1 1 (fo r IQ * = 70 ) an d5.1 2 (fo r IQ * = 85)
. Fo r

IQ * = 70 , ris k

estimate s base do nth e judgment s of Expert s G , H , J , an dK ar e simila r

fo r th e baselin e scenarios
. Th e 90 % credibl e interval s overla p inth e lowe r an duppe r

G M cases . I

nfact , the y ar e nearl y overlappin g acros s G M values
. Media n value s of increase dprobabilit y rang e fro m0.02 4 t o 0.0 4 fo r th e lowe r

G M values , an d fro m0.03 7 t o 0.06 8 fo r th e uppe r

G M values
. Fo r

th e uppe r

GM , precontro l scenario , media n ris k

estimate s rang e fro m0.0 1 t o 0.02 2 amon g thes e experts . Exper t K ris k estimate s ar e zer o fo r

th e remainin g scenarios
. Th e media nvalue s fo r th e othe r

expert s ar e abou t 0.004-0.01 , an duppe r

90 % confidenc e limi t

value s ar e 0.015-0.034
. Probabilit y distribution s determine dfo r Expert s H an dJ ineac hscenari o ar e quit e similar
. Th e ris k estimate s calculate dfo r IQ * = 8 5 ar e generall y abou t thre e t o fou r time s large r

tha n thos e fo r

IQ * = 7 0 fo r

Expert s G , H , an dJ , an dabou t 50 % highe r

fo r K . A s fo r

Sourc e 5 , ther e i s agreemen t amon g th e experts , a s indicate db y th e overlappin g 90 % credibl e intervals
. Fo r aspecifi c expert , th e credibl e interval s fo r th e lowe r an duppe r

G M value s overla p fo r

th e baselin e scenario
. Exper t Fris k estimate s agai n ar e smal l (media n value s of 0.00 3 an d0.00 7 fo r

th e lowe r

an duppe r

G M cases) . I

n th e postcontro l scenarios , th e Exper t G , H , an dJ ris k

estimate s hav e media nvalue s aroun d0.014-0.06 2 an duppe r 90 % credibl e interva l value s aroun d0.04-0.1 . Th e probabilit y distribution s fo r Exper t H an dJ ris k

estimate s agai nar e quit e similar , an d Exper t Gris k estimate s ar e abou t

one-thir dthos e fo r

H an dJ . A s fo r

th e othe r

healt h en dpoints , th e genera l patter n fo r estimate s of

th e increase dprobabilit y of havin g childre n wit hIQ s les s tha n o r equa l t o IQ * i s tha t thos e fo r

th e precontro l an d postcontro l period s ar e abou t one-thir dt o one-fourt hthos e fo r th e baselin e period , an d tha t th e 90 % credibl e interval s fo r th e lowe r

an duppe r

G M blood-lea dcase s overlap
.P. 3 9 5 REFERENCE SP. 4 96 APPENDI

X A FITTIN G FUNCTION S TO DAT A O N LEAD-INDUCED ELEVATE D ERYTHROCYTE PROTOPORPHYRI N LEVEL

S Sectio n 2 discusse s publishe ddat a(Piomell i e t al. , 1982 ) abou t

dose-respons e relationship s betwee n Pb B leve l an dE Plevel
. Becaus e th e dat aar e complet e an d reliable , probabilit y encodin g of th e judgment s of

expert s wa s no t

necessary . Th e availabl e data , whe n combine dwit hsample-siz e data , ar e sufficien t t o develo p probabilisti c dose-respons e functions
. Thos e function s ar e specifie dinthi s appendix
. Figur e 2. 1 present s publishe ddose-respons e dat aabou t lead-induce delevate dEP levels , an dTabl e 2. 1 present s sample-siz e data
. Fo r th e tw o EPlevel s (3 3 yg/d Lan d5 3 yg/dL ) addressed , expression s ca n b e determine dfo r th e mea ndose-respons e curve s shown
. 

# ( 0.107 ,

*" 1 (0.1 ( • w...w, , fo r L< 16. 6 yg/d L E P1 - 1 ~ i
. i, ~ io348-(L-16.6)-1.22 , fo r L> 16. 6 yg/d L fo r EPlevel s greate r

tha n o r equa l t o 3 3 yg/dL , an d 

# ( 0.024 , * _ 1 ( 0 . fo r L< 16. 6 yg/d L 10348-(L-16.6)-2) , fo r L> 16. 6 yg/d L fo r EPlevel s greate r

tha n o r equa l t o 5 3 yg/dL , where : R= populatio n respons e rat e (fractio nof childre nhavin g EP level s greate r

tha no r equa l t o aspecifi c EPlevel) , L= Pb B leve l (yg/dL) , an d < J (• ) = invers e of

th e cumulativ e distributio nfunctio nof a standardize dnorma l rando mvariable
. Piomell i e t

al.' s (1982 ) dat aindicat e athreshol dfo r E Peffect s a t

aPb B leve l abou t

16. 697

yg/dL
. Further , respons e rate s of 0.02 4 an d0.10 7 wer e foun dt o b e "natura l frequencies " fo r th e occurrenc e of

E Plevel s abov e 5 3 yg/d Lan d3 3 yg/dL , respectively
. Probabilit y distribution s ove r th e populatio nrespons e rat e determine dfo r 1 0 (PbB , EP ) leve l combination s ar e summarize di nTabl e A.l
. Thes e distribution s ar e eithe r bet a

8(R ) = CN-D i x- i (1

_ R ) N-X- I

B U ; (X-l)I(N-X-D ! RU R ;

o r norma l a t

eac hPb B level , wher e Ni s th e numbe r of childre na t

aspecifi c Pb B level , an dX i s th e numbe r

of childre n havin g E Plevel s greate r tha no r equa l t o eithe r

3 3 yg/d L o r 5 3 yg/dL
. Th e cumulativ e probabilit y functio nfo r th e bet adistributio ni s B(R) = 1 - V I IR 1 (l-R) 1 1 " 1 " 1

X- 1 /N- A. 

# -I 

# (J R l

Th e mea n E(R) an dvarianc e V(R ) of th e bet adistributio nand , wher e appropriate , it s norma l approximatio n ar e E(R ) = £an dV(R) = * ( N ~ X )

NNZ (N+1 )

Fo r mos t Pb B an dEPcombinations , th e quantit y NR(l-R ) was larg e enoug ht o allo w us e of th e norma l approximation
.TABL E A. 1 Probabilit y Distribution s and Parameter s fo rPiomelli' s Dat ao n Erythrocyt e Protoporphyri n (EP) Level s amon g Ne w Yor k Cit y Chil-dre

n

Pb B (yg/dL )
5 15 2 5 3 5 5 0 Functiona l

For m
Norma l Norma l Norma l Norma l Bet a E P > 3 3 yg/d L

Paramete r Value s E(R) a =0.10 7 E(R)=0.10 7 E(R)=0.33 7 E(R)=0.72 8 X=4 2 V(R) b =0.029 2

V(R)=0.009 2 V(R)=0.020 2 V(R)=0.043 2 N=4 3 Functiona l For m
Bet a Norma l Norma l Norma l Bet a E P > 5 3 yg/d L

Paramete r Value s
X= 3 E(R)=0.02 4 E(R)=0.12 4 E(R)=0.44 9 X=4 0 N=12 8

V(R)=0.004 2 V(R)=0.014 2 V(R)=0.047 2 N=4 3

a E(R ) denote s th e expecte dvalu e o f R . ^/(R ) denote s th e varianc e o f R . Source : Dat aar e fro mPiomell i e t al
. (1982) . V O o oP. 7
99 APPENDIX B HEMOGLOBI

N Appendi x B i s organize da s follows
. Sectio nB. l reproduce s th e protoco l use d durin g th e hemoglobi n encodin g sessions
. Sectio nB. 2 detail s th e mathematica l formulation s fo r

th e dose-respons e models
. Sectio nB. 3 tabulate s encode djudgments , specification s fo r

function s fi t

t o thos e judgments , an dcredibl e interval s fo r encode d judgment s an dfitte dfunctions
. Sectio nB. 4 summarize s th e discussion s hel dwit heac hof th e interviewe dexperts . B. 1 HEMOGLOBI

N PROTOCOL
B.1. 1 Introductio n Th e Environmenta l Protectio nAgenc y (EPA ) i s charge db y th e Clea nAi r Ac t wit hsettin g an drevisin g Nationa l Ambien t Ai r Qualit y Standard s (NAAQS ) fo r selecte d pollutants , a t

level s sufficien t

t o protec t

th e publi c healt hwit hanadequat e margi n of safety
. A s yo u know , th e scientifi c base s fo r NAAQ S ar e presente dan dreviewe din criteri adocuments
. I

n suppor t of th e forthcomin g revie w o f th e lea dNAAQS , EPA ha s jus t prepare dane w Air

Quality Criteria for

Lead. I t

present s scientifi c evidenc e fro m whic hth e mos t

susceptibl e population s ca nb e determine dan dfro mwhic hvariou s advers e healt heffect s ca n b e identified
. Th e criteri adocumen t summarize s an d evaluate s th e availabl e clinical , epidemiological , an danima l o r toxicologica l laborator y evidenc e wit hregar dt o th e physiologica l an dadvers e healt heffect s of lead , an d therefor e represent s ou r mos t up t o dat e knowledg e o nlea deffects
. A s on e aspec t

of th e revie w process , EP A assesse s healt hrisk s b y identifyin g th e mos t sensitiv e population s fo r eac hpollutant , an destimatin g probabilisticall y th e number s of

peopl e in th e population s wh o ma y suffe r eac ho f variou s well-define d advers e healt heffect s attributabl e t o th e pollutant
. I t i s believe dtha t

informatio nabou tP. 8 100 th e healt hrisk s associate dwit hvariou s potentia l standard s wil l ai dth e EPA administrato r

i n selectin g tha t

standar dwhich , inhi s judgment , protect s th e publi c healt hwit ha n adequat e margi n of safety
. Becaus e th e ris k

estimate s tha t

EPA seek s ar e ofte nbase di npar t o ndose

respons e relationship s an dlea dexposur e estimate s whic har e uncertain , i t i s necessar y t o mak e probabilit y judgment s abou t relevan t

dose-respons e function s base do n th e availabl e evidence , an dt o probabilisticall y estimat e lea dexposur e unde r alternativ e NAAQS . Obtainin g th e healt hris k estimate s the ninvolve s combinin g dose-respons e an d exposur e probabilit y estimates
. Th e proble mof

estimatin g dose-respons e relationship s i s simila r t o tha t whic h exist s inclinica l medicin e whe n ther e d o no t exis t dat atha t

bea r precisel y o n th e patient' s problem
. I

n tha t cas e i t i s necessar y t o us e scientifi c judgmen t t o extrapolat e fro mth e dat at o mak e abes t decisio nfo r

th e patient
. Here , too , i t i s necessar y t o us e scientifi c judgmen t

t o extrapolat e fro mth e availabl e data
. Th e extrapolatio ni s no t certai nand , therefore , w e wil l ai dyo u t o represen t you r opinio nprobabilistically
. Furthermore , sinc e th e extrapolatio ndepend s o none' s interpretatio nof th e literature , differen t peopl e wil l hav e differen t judgments
. Fo r

eac hhealt heffec t

w e inten dt o obtai n th e probabilisti c judgment s of abou t fiv e expert s t o sampl e th e rang e of respecte d opinions
. Th e mode l fo r estimatin g risk s wil l no t merg e thes e judgment s int o asingl e averag e judgment , bu t

rathe r wil l estimat e th e rang e of risk s base do nth e rang e of judgments
. I

f w e a s ris k

analyst s do ou r

jo b properly , the nno t onl y wil l w e b e abl e t o sho w th e EPA administrato r th e rang e of

estimate s base do nth e rang e of judgments , bu t w e wil l als o b e abl e t o sho w som e of th e source s of

th e disagreements
. Indeed , asid e benefi t of thi s exercis e in whic hw e prob e you r knowledg e i nastructure dmanne r ma y b e t o hel p identif

y source s of

greates t disagreement
. Base do n th e evidenc e in th e lea dcriteri adocument , tw o population s hav e bee n identifie da s bein g mos t susceptibl e t o th e effect s of lea dintoxication
. On e i s childre nP. 9
10 1 fro mbirt hthroug hth e sevent hbirthday , an dth e othe r i s pregnan t

women , o r

mor e precisely , th e fetuse s bein g carrie db y th e pregnan t women . A numbe r

of advers e healt h effect s hav e bee n identifie dfo r whic hw e woul dlik e t o estimat e dose-respons e function s includin g th e on e discusse dbelow
. B.l. 2 Lead-Induce d Hemoglobi n Decrement s W e woul dlik e t o represen t inprobabilisti c for myou r opinio nabou t

th e locatio n an dshap e of

dose-respons e function s fo r certai nwel l define dlevel s of lead-induce d hemoglobi nreductio n inth e populatio nof U.S . childre nfro mconceptio nthroug hth e sevent hbirthday
. W

e realiz e tha t

availabl e dat ad o no t

full y defin e thes e functions ; i f the y did , the n i t

woul db e unnecessar y t o obtai nyou r an dothe r

experts ' opinion s abou t them
. Nevertheless , i

f th e population , th e exposur e conditions , an dth e healt heffect s ar e al l precisel y defined ; the n suc hfunction s infac t exis t an dw e woul dlik e you r bes t judgmen t abou t wha t the y woul dloo k

lik e i f th e dat acoul db e collected
. B.l.2. 1 Definitio n o f

Hemoglobi n Decremen ta s a n Advers e Healt h Effec t Ther e ar e difference s of opinion , of

course , a s t o wha t

degre e of

reductio n i

n hemoglobi nleve l constitute s ahealt hrisk
. Th e Clea nAi r Ac t make s i t

clea r tha t EP A shoul dse t

it s standard s t o protec t agains t advers e healt heffects
. However , th e reductio n in hemoglobi n leve l considere dt o b e advers e may b e differen t fo r regulator y purpose s tha n fo r

clinica l action
. Sinc e i t i s generall y agree dfo r childre ntha t

a hemoglobi nleve l of

abou t 1 2 gram s pe r

decilite r

i s norma l an dabou t

9 gram s pe r decilite r i s anemic , w e wil l specif y tw o hemoglobi nlevel s intha t interval , namel y 9. 5 an d1 1 gm/dl , an dtrea t eac ha s th e physiologica l effec t fo r purpose s of

specifyin g a dose-respons e function
. W e wil l elici t

fro myo u probabilit y judgment s abou t th e shap e an dlocatio n of

th e dose-respons e curv e fo r eac hof th e tw o level s of

effect s in th e sensitiv e population
.P.1 0 102 B.1. 3 Populatio n a tRis k W e ar e definin g th e mos t susceptibl e grou p a s al l Unite dState s childre n fro m conceptio n throug hthei r sevent hbirthday
. However , yo u ma y believ e o nvariou s ground s tha t younge r an dolde r

childre n in thi s grou p hav e differen t dose-respons e function s fo r lead-induce dhemoglobi n reduction
. I f so , the nw e wil l elici t you r judgment s separatel y fo r th e ag e group s 0- 3 an d4-6 . B.1. 4 Exposure Condition s W e wil l b e askin g you r

judgmen t

abou t populatio nrespons e rate s a t variou s blood-lea dlevels
. Assum e tha t th e blood-lea dleve l unde r consideratio nfo r

agive n judgmen t i s in equilibriu ma s aresul t of asufficientl y long-ter mconstan t lea dexposur e withou t gros s excursion s abov e o r belo w th e state dlevel
. B.l. 5 Physiologica l Condition s Becaus e th e effec t

o f lea do nhemoglobi nleve l depend s o nman y parameter s of a person' s system , i t

i s necessar y t o specif y assumption s abou t

thos e parameter s in th e population
. Th e effec t of lea di nth e syste mdepend s o nth e person' s nutritiona l an d metaboli c status . Th e incidenc e of iro ndeficienc y i s greate r inchildre ntha ninadults , an dgreate r

ye t in childre n ag e 0- 3 tha nag e 4-6 , wit hawid e rang e of iro nlevel s in childre n up t o thei r

sevent hbirthday
. Assum e tha t th e distributio nof

iro nlevel s i s tha t whic hyou believ e i t

actuall y t o b e inth e ag e group s 0- 3 an d4-6 . Th e effec t of lea dals o depend s o n th e level s of zinc , copper , vitamin s A , C , D , an dE , calcium , phosphorou s an d magnesium
. Assum e in al l case s tha t thes e nutrient s ar e distribute di nth e tw o ag e group s a s yo u believ e the y i n fac t are , takin g int o accoun t th e wid e rang e of

diet s an d nutritiona l level s of

U.S . children
. I t i s wel l established , of course , tha t

erythrocyt e protoporphyri n(EP ) leve l i s positivel y correlate dwithblood-lea dlevel
. However , th e correlatio ni s no t perfect , an dP.1 1 10 3 ther e i s arang e o f

EPvalue s a t

an y give nbloo dlead
. Yo u may believ e tha t

th e effec t

of lea dvarie s wit hEPlevel
. I f so , assum e tha t

EPi s distribute da t

eac hblood-lea dleve l a s you believ e i t

in fac t is
. B.1. 6 Factor s t o Conside r I n orde r t o hel p yo u brin g t o min dth e relevan t evidenc e s o tha t

yo u may conside r i t systematically , an dals o in orde r t o hel p u s t o interpre t you r judgments , w e woul dlik e t o as k you t o discus s briefl y you r interpretation s of

variou s aspect s of

th e literature
. Firs t of all , coul dyo u tel l u s somethin g abou t how , inyou r

judgment , lea dan diro n interac t t o reduc e hemoglobi n level s an dsomethin g abou t th e relatio nbetwee niro n an d lea dlevel s in th e body ? Similarly , w e woul db e intereste dinyou r opinion s abou t

th e sam e question s wit hregar dt o zin c an dlea dan dt o calciu man dlead
. I t appear s tha t

lea d affect s hemoglobi n level s throug hthre e somewha t separat e routes : interferenc e wit h hem e synthesis , interferenc e wit hglobi nsynthesis , an ddecrease dlif e expectanc y of erythrocytes
. Briefly , wha t i s you r interpretatio nof

th e literatur e o nthes e variou s effect s of

lead ? EPleve l increase s wit hiro ndeficiency , bu t i t als o increase s wit hbloo d lea dan di s considere dt o b e aprox y measur e fo r th e amoun t

of lea drecentl y cumulate d inbody tissue
. Considerin g onl y tha t portio nof

EPelevatio ndu e t o lead , i nyou r judgment , i s th e relationshi p betwee nbloo dlea dan dhemoglobi ndifferen t a t differen t EPlevels ? Finally , w e kno w tha t

som e group s of

childre nar e a t

greate r ris k of exposur e t o lea ddu e t o thei r

livin g i n deterioratin g pre-195 0 housin g o r inurba narea s wit hlarg e amount s of

vehicula r

traffic
. Thes e childre nwoul dten dt o hav e hig hlea dlevels , bu t do yo u believ e tha t

ther e ar e als o independen t reason s t o thin k

tha t thei r dose-effec t

curve s wil l b e differen t

fro mchildre n who liv e inothe r circumstances ? Fo r

example , thes e may b e th e sam e childre n wh o ten dt o hav e poore r diet s an dles s acces s t o medica l care . Wha t i s you r opinio n regardin g th e possibilit y of acorrelatio nbetwee nincrease dP.1 2
10 4 exposur e an dincrease dsusceptibility ? Ar e ther e othe r factor s t o conside r

inthinkin g abou t th e dose-respons e function s fo r lead-induce dhemoglobi ndecrement s tha t w e shoul ddiscus s now ?
B.1. 7 Factor s t o Kee p in Min d Whe n Making Probability Judgment s Ther e i s usuall y uncertaint y associate dwit hconclusion s tha t w e dra w fro m research , an dmor e generall y in ou r everyda y thinking
. However , no t everyon e i s awar e o f al l th e source s tha t

shoul dcontribut e t o thei r uncertainty , no r

ar e mos t

peopl e familia r wit hth e proces s of

actuall y expressin g thei r uncertaint y inprobabilisti c terms . Whe nanexper t

i s aske dt o mak e probabilit y judgment s o nsociall y importan t matters , i t i s particularl y importan t tha t h e o r sh e conside r

th e relevan t

evidenc e inasystemati c an deffectiv e manne r

an dprovid e judgment s tha t represen t

hi s o r he r opinion s well
. Experimenta l psychologist s an ddecisio nanalyst s hav e amasse daconsiderabl e amoun t of dat aconcernin g th e way peopl e forman dexpres s probabilisti c judgments
. Th e evidenc e suggest s tha t whe n considerin g larg e amount s of comple x information , mos t peopl e emplo y simplifyin g heuristic s an ddemonstrat e certai nsystemati c distortion s of thought , i.e. , cognitiv e biases , whic hadversel y affec t thei r judgments
. Th e purpos e of thi s sectio n i s t o mak e yo u awar e of thes e biase s an dheuristic s s o that , a s muc ha s possible , yo u ca n avoi dthe min makin g probabilit y judgments
. W e wil l firs t

revie w th e mos t widesprea dbiase s an dheuristics , an dthe noffe r som e suggestion s t o hel p yo u mitigat e thei r

effects
. B.l.7. 1 Sequentia l Consideratio n o f Informatio n Generally , th e orde r

in whic hevidenc e i s considere dinfluence s th e fina l judgment , althoug hlogicall y tha t shoul dno t

b e th e case . O

f necessity , piece s of informatio nar e considere don e b y on e inasequentia l fashion
. However , thos e considere dfirs t

an dlas t

ten dt o dominat e judgment
. I npart , initia l informatio nha s it sP.1 3
105 undu e influenc e becaus e i t provide s th e framewor k whic hsubsequen t

informatio ni s the n tailore dt o fit
. Fo r

example , peopl e usuall y searc hfo r evidenc e t o confirm thei r initia l hypotheses ; the y rarel y loo k fo r evidenc e tha t

weighs against

them
. Th e late r

evidenc e ha s it s undu e effec t

simpl y becaus e i t

i s freshe r

inmemory . Relate dt o thes e sequentia l effect s i s th e phenomeno nof anchoring and adjustment. Base do n earl y partia l information , on e form s a ninitia l probabilit y estimat e regardin g th e even t

i n question
. Thi s ancho r judgmen t

i s the nadjuste da s subsequen t informatio n i s considered
. Unfortunately , suc hadjustment s ten dt o b e to o conservative
. I

n othe r words , to o littl e weigh t i s attache dt o informatio nconsidere d subsequen t

t o th e formatio n of

th e initia l judgment
. B.l.7. 2 Effect s o f

Memor y o n Judgmen t I t i s difficul t

fo r mos t peopl e t o conceptualiz e an dmak e judgment s abou t large , abstrac t universe s o r

populations
. A natura l tendenc y i s t o recal l specifi c member s an d the n t o conside r

the mrepresentativ e of th e populatio na s awhole
. However , th e specifi c instance s ofte n ar e recalle dprecisel y becaus e the y stan dou t insom e way , suc ha s bein g familiar , unusual , especiall y concrete , o r of persona l significance
. Unfortunately , th e specifi c characteristic s of thes e singula r

example s ar e the nattributed , ofte nincorrectly , t o al l th e member s of

th e populatio nof

interest
. Moreover , thes e memor y effect s ar e ofte n combine dwit hth e sequentia l phenomen adiscusse dearlier
. Fo r example , i

n considerin g th e evidenc e regardin g th e dose-respons e curv e of aparticula r

pollutant , you migh t naturall y firs t

thin k of astud y yo u o r

apersona l frien drecentl y completed
. O r yo u migh t

thin k of astud y yo u recentl y read , o r on e tha t

was unusua l an dtherefor e stand s out . Th e tendenc y migh t the nb e t o trea t

th e recalle dstudie s a s typica l of th e populatio n of

relevan t

research , ignorin g importan t difference s amon g studies
. Subsequen t

attempt s t o recal l informatio ncoul dresul t i nthinkin g primaril y of evidenc e consisten t

wit hth e initia l item s you though t of
.P. M 10 6 B.l.7. 3 Estimatin g Reliabilit y o f Informatio n Peopl e ten dt o overestimat e th e reliabilit y of information , ignorin g factor s suc h a s samplin g erro r

an dimprecisio n of

measurement . Rathe r the y summariz e evidenc e in term s of simpl e an ddefinit e conclusions , causin g the mt o b e overconfiden t in thei r judgments
. Thi s tendenc y i s stronge r whe non e ha s aconsiderabl e amoun t o f intellectua l and/o r persona l involvemen t

in aparticula r

field
. I

nsuc hcases , informatio ni s ofte n interprete din away whic hi s consisten t wit hone' s belief s an dexpectations , result s ar e overgeneralized , an dcontradictor y evidenc e i s ignore do r underestimated
. B.l.7. 4 Relatio n Betwee n Even tImportanc e and Probability Sometime s th e importanc e of events , o r

thei r possibl e cost s o r

benefits , influenc e judgment s abou t th e certaint y of

th e event s when , rationally , importanc e shoul dno t

affec t probability
. I

n othe r words , one' s attitude s toward s ris k ten dt o affec t one' s abilit y t o mak e accurat e probabilit y judgments
. Fo r example , man y physician s ten d t o overestimat e th e probabilit y of ver y sever e diseases , becaus e the y fee l i t i s importan t t o detec t an dtrea t

them ; an dsimilarly , man y smoker s underestimat e th e probabilit y of advers e consequence s o f smoking , becaus e the y fee l tha t th e odd s d o no t

appl y t o themselve s personally
. B.l.7. 5 Estimatio n o f

Probabilitie s Anothe r limitatio n i s relate dt o one' s abilit y t o discriminat e betwee nlevel s of uncertainty , an dt o us e appropriat e criteri aof discriminatio nfo r

differen t

range s of probability
. On e resul t of thi s fac t

i s tha t peopl e ten dt o estimat e bot hextrem e an d mid-rang e probabilitie s i n th e sam e fashion , usuall y doin g apoo r jo b i nth e extremes . I t help s her e t o thin k

in term s of

odd s a s wel l a s probabilities
. Thus , fo r example , changin g aprobabilit y estimat e fro m0.51 0 t o 0.50 1 i s equivalen t t o achang e inodd s fro m1.041: 1 t o 1.004:1 , bu t

achang e fro ma n estimat e of 0.99 9 t o 0.99 0 change s th e odd s b y afacto rP.1 5
10 7

of abou t 10 ? fro m999: 1 t o 99: 1 Th e close r t o th e extreme s (eithe r 0 o r 1 ) tha t on e i s estimatin g probabilities , th e greate r th e impac t

of smal l changes
. B.l.7. 6 Recommendation s Althoug hextensiv e an dcarefu l trainin g woul db e necessar y t o eliminat e al l th e problem s mentione dabove , som e relativel y simpl e suggestion s ca nhel p minimiz e them
. Mos t importan t

i s t o b e awar e of

one' s natura l cognitiv e biases , an dt o tr y consciousl y t o avoi dthem
. T o avoi dsequential

effects kee p inmin dtha t th e orde r

inwhic hyo u thin k

of informatio n shoul dno t

influenc e you r

fina l judgment
. I t

ma y b e helpfu l t o actuall y not e on pape r th e importan t

fact s yo u ar e considerin g an dthe nt o reconside r the mintw o o r mor e sequences , checkin g th e consistenc y of you r judgments
. Try t o kee p a nope nmin d unti l you hav e gon e throug hal l th e evidence , an ddon' t le t th e earl y informatio n yo u conside r swa y yo u mor e tha n i s appropriate
. T o avoi dadvers e memory effects, defin e variou s classe s of informatio ntha t

yo u dee mrelevant , an dthe n searc hyou r memor y fo r

example s of

each
. Don' t

restric t you r thinkin g onl y t o item s tha t stan dou t

fo r specifi c reasons . Make aspecia l attemp t t o conside r conflictin g evidence , an dt o thin k of dat atha t

ma y b e inconsisten t

wit ha particula r

theory
. Also , b e carefu l t o concentrat e o nth e give nprobabilit y judgmen t an d do no t le t you r ow n value s (ho w yo u woul dmak e th e decisio nyourself ) affec t thos e judgments
. T o accuratel y estimate the reliability of information, pa y attentio nt o suc h matter s a s sampl e siz e an dpowe r of th e statistica l tests . Kee p inmin dtha t dat aar e probabilisti c in nature , subjec t t o element s of

rando merror , imprecis e measurements , an dsubjectiv e evaluatio n an dinterpretation
. I naddition , th e furthe r on e mus t extrapolate , o r

generalize , fro maparticula r stud y t o asituatio nof interest , th e les s reliabl e i s th e conclusio n an dth e les s certaint y shoul db e attribute dt o it
. Rel y mor eP.1 6 10 8 heavil y o n informatio n whic hyo u conside r mor e reliable , bu t

d o no t trea t i t a s "absolut e truth. " Kee p in min dtha t the importance of

an event or an outcome should

not influence its judged

probability. I t

i s rationa l t o le t

th e costlines s o r

severit y o f

a noutcom e influenc e th e poin t

a t whic hactio n i s take nwit hrespec t t o it , bu t

no t th e judgmen t

tha t i s mad e abou t

th e outcome' s likelihood
. Finally , i n makin g probabilit y judgments , thin k primaril y interm s of

th e measur e (probabilit y o r

odds ) wit hwhic hyou fee l mor e comfortable , bu t sometime s translat e t o th e alternativ e scale , o r eve n t o measure s of

othe r event s (e.g, , th e probabilit y o f th e even t no t happening)
. When estimatin g ver y smal l o r ver y larg e likelihoods , i t i s usuall y bes t t o thin k in term s of

odds , whic har e unbounded , instea dof probabilities , whic har e bounded
. Fo r

example , on e ca nmor e easil y conceptualiz e odd s of 1:200 tha n a probabilit y of

.005
. B.1. 8 Possibl e Advers e Healt hEffect s o f Elevate dErythrocyt e Protoporphyri n (EP ) I t seem s wel l establishe dtha t ther e i s apositiv e dose-respons e relationshi p betwee n bloo dlea dari dEP . Althoug hthi s elevate dE Pca nb e trace dt o hem e synthesi s interference , ther e i s disagreemen t a s t o what , i

f an y advers e healt heffect s ar e associate dwit hlea dinduce delevate dEP . W e woul dlik e t o discus s you r view s o n thi s issu e inou r

secon dvisi t

afte r w e hav e complete dencodin g you r probabilisti c judgment s concernin g th e hemoglobi n blood-lea ddose-respons e function
. I n you r judgment , i s lead-induce delevate dEPassociate dwit halteration s in an y o f th e following , an di

f so , a t wha t leve l o r rang e of level s of

EPwoul dyo u conside r th e effect s t o becom e adverse ? Thes e ar e alteration s in : 1 . Neurochemistr y o r

othe r CN S functions , 2 . Live r

detoxificatio n capabilities , o rP.1 7
109 3 . Rena l o r

endocrin e functio n(inparticular , reduce dbiosynthesi s of 1,25

- dihydroxyvitami n D) . I s ther e arelatio n betwee nlea dinduce delevate dEPan danemi ao f an y sor t beyon dtha t

whic hca n b e indexe db y blood-lea dleve l alone ? Does elevate dEPsugges t tha t th e individua l i s mor e susceptibl e t o lea dtoxicit y du e t o subsequen t exposures ? Ar e ther e othe r

advers e healt heffect s tha t yo u believ e may b e associate dwit helevate dEP ?
B.1. 9 Final Preparatio n fo rElicitatio n o f Probability Judgment s Th e shap e an dlocatio n of th e dose-respons e curv e a s w e define di t abov e i s uncertain , becaus e th e existin g dat ad o no t determin e th e dose-respons e relationshi p exactly
. Yet , i

f w e hav e define dth e dose-respons e curv e precisely , inamathematica l sens e suc harelationshi p doe s exist
. Ou r goa l i s t o hav e yo u represen t probabilisticall y you r own uncertaint y abou t th e locatio nan dshap e o f thi s mathematicall y existen t function , base do n you r expertis e an dth e availabl e knowledge
. I nrespondin g t o th e question s w e wil l as k

you , pleas e thin k

carefull y abou t

th e relevan t

informatio nreviewe d i n th e criteri adocument , an dconsul t it , th e literature , o r you r file s a s yo u dee m appropriate
. Th e previou s sectio n suggest s ways t o thin k abou t th e relevan t

data
. Th e purpos e of tha t sectio n i s t o hel p minimiz e th e biasin g effect s tha t frequentl y accompan y th e informatio n overloa dnaturall y resultin g fro mrapi dconsideratio nof larg e amount s of comple x evidence
. You ma y fin di t helpfu l t o revie w th e sectio no r rais e question s abou t th e point s mad e in i t

befor e w e begin
. Uncertaint y abou t

ados e respons e relationshi p ca nb e represente d probabilisticall y in tw o differen t ways . 1 . Uncertaint y abou t

th e percentag e of

th e define dpopulatio ntha t woul db e affecte db y given blood-lead concentrations ca nb e represente dprobabilistically
.P.1 8
11 0 2 . Uncertaint y abou t th e blood-lea dconcentration s tha t woul db e require dt o affec t

agiven percentage of

the defined

population ca n b e represente dprobabilistically
. W e wil l concentrat e o n on e way a t atime , focusin g primaril y o nth e firs t one . Fo r thes e purpose s i t

i s helpfu l t o imagin e tha t everyon e inth e populatio nha s a specifie dblood-lea dleve l tha t ha s becom e stabilize dinth e manne r describe dabov e unde r Exposure Conditions. Then , a s aresult , som e percentag e of th e populatio n wil l suffe r th e hemoglobi n response . Now , in orde r

fo r u s t o determin e you r

uncertaint y abou t

th e percentage s of

th e populatio n tha t

woul db e affecte db y given blood lead levels w e mus t

introduc e a definition
. Le t

C b e th e give n blood-lea dconcentratio ninquestion
. Definition : R(C ) i s th e percentag e of th e populatio nfo r

whic hablood-lea dleve l of C woul dcaus e th e define dhemoglobi nhealt heffect
. Thus , R(C ) i s precisel y th e percen t o f th e populatio ntha t

woul dsho w arespons e i f th e entir e populatio n ha dblood-lea dlevel s of C unde r th e condition s define dabove
. R(C ) i s usuall y calle dth e populatio n respons e rate . Th e valu e of

R(C ) fo r

agive nC i s uncertain , an dw e woul dlik e t o obtai n probabilit y judgment s fro myo u abou t it s possibl e values
. W e wil l elici t

you r judgment s abou t th e possibl e value s of R(C ) b y specifyin g aparticula r percentag e an dhavin g yo u conside r how likel y i t

i s tha t R(C ) i s les s tha ntha t value
. T o hel p yo u mak e you r probabilit y judgments , w e wil l mak e us e of adevic e calle daprobabilit y wheel , whic hha s adjustabl e sector s o f

blu e an dorange . W e ca nrea do nth e bac k o f th e whee l th e percentag e of

th e whee l tha t

i s eac hcolor
. I

nmakin g you r

judgment s yo u ar e t o imagin e tha t th e whee l i s aperfectl y fai r rando mdevice , an dtha t therefor e th e probabilit y of it s stoppin g wit hth e pointe r o n blu e i s exactl y represente db y th e relativ e are atha t i s blue
. W e wil l the n procee da s follows
. Fo r eac hbloo dlea dconcentratio nC , w e wil l specif y aparticula r

percen t r , an dals o se t

th e probabilit y whee l t o hav e aspecifi c relativ e are aof

blue
. The n yo u ar e t o conside r carefull y th e question:P.1 9
11 1 D o yo u conside r

i t mor e probabl e tha t

th e tru e populatio nrespons e rat e R(C ) i s les s tha nr

or tha t th e whee l woul dsto p wit hth e pointe r o nblu e (o narando m spin) ? You ca n giv e on e of

thre e responses : 1 . You judg e i t

t o b e mor e probabl e tha t R(C ) i s les s tha nr ; 2 . You judg e i t

t o b e mor e probabl e tha t th e whee l woul dsto p wit h th e pointe r

in blue ; 3 . Yo u canno t judg e eithe r

even t a s mor e probabl e tha nth e other
. Fo r aparticula r

concentratio nC an dpercen t r , som e whee l setting s wil l hav e a smal l enoug hrelativ e are aof blu e tha t

yo u wil l fee l confiden t makin g respons e (1) . Othe r whee l setting s wil l hav e alarg e enoug hrelativ e are aof blu e tha t

yo u wil l fee l confiden t makin g respons e (2) . Th e intermediat e setting s wil l b e mor e difficul t t o judge
. However , w e wil l manipulat e th e whee l setting s t o fin dth e on e fo r whic hyo u fee l mos t comfortabl e makin g respons e (3) . Onc e w e hav e determine dth e poin t a t whic hyo u ar e mos t

comfortabl e wit h respons e (3) , an dstil l focusin g o n th e give nbloo dlea dC , w e wil l specif y ane w percen t r' , an drepea t

th e procedure
. Thi s wil l continu e fo r th e give nC unti l w e hav e specifie d variou s percents . The n w e wil l hav e elicite don e of th e probabilisti c representation s o f you r uncertaint y abou t

th e dose-respons e relationshi p w e need
. W e wil l obtai nth e nex t probabilisti c representatio n b y specifyin g ane w C an dcontinuin g a s before
. W e wil l do thi s fo r anumbe r

of value s of

C . I t frequentl y happen s tha t a nexpert' s judgment s alte r somewha t

ove r th e cours e of asessio n suc ha s this , a s h e o r sh e consider s th e evidenc e fro mvariou s perspective s an dthink s abou t

th e variou s response s calle dfor
. Hence , w e wil l grap hyou r response s and , a t appropriat e times , sho w the mt o yo u fo r you r consideratio nan dcomparison
. A t thes e time s yo u ma y wis ht o chang e som e of th e judgment s you gav e earlier
.P.2 0 11 2 W e shoul demphasiz e tha t th e judgment s w e ar e askin g yo u t o mak e ar e no t simpl e ones , no r

of cours e ar e ther e know ncorrec t answers . Rather , w e wan t you r bes t an dmos t

considere djudgmen t inligh t

of th e availabl e relevan t scientifi c data , Therefore , pleas e reflec t o n th e availabl e dat acarefully , feelin g fre e t o consul t th e lea d criteri adocumen t

o r othe r source s a s yo u wis ha s yo u formulat e you r judgments
. (Encod e judgment s fo r

a t leas t tw o concentration s of

on e dose-respons e function , the n continu e wit hinstructions. ) Recal l tha t

uncertaint y abou t

th e dose-respons e functio nca nals o b e expresse din term s of th e blood-lea dconcentratio nnecessar y t o produc e th e effec t inagive n percentag e of

th e populatio n r , if

th e entir e populatio nha dth e sam e blood-lea d concentration , stabilize da s th e resul t of exposur e inth e manne r discusse dearlier
. More specifically , proceedin g a s before , le t u s introduc e adefinition : Definition : C(R ) i s th e blood-lea dleve l tha t woul dcaus e th e define dhemoglobi n healt heffec t

in Rpercen t

of th e population
. Th e valu e of

C(R ) i s uncertai nfo r agive nR , an dw e wan t t o obtai nyou r judgment s abou t

it s possibl e values
. Analogousl y t o wha t w e hav e alread y done , fo r a give n Rw e wil l specif

y concentration s c an das k yo u t o conside r

how likel y i t

i s tha t th e tru e C(R ) i s les s tha n th e specifie dc . More specifically , utilizin g th e whee l a s before , w e wil l as k

yo u th e question: D o yo u conside r

i t mor e likel y tha t

th e tru e concentratio nC(R ) i s les s tha nc , or tha t th e whee l woul dsto p wit hth e pointe r o nblu e (o narando mspin) ? You ca ngiv e on e of

thre e responses : 1 . You judg e i t

mor e probabl e tha t

C(R ) i s les s tha nc ; 2 . You judg e i t

mor e probabl e tha t

th e whee l woul dsto p wit hth e pointe r in blue ; 3 . Yo u canno t judg e eithe r

even t a s mor e probabl e tha nth e other
.P.2 1
11 3 Afte r determinin g th e whee l settin g a t whic hyo u fee l mos t

comfortabl e wit h respons e (3) , w e wil l specif y ane w c an drepea t

th e process . A s before , fo r eac hRw e wil l elici t

you r comparativ e judgment s fo r variou s value s of

c . B. 2 DETAILE

D MATHEMATICA

L FORMULATIONS Thi s sectio ndiscusse s in detai l th e mathematica l technique s use dt o represen t probabilit y judgment s abou t dose-respons e relationships
. First , basi c definition s an dth e notatio n ar e introduced
. The n th e normal-on-log-odd s functio ni s discusse da s a distributio n tha t

ca n b e fitte dt o probabilit y judgment s an dtha t meet s certai ncriteria
. Method s ar e presente dfo r obtainin g least-square s estimate s of th e parameter s of

a normal-on-log-odd s distributio n an dfo r assessin g th e goodnes s of fit
. A famil y of

equal

varianc e normal-on-log-odd s distribution s may sacrific e som e goodnes s of fi t t o th e judgments , bu t

i t meet s al l th e criteri aspecified
. Thi s famil y i s presente dnext , alon g wit hmethod s fo r

obtainin g least-square s estimate s of it s parameter s an dassessin g it s goodnes s of

fit
. B.2. 1 Definition s and Notatio n Thi s sectio n present s definition s an dnotation
. Th e reade r i s assume dt o b e familia r wit hth e basi c concept s of probabilit y theor y (e.g. , definition s of rando m variables , probabilit y densit y functions , an dexpectatio nan dhighe r moments) . Fo r uncertai n quantit y X , le t
f jr(x ) = judgmenta l probabilit y densit y functio n(PDF ) fo r X an d F x ( x ) = cumulativ e judgmenta l densit y functio n(CDF ) fo r X

= / ° f Y (x)dx
.P.2 2
11 4 Thu s Fx^o- 1 1S th ei u d S m enta l probability * tha t X i s les s tha no r

equa l t o x Q . Furthermore , le t
y = E(X ) = expecte dvalu e o f X x

= J x f v ( x )d x

Jo X o o 2 o = V (X ) varianc e o f X

= J [ * - E(X)] Z f Y (x^)dx r t

O X 0 0 Th e uncertai n quantitie s of interes t inthi s repor t

ar e populatio nrespons e rates , denote dR , a t

eac hof severa l blood-lea dlevels , denote dL . Durin g encodin g session s wit hrecognize dexperts , judgment s representin g acumulativ e densit y functio n(CDF ) fo r arespons e rat e Rgive n apopulatio nblood-lea dleve l L[i.e. , judgment s representin g FJWJJR) ] wil l b e elicite dfo r anumbe r

of blood-lea dlevels
. Take ntogether , thes e judgment s wil l provid e afamil y of probabilisti c relationship s tha t represent s th e judgmenta l probabilit y tha t th e populatio nrespons e rat e ( afractio nbetwee n0 an d1 ) wil l b e les s tha n o r

equa l t o aparticula r

valu e R , give nablood-lea dleve l o f L , fo r aspecifi c advers e healt heffect , population , an dexposur e conditions
. A s alread y discussed , th e calculatio nof ris k generall y require s a ninterpolatio n betwee n specificall y assesse dpoints
. Suc hinterpolatio ni s bes t accomplishe dby fittin g a functio nt o th e judge dprobabilities
. Sectio nB.2. 2 describe s ametho dfo r doin g this
.

•Hereafter , al l probabilitie s referre dt o ar e judgmenta l probabilities , eve ni f no t explicitl y stated
.P.2 3
11 5 B.2. 2 Normal-on-Log-Odd s Functio n Becaus e probabilisti c judgment s abou t dose-respons e relationship s ar e generall y "s-shaped " ove r

th e close d[0,1 ] interval , the y ca nb e difficul t t o represen t

wit hclosed

formmathematica l functions
. On e particularl y usefu l functio ntha t i s relativel y eas y t o wor kwit hi s th e normal-on-log-odd s distribution
. Th e normal-on-log-odd s distributio n i s obtaine db y fittin g anorma l distributio nt o th e natura l lo g of th e odd s implie db y th e populatio n respons e rate s R . Thus , th e followin g relationship s ar e defined :
X = -j-l-jj , 0<X <

Y = ln(X) , - » < Y <

_»
wher e X i s th e odd s variabl e an dY i s th e lo g of th e odd s variable
. Th e variabl e Y i s

2 assume dt o b e normall y distribute dwit hmea ny an dvarianc e o . Th e degre e t o whic h th e assumptio n i s appropriat e ca n b e teste dwit heac hse t of judgments
. I

f Y i s normall y distributed , X i s log-normall y distributed
. Althoug hn o closed-for mexpressio ni s readil y availabl e fo r

th e distributio n o n R , al l probabilisti c an dstatistica l result s of interes t o n Rca n b e obtaine dthroug hth e distributio nonY sinc e pr( R< r ) = p r

X < T—-

—= p r

Y < I n r-^ —

——1- r r —1- r

an d

y o " y y o " V pr( Y < y ) = p r

Z< —= * —

—o —aa wher e pr(- ) denote s probabilit y an dZi s th e uni t norma l rando mdeviat e fo r whic h<i>(Z

) i s extensivel y tabulate dan davailabl e incompute r libraries
. Thu sP.2 4 11 6 

## V r > 

## - F 

## x(rb >

- <- Y

## i-(rrr )

. t ln( 

## r^ » - Z o

= * i H (B.l )
Tabl e B. l summarize s quantitie s of interes t fo r thes e variables
. Th e parameter s y an do ca nb e estimate dinaleast-square s sens e fro ma n assesse ddistribution
. Le t th e nassesse dpoint s fo r aCD Fb e denote d(Rj , Fj ) fo r i = 1 ,

... , n , wher e R

j i s th e populatio nrespons e rat e an dF j i s th e associate dcumulativ e judgmenta l probability
. Leas t square s estimate s y an d3 fo r y an do ca nb e obtaine db y linearl y re gressin g th e Z

j o n th e yj
. Th e reciproca l of th e slop e of

th e regressio nequatio ni s San dy i s th e y-intercept , i.e. , th e valu e of y correspondin g t o z = 0 inth e regressio nequation
. Sinc e mjudgmenta l distribution s ar e assessed , on e fo r eac hblood-lea dleve l j fo r j = 1 ,

... , m , ther e ar e mmean s (y^ , ... , y m ) an dstandar ddeviation s (oj_ , ... , o m ) , on e pai r fo r eac hof th e judge ddistributions
. Th e goodnes s of

fi t of eac hdistributio nfi t

t o th e judgment s fo r

eac hblood-lea d leve l i s give n b y th e standar dregressio nr statisti c obtaine db y regressin g th e F ^ o n th e F. , wher e

r 2 = l

-P.2 5

117 TABL E B. l Summar

y o f Variable s Pertainin g t o th e Normal-On-Log-Odd s Functio n

Quantit y o f Interes t Definin g Equation s Distribution 3

Mean b

Varianc e Y
Y = ln(X ) N(y,o 2 )

y

a 2 Variabl e

X
X = e Y = R/( l - A(y, a )

_y+a 2 / 2 y= e K X 2 2 2 2y+ a r

a a = e l e - R )

1 ) R =

y X " \


# , 2

# r R X 1 + X

- 2 a X ( 1 + y) 3

X 

# , . . 1 *

Median ye y

Mod e ye 2 1 e y 1 • e M 2 2 y- o + e

a N(y,a 2 ) denote s th e norma l PDF ; A(y,o 2 ) denote s the lognorma l PDF ; th e PDF fo r R canno t be expresse d i n close d form . Mean an d varianc e expression s fo r R ar e approximate ; theywer e derive d wit h th e metho d o f moments ; othe r estimate s can be obtaine d wit h numerica l method s on F

y= N(y, o ) .P.2 6 11 8

an dF £denote s th e estimate dFvalue s {i.e. , F ^ = «(y £- ]i)la, fro mEq . B.l} , an d o 2 obtainin g th e r

valu e of

thi s regression
. I

f th e r valu e i s sufficientl y high , th e normal

on-log-odd s distributio n wit hparameter s y j an do ; describe s th e judgment s wel l fo r lea d leve l j
. Thi s distributio n ca n the n b e use dfo r interpolation
. T o summarize , formula s wer e presente dt o calculat e th e parameter s of anormal

on-log-odd s distribution , whic hca nb e use dt o represen t ajudge dprobabilit y distributio n ove r populatio n respons e rat e fo r agive nblood-lea dlevel
. Goodnes s of fi t i s give n b y a regressio nr

statistic
. Th e normal-on-log-odd s distributio nvariabl e an dit s PD Fca n b e use dt o estimat e judgmenta l probabilitie s fo r th e respons e rat e variabl e R , whic hi s the n use dt o estimat e risk
. B.2. 3 Representin g aProbabilisti cDose-Respons e Surfac e wit h aFamil y o f Equal-Varianc e Normal-on-Log-Odd s Distribution s I f th e o ; ar e approximatel y equal , i t i s desirabl e t o se t

the mequa l t o asingl e poole dvalu e befor e proceedin g furthe r (i.e. , se t

o : = a' = a = o fo r

al l j)
. Thi s ste p assure s tha t

th e fitte ddistribution s fo r tw o differen t

lea dlevel s neve r

cros s on e another
. (Crosse ddistribution s woul dimpl y tha t exceedin g aspecifie drespons e rat e i s mor e probabl e a t

blood-lea dleve l L , tha na t L« , wher e L« i s greate r tha nL.. ) Becaus e of th e manne r

in whic hjudgment s wer e obtaine dfro mth e pilo t subjects , crossing s di d no t occur . Furthermore , judgment s wil l b e obtaine dfro mth e healt hexpert s ove r awide r probabilit y rang e s o tha t crossing s woul donl y b e possibl e a t cumulativ e probabilitie s ver y nea r t o 0 an d1 . However , eve ncrossing s lik e thes e represen t a ninconsistenc y th e expert s ough t

t o avoi dan dtherefor e shoul dno t b e allowed
. A poole destimat e of

o , denote dol , ca nb e obtaine db y firs t subtractin g th e mea n y - fo r eac hse t of assesse dpoints ,
y . . = y . . - y' . fo r

i = 1 , ... , n . an di = 1 , ... , m J , i J» i J JP.2 7

11 9 wher e n ^ i s th e numbe r

o f assesse dpoint s fo r

F D n . an dy- -. i s a n assesse dpoin t o n F R/L- ' Th e y ' ' ca n the n^ e usec * * t o caiculat e amea n (whic hshoul db e ver y clos e t o zero ) an davarianc e (whic hwil l b e th e pooled , least-square s estimat e o ' ) b y regressin g P th e Z- . o n th e y . • . Th e individual , least-square s estimate s o f th e mean s ca nb e J* 1 JJ 1 recalculate da t

eac hlea dleve l b y findin g th e best-fittin g lin e (i n th e leas t square s sense ) wit haslop e o f

Ilo'. Unde r

thes e conditions , th e resul t i s simpl y

n . J y . = — ) y . . . J n j i- 1 J' 1
Denot e th e result s o f thes e las t

step s a s y' , ... , y' . Goodnes s o f fi t agai n ca nb e 1 m obtaine db y regressin g th e recalculate destimate s (whic hma y b e denote da s th e F ' . ) o n J » 1 th e origina l F

j j
. I f afunctiona l relationshi p ca n b e establishe dbetwee n blood-lea dlevel s an dth e y ' , ajudgmenta l probabilit y densit y functio n ove r Rca n b e calculate dfo r an y blood-lea d level , shoul dtha t

b e necessar y fo r

interpolatin g betwee n blood-lea dlevels
. Thi s continuu mo f

densit y function s i n essenc e i s aprobabilit y surfac e ove r th e dose-respons e plane
. An y blood-lea ddistributio n ca n b e combine dwit hth e dose-respons e curv e correspondin g t o judgmenta l cumulativ e probabilit y F , Dp(L) , t o yiel da n estimat e o f th e overal l fractio n o f

th e populatio n Rsufferin g th e advers e healt heffec t wit hcumulativ e probabilit y F . Suc hcalculation s resul t i n th e ris k

estimate s summarize di n Sec . 5 an d describe di n detai l i n App . D . B. 3 RESULT S Result s ar e presente di n thre e tables : Tabl e B. 2 cover s encode djudgments , Tabl e B. 3 summarize s th e function s fi t t o th e judgments , an dTabl e B. 4 compare s th eP.2 8
12 0 TABL E B. 2 Encode d Probability Judgment s o f Expert s Regardin g Lead-Induce d Hemoglobi n Decrement s

Exper t A , Hemoglobi n< 1 1 g/dL , Age s 0- 3 Year s

Blood-Lead Level s 4 5 y 

## R f 0.0 1 0.0 2 0.0 4 0.0 5 0.0 7 0.0 9 0. 1 8/d

L 

# ll 0. 1 0.2 5 0. 4 0. 5 0. 8 0.9 5 0.9 9 0.1 9 5 5 y

R 0.0 1 0.0 3 0.0 6 0.0 9 0.1 2 0.1 5 0.1 6 0.99 9 g/d L F 0.0 5 0.1 8 0. 4 0. 5 0. 6 0.9 5 0.9 9 6 5 y

g R 0.0 4 0.0 7 0. 1 0.1 3 0.1 6 0.1 9 0.2 2 /d

L F 0.0 5 0.1 5 0.3 5 0.4 5 0. 6 0. 9 0.9 8 0. 4 7 5 yg/dL

R F 0.0 5 0.0 5 0. 1 0. 2 0.1 5 0. 4 0. 2 0. 5 0.2 5 0. 6 0. 3 0. 7 0.3 5 0.9 5 0.9 9 Exper t A , Hemoglobi n< 1 1 g/dL , Age s 4- 6 Year s 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L R 0.0 1 0.0 2 0.0 3 0.0 5 0.0 6 F 0.0 5 0. 4 0. 5 0. 9 0.9 5 R 0.0 3 0.0 5 0.0 9 0.1 2 0.1 5 F 0.0 2 0. 2 0.4 5 0.5 5 0. 6 R 0.0 4 0.0 5 0. 1 0.1 5 0. 2 F 0.0 5 0. 1 0. 4 0. 5 0. 8 0.0 8 0.9 9 0.1 8 0.9 8 0.2 5 0.9 8

a R denote s populatio n respons e rat e (fractio n having hemoglobi n level s < 9. 5 o r 1 1 g/dL) . F denote s cumulativ e probability .P.2 9
12 1 TABL E B. 2 (Cont'd )

5 yg/d L R 0.00 5 0.0 1 0.017 5 0.0 3 0.03 5 0.04 5

0.0 3 0.0 6 0.0 8 0.0 9 0.1 2 0.1 5 F 0.0 1 0.0 5 0. 5 0. 8 0.9 5 0.9 9

0.0 1 0.2 8 0. 5 0. 5 0.9 6 0.9 9 Exper t C ,

1 5 yg/d L R F 0.01 5 0.00 1 0.0 2 0.0 2 0.0 3 0. 5 0.0 4 0.7 5 0.0 5 0.9 9 0.0 6 0.99 9
Exper t C , 0.0 5 0.0 3 0.0 8 0. 2 0.0 9 0. 5 0.1 1 0. 6 0.1 4 0.9 1 0.1 7 0.9 9 0. 2 0.99 9 Exper t D , 0.0 1 0. 5 0.0 3 0.99 9 Hemoglobi n< 9. 5 g/dL , Age s

Blood-Lead Level s 2 5 yg/d L 3 5 yg/d L R 0.02 5 0.0 3 0.03 5 0.0 4 0.0 5 0.0 6 0.067 5 Hemoglo b 0.0 5 0.0 9 0.1 2 0.1 3 0.1 7 0.2 1 F R F 0.0 1 0.03 5 0.0 1 0.0 2 0.0 4 0.0 4 0.2 5 0.0 5 0. 5 0. 5 0.0 6 0.7 5 0.7 5 0.0 7 0.9 7 0.9 7 0.07 5 0.9 9 0.9 9 i n< 1 1 g/dL , Age s 0.00 1 0. 1 0.0 1 0.1 1 0.1 4 0. 2 0. 5 0.1 6 0. 5 0. 7 0.1 8 0. 7 0.9 8 0.2 2 0.9 8 0.9 9 0.2 5 0.9 9
Hemoglobi n< 9. 5 g/dL , Age s 0.00 5 0.0 3 0.0 7 0.0 1 0.0 3 0.00 1 0. 5 0.0 6 0.2 5 0.99 9 0.0 8 0. 5 0.1 1 0.7 5 0.1 5 0.99 9 0- 6 Year s

4 5 yg/d L R F 0.04 5 0.0 1 0.0 5 0.0 5 0.0 6 0. 5 0.0 7 0. 8 0.0 8 0.9 7 0.08 5 0.9 9

0- 6 Year s 0.1 5 0.0 1 0. 2 0. 5 0.2 5 0. 7 0. 3 0.9 8 0.3 5 0.99 9

0. 3 Year s 0.0 7 0.00 1 0.1 1 0.2 5 0.1 6 0. 5 0.1 9 0.7 5 0.2 5 0.99 9 5 5 y

g R 0.0 5 0.0 6 0.0 7 0.0 8 0.0 9 0. 1

0.1 5 0. 2 0.2 5 0.2 7 0. 3 0.3 5 0. 4

0. 1 0.1 6 0. 2 0.2 5 0.3 3 /dL F 0.0 1 0.0 5 0. 5 0. 8 0.9 5 0.9 9

0.00 1 0.0 8 0. 3 0. 5 0. 8 0.9 8 0.99 9

0.00 1 0.2 5 0. 5 0.7 5 0.99 9TABL E B. 2 (Cont'd )

5 y g R

0.0 1 0.0 2 0.0 4 0. 1 0.11 8

0.0 1 0.0 1 0.0 2 0.0 6

0.00 1 0.0 1 0.0 3 0. 1 0.1 5 /dL

F

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.9 9

0.0 1 0. 1 0. 5 0. 9 0.9 9 Exper t D ,

1 5 yg/d L R F

Exper t D , 0.0 2 0.0 1 0.0 4 0.2 5 0.0 6 0. 5 0.1 2 0.7 5 0.1 5 0.9 9 Exper t D 0.0 1 0.0 1 0.0 2 0.2 5 0.0 3 0. 5 0.0 9 0.9 9
Exper t E , 0.00 2 0.0 1 0.0 3 0.0 5 0.0 7 0. 5 0.1 1 0.6 1 0.1 5 0.8 3 0.1 9 0. 9 0.2 3 0.9 9 —--•*--- " *W * ' • " ' * 12 2

Hemoglobi n< 9 . Blood-Lead
2 5 yg/dL R F 0.0000 5 0.00 1 0.00 5 0. 5 0.01 5 0.99 9 5 g/dL ,

Level s Age s

3 5 yg/d L R 0.0 2 0.0 5 0.0 6 0.0 8
Hemoglobi n < 1 1 g/dL , 0.1 1 0.0 1 0.11 5 0.2 5 0.1 5 0. 5 0.17 8 0.7 5 0.2 1 0.9 9

, Hemoglobi n < 0.0 5 0.0 1 0.0 7 0. 5 0.08 5 0.7 5 0.1 2 0.9 9
Hemoglobi n < 9 . 0.00 3 0.0 1 0.03 5 0.0 5 0.0 4 0. 1 0.0 7 0.2 5 0.0 9 0. 5 0.1 5 0.7 5 0.2 1 0. 9 0.2 5 0.9 9 0.1 5

0.1 6 0.1 8 0.2 2 0.2 4 F 0.00 1 0. 5 0.7 5 0.99 9
Age s 0.0 1 0.2 5 0. 5 0.7 5 0.9 9 g/dL , Age s 4
- 0.0 7 0.0 9 0.10 5 0.1 4

5 g/dL , 0.02 5 0.0 5 0. 1 0.1 5 0. 2 0.2 6 0.0 1 0. 5 0.7 5 0.9 9
Age s 0.0 1 0.0 8 0.2 7 0.5 6 0.8 1 0.9 8 4- 6 Year s

4 5 yg/dL R F 0.0 4 0.00 1 0.0 6 0.2 5 0.0 8 0. 5 0. 1 0.7 5 0.1 2 0.99 9 0. 3 Year s 0.1 7 0.0 5 0.1 9 0.2 5 0.2 2 0. 5 0.2 6 0.7 5 0.2 9 0.9 5

- 6 Year s 0.0 8 0.0 1 0. 1 0. 5 0.1 6 0.9 9

0. 3 Year s 0.0 3 0.0 1 0.0 6 0.0 6 0. 1 0. 2 0.1 9 0. 5 0.3 1 0.7 5 0.4 1 0.9 9 •

5 5 yg/d L R 0.0 6 0.0 8 0. 1 0.1 1 0.1 5

0.2 3 0.2 6 0. 3 0. 4 0.4 7

0. 1 0.1 2 0.1 4 0.15 5 0.1 7

0.0 5 0.0 8 0.2 2 0.3 6 0. 4 0.4 7 F 0.00 1 0.2 5 0. 5 0.7 5 0.99 9

0.12 5 0.2 5 0. 5 0.7 5 0.87 5

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0. 1 0. 5 0.7 5 0. 9 0.9 9 P.3 0

•P.3 1
12 3 TABL E B. 2 (Cont'd )

5 yIPO 0.00 4 0.0 1 0.0 6 0.0 9

0.0 2 0.0 4 0.0 8 0.1 2 0.1 6 0. 2 0.2 4

0.0 2 0.0 5 0.0 8 0.1 1 0.1 4 g/d L 

### F 0.1 5 0. 5 0.7 8 0.9 8

0.0 1 0.1 5 0. 5 0.6 1 0.8 3 0. 9 0.9 8

0.1 5 0.4 7 0.5 5 0.7 8 0.9 8 Exper t E ,

1 5 yg/dL R F 0.0 1 0.1 5 0.0 2 0. 5 0.0 7 0.7 8 0. 1 0.9 8

Exper t E , 0.0 3 0.0 1 0.0 6 0.1 5 0. 1 0. 5 0.1 4 0.6 1 0.1 8 0.8 3 0.2 2 0. 9 0.2 6 0.9 8 Exper t E , 0.0 1 0.0 1 0.0 4 0.1 5 0.0 7 0.4 7 0. 1 0.5 5 0.1 3 0.7 8 0.1 6 0.9 8 Hemoglobi n< 9 . 5 g/dL , Age s

Blood-Lead Level s 2 5 yg/dL R 0.0 2 0.0 4 0. 1 0.1 3

Hemoglo b 0.03 5 0.0 6 0.09 5 0.1 5 0.19 5 0.2 5 0.2 8 Hemoglo b 0.0 5 0.0 8 0.1 1 0.1 7 0. 2 F 0.1 7 0. 5 0. 9 0.9 9 3 5 yg/dL R F 0.01 5 0. 1 0.0 3 0.2 2 0.0 6 0.5 4 0. 1 0.8 5 0.1 3 0.9 5

i n < 1 1 g/dL , Age s 0.0 1 0. 1 0.2 5 0. 5 0.7 5 0. 9 0.9 9 0.0 4 0.0 1 0.0 8 0.0 8 0.1 5 0.2 7 0. 2 0.5 6 0.2 5 0.8 1 0. 3 0.9 8

i n < 1 1 g/dL , Age s 0.0 6 0.1 6 0. 5 0. 9 0.9 9 0.0 5 0.0 7 0.0 8 0. 1 0.1 1 0.2 7 0.1 4 0.5 4 0.1 7 0.8 5 0. 2 0.9 5 4- 6 Year s

4 5 yg/dL R F 0.0 2 0.0 3 0.06 5 0. 1 0.10 5 0.4 2 0.16 5 0. 6 0.21 5 0. 8 0.26 5 0.9 9 0- 3 Year s 0.0 6 0.0 1 0. 1 0.0 7 0.1 6 0.2 5 0.2 2 0. 5 0.3 5 0.7 5 0.4 5 0.9 9

4- 6 Year s 0.0 5 0.0 3 0. 1 0. 1 0.1 5 0.4 3 0. 2 0. 6 0.2 5 0. 8 0. 3 0.9 9 5 5 y

g R 0.0 6 0.1 1 0.1 5 0.2 2 0.2 6 0. 3

0. 1 0. 2 0. 3 0. 4 0. 5 0.5 5

0.0 5 0. 1 0.1 5 0. 2 0.2 5 0. 3 0.3 5 /d L F 0.0 5 0. 4 0. 5 0.7 5 0. 9 0.9 8

0.0 1 0.3 5 0. 5 0.6 2 0.9 4 0.9 9

0.0 1 0.0 5 0. 4 0. 5 0.7 5 0. 9 0.9 8P.3 2 124 TABL E B. 3 Summar

y of Function s Fi tt o th e Probabilisti cJudgment s o f Expert s Regardin g Lead-Induce d Hemoglobi n Decrement s

Exper t A , Hemoglobi n< 1 1 g/dL , Age s 0- 3 Year s

Blood-Lead Leve l (yg/d L 4 5 5 5 6 5 7 5 Parameter s o f

Normal-on-L n (R/U-R) ) Distributio n Mea n -3.354 6 -2.933 8 -2.072 4 -1.575 4 SD a

0.682 0 0.682 0 0.682 0 0.682 0 Momen t s o f

NOL O Distributio n E[R] b 0.041 2 0.060 7 0.127 5 0.186 9 Ove r R

SD[R] C 0.031 1 0.045 4 0.091 0 0.126 3 r 2 fo r

Regressio n o f F o n F 0.891 4 0.838 8 0.930 5 0.940 7 Exper t A , Hemoglobi n< 1 1 g/dL , Age s 4- 6 Year s 5 5 6 5 7 5 -3.682 6

-2.271 3 -2.061 7 0.594 5

0.594 5 0.594 5 0.028 8

0.105 1 0.125 4 0.018 4

0.063 5 0.074 5 0.973 4

0.896 8 0.946 4

a S D denote s standard deviation . E[R ] denote s the mea n o f the distributio n fo r R . SD[R ] denote s the standard deviatio n o f the distributio n fo r R .I — 1 P.3 3
12 5 TABL EB. 3 (Cont'd )

Blood-Lea d Leve l (yg/d L 5 1 5 2 5 3 5 4 5 5 5 Exper t C , Hemoglobi n< 9. 5 g/dL , Age s 0- 6 Year s

Parameter s Normal-on
o f

-L n (R/U-R) ) Distribu t Mea n -3.999 5 -3.448 1 -3.129 8 -2.918 7 -2.742 4 -2.578 1 io

n SD a 0.276 4 0.276 4 0.276 4 0.276 4 0.276 4 0.276 4 Moment s o f

NOL O Distributio n E[R] b 0.018 7 0.031 9 0.043 3 0.052 9 0.062 4 0.072 7 Ove r R

SD[R] C 0.005 2 0.008 7 0.011 7 0.014 2 0.016 6 0.019 1 r 2 fo r

Regressio n o f 0.980 6 0.989 9 0.990 6 0.991 7 0.990 0 0.971 3
Exper t C , Hemoglobi n< 1 1 g/dL , Age s 0- 6 Year s 5 1 5 2 5 3 5 4 5 5 5 -3.682 6

-2.271 3 -2.061 7 -1.696 5 -1.319 0 -1.049 8 0.594 5

0.594 5 0.594 5 0.272 0 0.272 0 0.272 0 0.028 8

0.105 1 0.125 4 0.158 2 0.214 4 0.262 4 0.018 4

0.063 5 0.074 5 0.037 2 0.047 1 0.054 2 0.973 4

0.896 8 0.946 4 0.985 7 0.968 3 0.981 6P.3 4 12 6
TABL E B. 3 (Cont'd )

Exper t D , Hemoglobi n< 9. 5 g/dL , Age s 0- 3 Year s

Blood-Lead Leve l (yg/dL 1 5 2 5 3 5 4 5 5 5 Parameter s o f

Normal-on-L n (R/(l-R) ) Distributio n -4.585 2 -3.875 9 -2.499 1 -1.776 9 -1.409 7 SD a

0.355 7 0.355 7 0.355 7 0.355 7 0.355 7 Moment s o f

NOL O Distributio n E[R] b 0.010 7 0.021 5 0.079 7 0.150 0 0.201 9 Ove r R

SD[R] C 0.003 9 0.007 8 0.027 2 ' 0.047 5 0.060 2 r 2 fo r

Regressio n o f F o n F 1.000 0 0.842 1 0.980 5 0.965 4 0.993 5 Exper t D , Hemoglobi n< 9. 5 g/dL , Age s 4- 6 Year s 2 5 3 5 4 5 5 5 -6.460 4

-3.044 3 -2.512 3 -2.243 3 1.040 9

0.217 7 0.217 7 0.217 7 0.002 7

0.046 4 0.076 4 0.097 6 0.003 7

0.009 8 0.015 6 0.019 5 0.837 4

0.953 6 0.943 7 0.982 0 Exper t D , Hemoglobi n< 1 1 g/dL , Age s 0- 3 Year s

Blood-Lead Leve l (yg/dL 5 1 5 2 5 3 5 4 5 5 5 Parameter s

Normal-on
o f

-L n (R/(l-R) ) Distribu t Mea n -3.174 7 -2.709 7 -1.744 2 -1.465 5 -1.248 5 -0.725 4 Lo

n SD a 0.491 9 0.491 9 0.491 9 0.491 9 0.491 9 0.491 9 Momen t s o f

NOL O Distributio n E[R] b 0.044 5 0.068 6 0.158 6 0.197 5 0.232 2 0.331 2 Ove r R

SD[R] C 0.022 5 0.034 0 0.072 0 0.085 8 0.096 7 0.119 6 rl

fo r Regressio n o f 0.928 5 0.956 5 0.969 3 0.967 4 0.996 6 0.972 9P.3 5
12 7
TABL E B. 3 (Cont'd )

Exper t D , Hemoglobi n< 1 1 g/dL , Age s 4- 6 Year s

Blood-Lead Leve l (yg/dL 5 1 5 2 5 3 5 4 5 5 5 Parameter s o f

Normal-on-L n (R/(l-R) ) Distributio n Mea n -3.875 9 -3.486 6 -2.504 9 -2.244 6 -2.099 3 -1.857 3 SD a

0.489 4 0.489 4 0.177 7 0.177 7 0.177 7 0.177 7 Moment s o f

NOL O Distributio n E[R] b 0.022 7 0.033 1 0.076 4 0.096 9 0.110 4 0.136 4 Ove r R

SD[R] C 0.011 6 0.016 8 0.012 7 0.015 7 0.017 6 0.021 2 r 2 fo r

Regressio n o f F o n F 0.944 8 0.996 8 0.957 9 0.967 4 0.935 8 0.974 9 Exper t E , Hemoglobi n< 9. 5 g/dL , Age s 0- 3 Year s

Blood-Lead Leve l (yg/dL 5 1 5 2 5 3 5 4 5 5 5 Parameter s

Normal-on
Dis t Mea n -3.782 0 -2.799 2 -2.472 5 -1.960 2 -1.564 3 -1.400 2 o f

-L n (R/U-R) ) ribu t io n SD a 0.960 0 0.960 0 0.960 0 0.960 0 0.960 0 0.960 0 Momen t s o f

NOL O Distributio n E[R] b 0.033 1 0.077 3 0.099 4 0.141 3 0.178 6 0.195 1 Ove r R

SD[R] C 0.041 4 0.098 7 0.128 0 0.183 6 0.230 1 0.248 6 r 2 fo r

Regressio n o f F o n F 0.981 7 0.955 3 0.958 6 0.964 6 0.985 4 0.986 6 Exper t E , Hemoglobi n< 9. 5 g/dL , Age s 4- 6 Year s 5 1 5 2 5 3 5 4 5 5 5 -4.162 3

-3.685 6 -3.337 6 -3.021 8 -2.114 1 -1.912 1 0.822 4

0.822 4 0.822 4 0.822 4 0.822 4 0.822 4 0.020 9

0.032 9 0.045 4 0.060 2 0.127 5 0.148 1 0.020 6

0.032 3 0.044 4 0.058 8 0.121 7 0.139 8 0.980 2

0.988 4 0.980 4 0.950 3 0.984 8 0.932 70 0

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_m i n i n i n m •"HcMro-iTi nTABL

E B. 4 Summar

y and Compariso n o f

Judgment s an

d Fitte d Function s Concernin g Lead-Induce d Hemoglobi n Decrement s Exper tA , Hemoglobi n < 1 1 g/dL , Age s 0- 3 Year s Blood-Lea d Leve l Inde x 4 5 yg/d L5 5 yg/d L6 5 yg/d L7 5 yg/d L Encode d Judgment s Media n 0.0 5 0.0 9 0.1 4 0.2 0 50 % C.I. a(0.02 , 0.07 ) (0.04 , 0.13 ) (0.09 , 0.18 ) (0.11 , 0.31 ) 90 % C.I . (0.01 , 0.09 ) (0.01 , 0.15 ) (0.04 , 0.21 ) (0.05 , 0.35 ) Pitte d Function s Media n 0.0 3 0.0 5 0.1 1 0.1 7 50 % C.I . (0.02 , 0.05 ) (0.03 , 0.08 ) (0.07 , 0.17 ) (0.12 , 0.25 ) 90% C.I . (0.01 , 0.10 ) (0.02 , 0.14 ) (0.04 , 0.28 ) (0.06 , 0.39 ) 98 % C.I . (0.01 , 0.15 ) (0.01 , 0.21 ) (0.03 , 0.38 ) (0.04 , 0.50 ) Exper tA , Hemoglobi n < 1 1 g/dL , Age s 4- 6 Year s r o v o

Encode dJudgment s Median 0.0 3 0.1 1 0.1 5 50 % C.I . (0.02 , 0.04 ) (0.06 , 0.16 ) (0.08 , 0.19 ) 90 % C.I . (0.01 , 0.06 ) (.03 , 0.18 ) (0.04 , 0.24 ) Fitte d Function s Median 0.0 2 0.0 9 0.1 1 50 % C.I . (0.02 , 0.04 ) (0.06 , 0.13 ) (0.08 , 0.16 ) 90 % C.I . (0.01 , 0.06 ) (0.04 , 0.22 ) (0.05 , 0.25 ) 98 % C.I . (0.01 , 0.09 ) (0.03 , 0.29 ) (0.03 , 0.34 ) "CI . denote s Credibl e Interval .TABL E B. 4 (Cont'd ) (a Exper tC , Hemoglobi n < 9. 5 g/dL , Age s 0- ^ Year s

Inde x
Media n 50 % C.I . 90 % C.I .
Media n 50 % C.I . 90 % C.I . 98 % C.I . 5 yg/d L
0.0 2 (0.01 , 0.03 ) (0.01 , 0.04 )
0.0 2 (0.01 , 0.02 ) (0.01 , 0.03 ) (0.01 , 0.04 ) Blood-Lea d Leve l

1 5 yg/d L2 5 yg/d L3 5 yg/d L

Encode d Judgment s 0.0 3 (0.02 , 0.04 ) (0.02 , 0.05 )

0.0 3 (0.03 , 0.04 ) (0.02 , 0.05 ) (0.02 , 0.06 ) 0.0 4

(0.04 , 0.05 ) (0.03 , 0.06 ) Fitte d Function s 0.0 4 (0.04 , 0.05 ) (0.03 , 0.06 ) (0.02 , 0.08 ) 0.0 5

(0.04 , 0.06 ) (0.04 , 0.07 )

0.0 5 (0.04 , 0.06 ) (0.03 , 0.08 ) (0.03 , 0.09 ) 4 5 yg/d L

0.0 6 (0.05 , 0.07 ) (0.05 , 0.08 )

0.0 6 (0.05 , 0.07 ) (0.04 , 0.09 ) (0.03 , 0.11 ) 5 5 yg/dL )

0.0 7 (0.06 , 0.08 ) (0.06 , 0.09 )

0.0 7 (0.06 , 0.08 ) (0.05 , 0.11 ) (0.04 , 0.13 ) CO o Exper t C , Hemoglobi n< 1 1 g/dL , Age s 0- 6 Year s

Media n 50 % C.I , 90 % C.I , 0.0 8

(0.06 , 0.10 ) (0.03 , 0.10 ) 0.0 9

(0.08 , 0.12 ) (0.05 , 0.13 ) Encode d Judgment s 0.1 2 (0.10 , 0.14 ) (0.07 , 0.15 ) Fitte d Function s 0.1 6

(0.14 , 0.19 ) (0.11 , 0.20 ) 0.2 0

(0.17 , 0.26 ) (0.15 , 0.27 ) 0.2 7

(0.24 , 0.29 ) (0.18 , 0.31 )

Media n 50 % C.I . 90 % C.I . 98 % C.I . 0.0 7

(0.06 , 0.09 ) (0.05 , 0.11 ) (0.04 , 0.13 ) 0.1 0 •

(0.08 , 0.11 ) (0.06 , 0.14 ) (0.05 , 0.17 ) 0.1 2

(0.10 , 0.14 ) (0.08 , 0.17 ) (0.06 , 0.20 ) 0.1 5

(0.13 , 0.18 ) (0.10 , 0.22 ) (0.09 , 0.26 ) 0.2 1

(0.18 , 0.24 ) (0.15 , 0.29 ) (0.12 , 0.33 ) 0.2 6

(0.23 , 0.30 ) (0.18 , 0.35 ) (0.16 , 0.40 )TABL E B. 4 (Cont'd ) Exper tD , Hemoglobi n < 9. 5 g/dL , Age s 0- 3 Year s Blood-Lea d Leve l /f 3% 35T <+< 5 T Inde x / 5 yg/d LXb yg/d L> 5 yg/d Ltf> yg/d L4-$ yg/d L-5 5 yg/UL )

Encode d Judgment s Median 0.0 1 0.0 3 0.0 8 0.1 6 0.2 0 50 % C.I . (— , 0.02 ) (0.02 , 0.05 ) (0.06 , 0.11 ) (0.11 , 0.19 ) (0.16 , 0.25 ) 90 % C.I . (— , 0.03 ) (0.01 , 0.07 ) (0.04 , 0.14 ) (0.08 , 0.24 ) (0.11 , 0.31 ) Fitte d Function s Median 0.0 1 0.0 2 0.0 8 0.1 4 0.2 0 50 % C.I . (0.01 , 0.01 ) (0.02 , 0.03 ) (0.06 , 0.09 ) (0.12 , 0.18 ) (0.16 , 0.24 ) 90 % C.I . (0.01 , 0.02 ) (0.01 , 0.04 ) (0.04 , 0.13 ) (0.09 , 0.23 ) (0.12 , 0.30 ) 98 % C.I . (0.00 , 0.02 ) (0.01 , 0.04 ) (0.03 , 0.16 ) (0.07 , 0.28 ) (0.12 , 0.36 ) Exper t D , Hemoglobi n < 9.5 , Age s 4- 6 Year s

Encode d Judgment s Median 0.00 5 0.0 5 0.0 8 0.1 0 50 % C.I . (0.00 , 0.01 ) (0.03 , 0.06 ) (0.06 , 0.10 ) (0.08 , 0.11 ) 90 % C.I . (0.00 , 0.01 ) (0.02 , 0.08 ) (0.04 , 0.12 ) (0.06 , 0.14 ) Fitte d Function s Median 0.00 2 0.0 5 0.0 7 0.1 0 50 % C.I . (0.00 , 0.00 ) (0.04 , 0.05 ) (0.07 , 0.09 ) (0.08 , 0.11 ) 90 % C.I . (0.00 , 0.01 ) (0.03 , 0.06 ) (0.05 , 0.10 ) (0.07 , 0.13 ) 98 % C.I . (0.00 , 0.02 ) (0.03 , 0.07 ) (0.0 5 0.12 ) (0.06 , 0.15 ) COTABL E B. 4 (Cont'd )
Exper t D , Hemoglobi n< 1 1 g/dL , Age s 0- 3 Year s

Index
Median 50 % C.I . 90 % C.I .
Median 50 % C.I . 90 % C.I . 98 % C.I . 5 yg/d L

0.0 4 (0.02 , 0.10 ) (0.01 , 0.03 )

0.0 4 (0.03 , 0.06 ) (0.02 , 0.09 ) (0.01 , 0.12 ) 1 5 yg/d L

0.0 6 (0.04 , 0.12 ) (0.02 , 0.15 )

0.0 6 (0.05 , 0.08 ) (0.03 , 0.13 ) (0.02 , 0.17 ) Blood-Lea d Leve l 2 5 yg/d L 3 5 yg/d L Encode d Judgment s 0.1 5 (0.11 , 0.18 ) (0.11 , 0.21 ) Fitte d Function s 0.1 5 (0.11 , 0.20 ) (0.07 , 0.28 ) (0.05 , 0.35 ) 0.1 8

(0.16 , 0.22 ) (0.14 , 0.26 )

0.1 9 (0.14 , 0.24 ) (0.09 , 0.34 ) (0.07 , 0.42 ) 4 5

0.2 2 (0.19 , 0.26 ) (0.17 , 0.29 )

0.2 2 (0.17 , 0.29 ) (0.11 , 0.39 ) (0.08 , 0.47 ) 5 5

0.3 0 (0.26 , 0.40 ) (0.21 , 0.52 )

0.3 3 (0.26 , 0.40 ) (0.18 , 0.52 ) (0.13 , 0.60 ) CO IN J
Exper t D , Hemoglobi n< 1 1 g/dL , Age s 4- 6 Year s

Median 50 % C.I . 90 % C.I . 0.0 2

(0.01 , 0.04 ) (0.01 , 0.06 ) 0.0 3

(0.02 , 0.06 ) (0.01 , 0.09 ) Encode d Judgment s 0.0 7 (0.06 , 0.09 ) (0.05 , 0.11 ) Fitte d Function s 0.0 9

(0.08 , 0.11 ) (0.07 , 0.13 ) 0.1 0

(0.09 , 0.13 ) (0.08 , 0.16 ) 0.1 4

(0.12 , 0.16 ) (0.10 , 0.17 )

Median 50 % C.I . 90 % C.I . 98 % C.I . 0.0 2

(0.01 , 0.03 ) (0.01 , 0.04 ) (0.01 , 0.06 ) 0.0 3

(0.02 , 0.04 ) (0.01 , 0.06 ) (0.01 , 0.09 ) 0.0 8

(0.07 , 0.08 ) (0.06 , 0.10 ) (0.05 , 0.11 ) 0.1 0

(0.09 , 0.11 ) (0.07 , 0.12 ) (0.07 , 0.14 ) 0.1 1

(0.10 , 0.12 ) (0.08 , 0.14 ) (0.07 , 0.16 ) 0.1 4

(0.12 , 0.15 ) (0.10 , 0.17 ) (0.09 , 0.19 )TABL E B. 4 (Cont'd )
Exper t E , Hemoglobi n< 9. 5 g/dL , Age s 0- 3 Year s

Index Median 50 % C.I . 90 % C.I .
Median 50 % C.I . 90 % C.I . 98 % C.I . 5 yg/d L 0.0 3 (0.02 , 0.07 ) (0.01 , 0.12 )

0.0 2 (0.01 , 0.04 ) (0.00 , 0.10 ) (0.00 , 0.18 ) 1 5 yg/d L 0.0 7 (0.05 , 0.13 ) (0.03 , 0.21 )

0.0 6 (0.03 , 0.10 ) (0.01 , 0.23 ) (0.01 , 0.36 ) Blood-Lea d Leve l 2 5 yg/dL 3 5 yg/d L 0.0 9 (0.06 , 0.15 ) (0.03 , 0.23 ) Fitte d Function s 0.0 8 (0.04 , 0.14 ) (0.02 , 0.29 ) (0.01 , 0.44 ) 0.1 4

(0.09 , 0.19 ) (0.04 , 0.24 )

0.1 2 (0.07 , 0.21 ) (0.03 , 0.41 ) (0.01 , 0.57 ) 4 5 yg/d L 0.1 9 (0.11 , 0.31 ) (0.05 , 0.39 )

0.1 7 (0.10 , 0.29 ) (0.04 , 0.50 ) (0.02 , 0.66 ) 5 5 yg/dL ) 0.2 2 (0.13 , 0.36 ) (0.06 , 0.44 )

0.2 0 (0.11 , 0.32 ) (0.05 , 0.54 ) (0.03 , 0.70 ) u > CO Exper t E , Hemoglobi n< 9. 5 g/dL , Age s 4- 6 Year s

Encode d Judgment s Median 50 % C.I . 90 % C.I . 0.0 1

(0.01 , 0.05 ) (0.00 , 0.09 ) 0.0 2

(0.01 , 0.06 ) (0.00 , 0.10 ) 0.0 4

(0.01 , 0.07 ) (0.00 , 0.11 ) 0.0 6

(0.03 , 0.09 ) (0.01 , 0.13 ) 0.1 3

(0.08 , 0.20 ) (0.03 , 0.25 ) 0.1 5

(0.09 , 0.22 ) (0.06 , 0.29 ) Fitte d Function s Median 50 % C.I , 90 % C.I , 98 % C.I , 0.0 2

(0.01 , 0.06 ) (0.00 , 0.06 ) (0.00 , 0.10 ) 0.0 2

(0.01 , 0.09 ) (0.02 , 0.09 ) (0.00 , 0.15 ) 0.0 3

(0.02 , 0.12 ) (0.01 , 0.12 ) (0.01 , 0.19 ) 0.0 5

(0.03 , 0.16 ) (0.01 , 0.16 ) (0.01 , 0.25 ) 0.1 1

(0.06 , 0.32 ) (0.03 , 0.32 ) (0.02 , 0.45 ) 0.1 3

(0.08 , 0.36 ) (0.04 , 0.36 ) (0.02 , 0.50 )

•p .TABL E B. 4 (Cont'd )
II Exper tE , Hemoglobi n <-9T 5 g/dL , Age s 0- 3 Year s

Inde x
Median 50 % C.I . 90 % C.I . 5 yg/d L

0.0 8 (0.05 , 0.14 ) (0.03 , 0.22 ) Blood-Lead Leve l

1 5 yg/d L 2 5 yg/d L 3 5 yg/d L

Encode d Judgment s 0.1 0 (0.07 , 0.16 ) (0.04 , 0.24 ) 0.1 5

(0.09 , 0.19 ) (0.05 , 0.26 ) Fitte d Function s 0.1 9

(0.14 , 0.24 ) (0.06 , 0.28 ) 4 5 yg/d L

0.2 2 (0.16 , 0.35 ) (0.09 , 0.43 ) 5 5 yg/dL )

0.3 0 (0.17 , 0.44 ) (0.11 , 0.51 )

Median 50 % C.I . 90 % C.I . 98 % C.I .

Median 50 % C.I . 90 % C.I . 0.0 9

(0.06 , 0.13 ) (0.03 , 0.20 ) (0.02 , 0.28 )

0.0 6 (0.03 , 0.10 ) (0.01 , 0.14 ) 0.1 1

(0.07 , 0.15 ) (0.04 , 0.24 ) (0.03 , 0.33 ) 0.1 3 0.1 6

(0.09 , 0.18 ) (0.11 , 0.22 ) (0.05 , 0.28 ) (0.07 , 0.34 ) (0.03 , 0.37 ) (0.05 , 0.44 ) Exper t E , Hemoglobi n < 1 1 g/dL , Age s 4- 6 Yea r

0.0 8 (0.05 , 0.12 ) (0.02 , 0.16 ) Encode d Judgment s 0.1 1 0.1 3 (0.09 , 0.15 ) (0.10 , 0.16 ) (0.04 , 0.19 ) (0.04 , 0.20 ) 0.2 1 (0.15 , 0.29 ) (0.09 , 0.42 ) (0.06 , 0.52 )

s

0.1 6 (0.12 , 0.24 ) (0.06 , 0.29 ) 0.2 8

(0.21 , 0.37 ) (0.13 , 0.52 ) (0.09 , 0.62 )

0.2 0 (0.13 , 0.25 ) (0.10 , 0.33 ) i — * U J

Media n 50 % C.I . 90 % C.I . 98 % C.I . 0.0 5

(0.04 , 0.08 ) (0.02 , 0.13 ) (0.01 , 0.09 ) 0.0 7

(0.05 , 0.10 ) (0.03 , 0.16 ) (0.02 , 0.22 ) Fitted Function s 0.1 0 (0.07 , 0.14 ) (0.04 , 0.22 ) (0.03 , 0.30 ) 0.1 2

(0.08 , 0.17 ) (0.05 , 0.27 ) (0.03 , 0.35 ) 0.1 5

(0.11 , 0.21 ) (0.06 , 0.32 ) (0.04 , 0.42 ) 0.1 8

(0.13 , 0.24 ) (0.08 , 0.36 ) (0.05 , 0.46 )P.4 3
13 5 encode djudgment s an dth e fitte dfunctions
. Eac htabl e i s organize ds o tha t eac h expert/hemoglobin-level/age-categor y combinatio ni s liste di nth e table , beginnin g wit h Exper t A , continuin g in alphabetica l order , an dendin g wit hExper t E . B.3. 1 EXPER T A Exper t A chos e t o separat e th e populatio nof U.S . childre nage d0- 6 year s int o tw o subpopulations , age s 0- 3 an d4- 6 years . Thi s individua l provide djudgment s onl y a t th e 1 1 g/d Lhemoglobi n level
. Sinc e hi s judgment s indicate dtha t ther e i s aver y smal l lead-induce dhemoglobi n effec t a t blood-lea dlevel s belo w 4 5 yg/dL , i t wa s no t necessar y t o obtai nprobabilisti c judgment s a t th e 9. 5 g/d Llevel
. Th e probabilisti c judgment s of Exper t A regardin g th e effect s of lea dexposur e o n hemoglobi n level s amon g U.S . childre nage d0- 3 year s ar e liste di nTabl e B. 2 fo r th e 11. 0 g/d Lhemoglobi n level
. Th e probabilit y judgment s ar e cumulativ e distributio n function s (CDFs ) of

judgmenta l probability
. Tha t is , fo r eac hblood-lea dleve l L , th e entrie s in colum n Fin Tabl e B. 2 represen t th e judge dprobabilit y tha t th e tru e respons e rat e R j i s les s tha n o r equa l t o th e rat e Rshow nincolum nRof th e table
. Ther e ar e fou r CDFs , on e eac hfo r

blood-lea dlevel s of

45 , 55 , 65 , an d7 5 yg/dL
. Exper t A di dno t fee l tha t ther e was ameasurable , lead-induce dhemoglobi neffec t a t blood-lea dlevel s belo w 4 5 yg/dL
. Th e curve s displa y awide r rang e of

plausibl e populatio nrespons e rate s a t successivel y highe r

blood-lea dlevels
. Thi s ma y b e interprete dt o mea nth e Exper t A i s les s certai n abou t

wha t actua l respons e rate s ma y b e a t th e highe r

blood-lea dlevels
. Ther e i s n o indicatio n of athreshol dfo r

ahemoglobi neffec t

inth e rang e o f

45-7 5 yg/dL
. Fo r th e reason s presente dinSec . 1 , mathematica l function s wer e fi t t o th e judgment s of

Exper t A (an dth e judgment s of th e othe r

experts) . Fo r

Exper t A , th e mathematica l representation s fo r th e variou s blood-lea dlevel s ar e guarantee dneve r t o cross . The y wer e obtaine db y fittin g regressio nline s t o transformation s of th e judgments
. Th e transformatio n use dwa s th e normal-on-log-odd s transformation
. I tP.4 4
13 6 happen s tha t

thi s transformatio n lead s t o distribution s tha t ar e norma l distributions , wit h ahig hdegre e of

accuracy . Thes e distribution s ar e als o convenien t fo r us e insubsequen t analysis
. W

e cal l thes e fitte drepresentation s "normal-on-log-odds " (NOLO ) functions
. The y ar e uniquel y define db y th e mea nan dvarianc e of th e underlyin g norma l distributions , an dth e transformatio nfunctions ; thes e ar e summarize di nSec . B.2 . Tabl e B. 3 summarize s relevan t parameter s fo r

eac hof

th e conditiona l CDF s fi t t o th e judgment s of

Exper t A . Include dinth e tabl e fo r eac hlea dleve l a t

whic haCD Fwa s assesse dar e th e mea n an dstandar ddeviatio nof th e underlyin g norma l distribution , th e mea nan dstandar ddeviatio n of th e NOLO distribution , an dth e R-square s of regression s of th e fitte drepresentation s o n encode djudgments
. I ngeneral , th e regressio nR-squar e value s ar e reassuringl y high
. Finally , Tabl e B. 4 summarize s an dcompare s th e judgment s an dth e fitte drepresentations
. Include dinth e tabl e ar e median s an dsevera l credibl e intervals
. Th e media n i s tha t valu e tha t

i s exceede dwit hprobabilit y 0.5
. Th e 90 % credibl e interva l i s ase t of respons e rat e value s suc htha t ther e i s a0. 9 probabilit y of th e tru e valu e fallin g withi n it
. Fo r exampl e fo r

childre nage d0- 3 havin g blood-lea d level s of 5 5 yg/dL , th e media n encode drespons e rat e i s 9% , an dth e 90 % credibl e interva l i s 1 % t o 15% ; tha t

is , wit hprobabilit y 0.0 5 th e tru e respons e rat e i s les s tha no r equa l t o 1% , an dwit hprobabilit y 0.0 5 i t i s greate r

tha n15%
. Simila r

statement s appl y t o th e fitte drepresentation
. Not e th e th e encode dmedia nvalue s ar e fairl y clos e t o th e median s of

th e fitte drepresentations , differin g b y tw o t o fou r percentag e points
. However , th e fitte drepresentation s exhibi t mor e uncertaint y tha nd o th e judgments
. Thes e feature s an ddifference s wer e carefull y pointe dou t t o Exper t

A . H e finall y conclude dtha t

th e fitte drepresentation s bette r capture dhi s bes t

judgment s abou t

th e effect s of

lea do n hemoglobi n level s amon g U.S . children
.P.4 5
13 7 B.3. 2 Exper t

B Exper t B di dno t

fee l comfortabl e wit hth e proces s of givin g probabilisti c judgment s abou t

th e effect s o

f lea do nhemoglobi nlevel s amon g children
. However , h e wa s abl e t o discus s qualitativel y th e effect s of lea dexposur e o nhemoglobi nan dE P levels
. A summar y of

tha t discussio ni s presente di nSec . B.4 . B.3. 3 Exper t

C Exper t C chos e t o provid e judgment s fo r th e populatio nof

childre nage d0- 6 years . H e acknowledge dtha t ther e certainl y wer e difference s inmetabolis mbetwee n childre nage d0- 3 an d4-6 , bu t h e fel t tha t thes e difference s wer e difficul t t o quantif

y considerin g othe r

uncertainties
. Thus , h e provide dtw o set s of judgment's , on e se t

a t eac h of th e hemoglobi n level s of interest
. Followin g th e forma t

introduce dfo r

discussin g th e judgment s of Exper t A , i t ca n b e see n tha t

th e fitte dfunction s closel y matc hth e encode djudgments
. Th e media n respons e rat e value s ar e n o mor e tha n1 % apart . Th e fitte dfunction s d o displa y large r uncertaint y a t

th e highe r

blood-lea dlevels
. Exper t C concluded , afte r

stud y an d reflection , tha t

th e mathematica l representation s di dcaptur e hi s bes t judgments
. B.3. 4 Exper t

D Exper t D chos e t o divid e th e populatio nint o tw o subgroups , childre nage d0- 3 an d 4- 6 years , an dprovide djudgment s a t bot hth e 9. 5 an d11. 0 g/d Lhemoglobi nlevels
. Thi s resulte di nfou r

set s of judgment s fo r

Exper t D . A t th e 9. 5 g/d Lhemoglobi nlevel , ther e i s evidenc e of asligh t threshol dbetwee n blood-lea dlevel s 2 5 an d3 5 yg/dL , indicate db y th e wide r spacin g betwee nthes e level s compare dt o th e othe r

levels
. A t

th e 1 1 g/d Lhemoglobi nlevel , athreshol di s indicate d betwee n th e 1 5 an d2 5 yg/d Lblood-lea dlevels
. Thi s wa s recognize dan dagree dt o b y Exper t D .P.4 6
13 8 I ngeneral , ther e i s agai ngoo dagreemen t betwee nth e mathematica l representation s an dth e judgment s fo r Exper t D . R-squar e value s fo r regression s of

Fon Far e generall y aroun d0.95
. B.3. 5 EXPER

T E Lik e Exper t

D , Exper t

Eprovide dfou r

set s of judgments , on e fo r

eac hof th e ag e an dhemoglobi n leve l combination s tha t resul t fro mdividin g th e ag e rang e int o subgroup s age d0- 3 an d4- 6 years . Th e judgment s an dfitte dmathematica l representation s ar e liste dan dcompare din th e table s alread y mentioned
. Onl y on e cas e fo r

Exper t Eshowe devidenc e of

athreshol deffect
. Tha t wa s a t th e 9. 5 g/d Lhemoglobi n leve l fo r childre nage d4- 6 years . Th e threshol dappear s betwee n th e blood-lea dlevel s of 3 5 an d4 5 yg/dL
. I

nthi s case , a s wel l a s th e other s fo r Exper t E , th e fitte dmathematica l representation s matche dth e judgment s quit e well , th e R-squar e value s of

th e regression s of

Fo nFwer e generall y aroun d0.95
. B. 4 SUMMAR

Y DISCUSSIONS
B.4. 1 Summar y o f

Discussio n with Exper tA 1 . Ther e i s absolutel y no evidenc e tha t ZP Pi s toxi c pe r

se . 2 . Th e biosyntheni s of hem e i s regulate db y anegativ e feedbac k proces s (Stanbury , "Metaboli c Basi s of Inherite dDisease")
. Th e rat e limitin g factor s ar e heme , hem e oxygenase , an dALA synthase
. Th e enzyme s i nth e pathwa y fro mALAD dehydratas e t o ferrochelatas e ar e presen t insubstantia l excess . Ther e i s normall y asubstantia l exces s capacit y of thes e intermediar y enzymes . Fo r

example , ther e i s sixtee ntime s a s muc hALAD

dehydratas e a s i s necessar y t o metaboliz e th e amoun t of AL AP.4 7
13 9 produce db y AL

A synthase
. Overall , fo r ever y 10,00 0 molecule s of hem e produced , th e equivalen t of on e molecul e i s los t

a s ALA , coppe r porphyrin , an dprotoporphyrin
. 3 . Lea dcause s partia l inhibitio nof AL A dehydratas e an dferrochela

tase . E Pi s amarke r

of th e partia l inhibitio ntha t occur s a t

th e ferrochelatas e step . I

nth e presenc e of

lead , i t ha s bee nobserve d tha t increase dFE Plevel s correlat e wit hdecrease dALAD levels
. Som e geneti c studie s sugges t tha t hig hFE Plevel s ar e associate dwit hdecrease dALAD activities , eve ninth e absenc e of lead
. 4 . ZP Pi s boun dt o th e re dcel l an dtherefor e remain s throughou t th e lif e of th e re dcell , whic hi s abou t 120 days
. Insofar

a s i s known , al l cell s synthesiz e th e hem e necessar y fo r th e cell' s function , an d lea dinhibit s hem e synthesi s inmos t othe r cell s of

th e body , includin g liver , kidney , an dbrain
. Th e hem e enzyme s inthes e othe r cell s ma y hav e ver y shor t hal f lives
. Thes e ar e probabl y quit e importan t

in considerin g lea deffects
. On e of thes e i s th e P-45 0 famil y of

enzymes . Als o of

concer ni s th e activatio nrat e of a n enzym e in th e kidney , whic hmay b e inhibite dt o aharmfu l level
. I

nth e liver , th e P-45 0 enzyme s ar e essentia l inth e metabolis mof

drugs
. 5
. Ther e i s adose-dependen t decreas e inth e leve l of 1,2 5 dihydroxy

vitami n D in serum . Thi s relationshi p i s nonlinear , an dth e leve l decrease s a t

amuc hhighe r

rat e a s lea drise s abov e 35-4 0 yg/dL
. Althoug hth e mechanis mfo r th e reductio nof

1,2 5 dihydroxy

vitami nD in seru mi s no t full y understood , i t

i s possibl e tha t

thi s may b e realte dt o an effec t of lea do nproductio nof

P-45 0 inth eP.4 8
14 0 kidney
. P-45 0 i s on e of th e factor s necessar y fo r th e hydroxylizatio n of

1,25 dihydroxyvitami n D a t th e 1 position , whic hoccur s in th e kidney
. Furthe r researc hwil l b e require dt o evaluat e th e biologica l significanc e of reduce dseru mlevel s of 1,25 dihydroxyvitami n D . 6 . A ne w diseas e relate dt o th e virtua l absenc e of ALAD ha s bee n described
. Thi s i s ageneti c disorde r transmitte da s arecessiv e trait
. Peopl e s o affecte dhav e symptom s simila r t o thos e havin g acut e intermitten t

prophyria , anothe r

geneti c disorde r

of porphyri n metabolism
. I t i s extremel y doubtfu l tha t thi s ha s anythin g t o d o wit hlow-leve l lea dexposure , althoug ha t hig hPb B level s (70-8 0 yg/d Lo r higher) , i t

i s possibl e tha t

lea dinhibit s ALAD t o th e sam e exten t a s tha t foun dinthi s ne w disease
. I n thi s ne w disease , ALAD activitie s ar e abou t 1 % of normal
. Furthermore , peopl e hav e bee nidentifie dwit hALAD level s a t abou t 20 % of normal , an dthes e peopl e ar e health y an dwithou t an y symptom s whatsoever
. 7 . Clinicall y speaking , childre nwit hbloo dlead s aroun d40 yg/dL , elevate dEP , an dothe r

evidenc e of

iro ndeficienc y ca nb e treate d wit hiro nan dthi s anemi aand/o r iro ndeficienc y ca nb e corrected , eve n thoug hn o specifi c treatmen t fo r lea di s given
. Th e symptom s associate dwit hanemi awoul db e th e sam e irrespectiv e of whethe r

th e caus e wa s lea dexposur e o r iro ndeficiency
. However , th e presenc e of iro ndeficienc y increase s th e absorptio n of lea dfro mth e gut . 8 . Anothe r

possibl e effec t

involve s tryptophan e pyrrolase
. Thi s i s a heme-dependen t

enzym e inth e liver
. I t ha s bee npostulate dtha tP.4 9
14 1 th e reduce dleve l of

hem e inporphyri amay b e responsibl e fo r som e o f th e symptom s see ninacut e intermitten t porphyria
. A Science articl e b y Corrie aabou t ayea r ag o addresse s thi s issue
. 9 . Regardin g th e possibl e effect s of ALA itself , effect s ar e no t likel y becaus e AL

A doe s no t

readil y cros s th e blood-brai nbarrier
. 10 . Dic k

Bul l an dMcCaule y (EPA , Cincinnati ) hav e foun ddela y of myelinizatio n of

th e nerv e sheath s inth e brai ninconjunctio n wit hlea dinth e 30-4 0 yg/d Lrang e inneonata l rats . I t i s know n tha t lea dinterfere s wit hoxidativ e phosphorylatio nan dhenc e energ y production
. Thi s lead-relate ddisruptio nof energ y productio n may b e responsibl e fo r thi s dela y inmylenization
. 11 . Patient s wit hsickle-cel l anemi aappea r t o b e mor e susceptibl e t o th e toxi c effect s of

lead , althoug hth e mechanism s responsibl e fo r thes e ar e no t

understood
. 12 . I ngeneral , ther e seem s t o b e goo devidenc e tha t elevate dEP level s indicat e increase dris k of advers e healt heffects
. I t seem s t o b e agoo dindicato r

o f bot hFe D an dP b exposure . Thi s place s a chil din doubl e jeopard y sinc e bot hlea dt o th e sam e result
. EP leve l i s usefu l fo r

monitorin g long-ter mexposure . 13 . Epidemiologica l studie s shoul db e base do ndat aacquire dthroug h extractio n technique s rathe r tha nthroug hth e hematofluorometer
. Extractio ntechnique s ar e use dt o calibrat e hemotofluoremeters
. Ther e ar e dat ashowin g tha t hemotofluore

meter s giv e reading s tah t ar e systematicall y low
. I t woul dappea r tha t hematofluoremeter s shoul db e recalibrate da t th e factor y ever y thre e month s o r

so . A t thi s time , th e technica l difficultie s wit hth e hematofluoremete r hav e no t

bee nresolved
.P.5 0
14 2 B.4. 2 Summar

y o f Discussio n wit h Exper tB Th e discussio n wit hExper t B covere dtw o mai ntopics : hemoglobi nan dEP . 1 . A chil dca n hav e ahig hPb B (say , 50 0 mcg/dL) , n o reductio nin hemoglobi n level , an ddie
. Thus , hemoglobi nleve l i s no t aver y usefu l inde x fo r

advers e healt heffect s of lead , a t leas t fro ma clinica l poin t

of view
. 2 . Neurologica l an dbehaviora l (aggression , hyperactivity ) effect s occu r muc hmor e quickl y inchildre ntha nhematologica l effects , an da t muc hlowe r

level s (abou t

4 0 mcg/dL)
. 3 . Th e bod y ca n als o compensat e fo r reduce dhemoglobin ; othe r processe s wil l begi n t o transpor t oxygen , offsetting , t o som e degree , th e possibl e advers e effect s of reduce dhemoglobin
. 4 . Anemi aonl y become s aproble mwhe nth e body' s abilit y t o compensat e i s lost
. 5
. Damag e t o th e hem e syntheti c pathwa y i s crucial ; bu t thi s i s no t attributabl e t o reduce dhemoglobin
. 6 . A roug hdose/effec t relationshi p betwee nPb B an dHb wa s expressed , on e fo r

F e deficien t

kids , an don e fo r

non-F e deficien t kids
. Exper t

B estimate dthat , o nth e average , non-F e deficien t kid s wit hPbB=1 0 mcg/d Lwoul dhav e hemoglobi nlevel s of abou t 1 2 g/dL ; a t

PbB=50 , Hb=10.5
. Fo r F e deficien t

kids , Exper t

B estimate dHb=1 0 a t

PbB=10 , an dHb=6.5-7. 0 a t PbB=50
. However , Exper t B fel t tha t i t wa s quit e possibl e tha t i t coul db e eve n lowe r fo r th e late r

kid s a t PbB=50 , bu t

jus t couldn' t b e sure , an d coul dno t expres s thes e feeling s quantitatively , despit e effort s t o assis t Exper t B usin g judgmenta l probabilit y encodin g techniques
.P.5 1
14 3 B.4. 3 Summar

y o f Discussio n with Exper tC 1 . Very hig hEPlevel s ca ncaus e porphyri adu e t o error s in metabolis mwit hclinicall y recognizabl e ski nan dCN S effects
. However , ther e i s n o evidenc e of alea dworke r

eve r developin g porphyri aa s aresul t

of lea dexposure . Thus , i t i s reasonabl e t o conclud e tha t

lea dexposur e doe s no t caus e porphyria
. 2 . Ther e i s n o evidenc e inth e literatur e tha t lead-induce delevate d EPitsel f

cause s healt hproblems ; i t simpl y i s amrker , o r indicator , o f

advers e healt heffect s due , possible , t o lea d exposure . EPlevel s > 1 sigm aabov e th e mea nshoul db e followe d b y aloo k a t bloo dlead
. 3 . Sinc e E Plevel s ten dt o la g change s i nPb B levels , i t i s importan t t o b e lookin g a t

bot hove r

tim e t o ge t

agoo dide aof

wha t i s goin g on . Th e rat e of

ris e of E Pvs . a nincreas e inPb B i s greate r tha n linear , bu t

lagge di n time
. A plo t of lo g (EP ) versu s Pb B woul db e roughl y linea r

unde r chroni c relativel y constan t lea dexposur e conditions
. 4 . Lead-induce delevate dEPi s anindicato r of interferenc e wit h hem e synthesi s whic hma y o r may no t

b e compensate db y derepressio no

f AL A synthetase , th e rate-limitin g enzym e involve di n hem e systhesis , dependin g o nth e degre e of lea d exposure . 5
. I t i s possibl e tha t

elevate dEPi s anindicato r of a ninterferenc e b y lea dof

th e body' s abilit y t o produc e 1,2 5 dihydroxyvitami nD . Th e cytochrom e P-45 0 enzymes , of whic hther e ar e ove r 5 0 differenc t

isozymes , ar e relate dt o th e synthesi s of 1,25 dihydroxyvitami n D . Ther e ar e stron g indication s tha t lea dP.5 2
144 reduce s synthesi s of

th e P-45 0 enzymes . Thi s i ntur nmay reduc e th e metabolis mof

25-(OH)D , anecessar y ingredien t inth e biosynthesi s of

1,25 dihydroxyvitami nD . Referenc e was mad e t o a n importan t

revie w pape r

concernin g 1,25 dihydroxyvitami nD metabolis m[D.R . Fraser , Physiologica l Reviews , 60:55 1 (1983)] . 6 . Ther e i s als o suggestiv e evidence , bu t no t proof, tha t

elevate dEP indicate dreduce dabilit y of th e live r

t o detoxify , thi s effec t ha s bee n show n in anumbe r of studie s involvin g hig hlea dexposur e in worker s an dchildren
. 7 . Furthermore , elevate dEPlevel s may indicat e sufficien t exposur e t o lea d(and/o r

othe r metals ) t o accelerat e th e destructio n(i.e. , reduc e thei r

half-lives ) of

th e hemoprotein s [M.D . Maines , Annal s of Clinica l Research , 8:3 9 (1976)] . 8 . Regardin g th e CNS , i t i s no t clea r whethe r

elvate dEPge r

s e cause s an y effects
. Ther e ar e som e anima l studie s concernin g CN S effect s whe n ver y larg e dose s of th e EPprecurso r

ALA ar e administered
. Som e repor t CN S effect s an dother s no t [M . Moor e <S c P.A . Meredith , Trac e Substance s inEnvironmenta l Hlth
. 10:36 3 (a977) ; S . Edwards , Neurosci
. Lett . 50:16 9 (1984)] . 9 . I n alea dworke r

stud y [Hammond , e t

al , J . Occ . Med. , 2:475-48 4 (July , 1980)] , AL

A in plasm aan dinurin e was foun dt o b e a s goo d amarke r of th e degre e of

toxicit y of

P b a s wa s PbB ; AL

A wa s a s goo damarke r

a s E Pfo r

hematopoieti c syste mdamage ; fo r othe r effect s (neurological , renal , etc.) , ALA an dPb B wer e bette r indicator s of

damag e tha nEP . Anothe r stud y b y Rut hLilli s e t al
. a t Mt . Sina i showe dtha t EPwa s abette r

indicato r

of hematopoieti c effect s tha nAL A an dPbB
. Th e difference sP.5 3
14 5 betwee n th e tw o studie s may b e du e t o differentia l measuremen t reliabilitie s in th e tw o labs
. 10 . Ther e i s n o evidenc e of a nEPvs . hemoglobi nrelationshi p in childre n a t

PbB' s <50
. Ther e ar e factor s othe r tha nlea dtha t affec t EPlevel
. 11 . Th e possibilit y of

P b exposur e causin g hypertensio ni s ane w issue
. 12 . T o summarize , ther e i s n o evidenc e tha t elevate dEPpj r

s e du e t o lea dcause s advers e healt heffects
. B.4. 4 Summar

y o f Discussion s wit h Exper tD Th e discussio n wit hExper t D include dFEP , liver , calcium , an d1,25 dihydroxy

vitami n D (l,25(OH) 2 D ) effects
.
FEP : 1 . Elevate dEPdu e t o lea dexposur e indicate s direc t toxi c effect s of lea do n heme , whic hi s abasi c physiologica l syste mtha t i s commo n t o man y organ s an dcel l types . 2 . Piomell i ha s postulated , an dSilbergel dhav e publishe dsom e data , an dbot hsugges t

tha t som e of

th e CN S effect s of

lea dmay b e attributabl e t o altere dmetabolis mof porphyri ncompounds
. Other s hav e suggeste dtha t ther e may b e perturbation s inCN S intracellula r

calciu mmetabolism
. Liver : 3 . Ther e i s evidenc e a t 30-4 0 ygPb/d Ltha t

live r metabolis mof model compound s (e.g. , Cortiso l i s altered
. Thi s implie s areduce d abilit y t o detoxif

y th e bloo dstream . Sinc e man y drug s hav eP.5 4
14 6 metaboli c pathwa y tha t ar e simila r

t o tha t of Cortisol , thei r metabolis mmay als o b e affecte db y lead
. Calcium : 4 . Ther e i s evidenc e tha t calcium-mediate dbasi c enzymati c system s in al l mamallia n cell s ar e affecte da t lea dlevel s abov e abou t 5 micromolar
. An y disruptio no f thes e system s may hav e pervasiv e effects
. Calciu mfro mcalmoduli nca nb e displace db y lead
. Calmoduli ni s acentra l componen t of th e norma l chemistr y of cells
. Lea dca n purtur b thi s process . 1,25 Dihydroxy-vitami n D :

5
. A comple x enzym e syste mi s responsibl e fo r th e productio nof thi s vitami n D hormone
. Lea di s know nt o impai r severa l ingredient s of

thi s enzym e system . Som e of thes e ingredient s includ e electro n transport , mitochondria l function , an dth e cytochrom e P-45 0 famil y of enzymes . Observation s of impairmen t

in th e productio nof

th e vitami nD hormon e inlead

toxi c childre n hav e bee nconfirme dinexperimenta l studie s in viv o an din vitro
. 6 . A t 33-5 5 ygPb/dL , ther e i s evidenc e of abou t 66 % decreas e i nth e kidney' s abilit y t o produc e th e vitami nD hormone
. 7 . A t level s abov e 6 2 ygPb/dL , ther e i s evidenc e of adecreas e in l,25(OH) 2 D level s t o adegre e tha t hav e bee nreporte dinchildre n wit hinbor n error s i n metabolism
. 8 . Betwee n 1 2 t o 120 ygPb/dL , ther e i s astatisticall y significan t negativ e correlatio n betwee nvitami nD leve l an dlea dlevel
.P.5 5
147 9 . A t blood-lea dlevel s abov e 5 5 ygPb/dL , chelatio ntherap y i s immediatel y used
. A t 25-5 5 ygPb/dL , th e result s of th e EDT

A provocativ e tes t

i s use dt o determin e whic hchildre n woul d benefi t fro mchelatio ntherapy
. 10 . l,25(OH)2 D affect s th e maturatio nof cell s an denhance s th e differentiatio n of

cells
.
• Rat s an dmic e havin g leukemi awer e treate dwit hpicomola r concentration s of

l,25(OH) 2 D . Result s indicate dtha t th e lifespan s of

th e animal s wer e extended
.
• I nvitr o experiment s o navariet y of huma ncell s (e.g . lymphoma , myeloi dleukemi acells , monocytes ) hav e replicate dsuc hfindings
. 11 . Ther e i s recen t

researc hshowin g tha t

l,25(OH)9 D evidence s som e immuno-regulator y function s lik e othe r steroi dhormones
. 12 . Ther e i s early , evolvin g evidenc e tha t l,25(OH)9 D ha s arol e i n controllin g insuli n secretio nfro mth e pancreas . 13 . Th e action s of

th e vitami nD hormon e involv e no t onl y minera l absorption , bon e remodeling , an dcalciu mhomeostasi s invirtuall y all l mammalia n cells , bu t recentl y reporte dinformatio nindicate s tha t th e vitami n D hormon e ha s eve nmor e pervasiv e effect s in humans
. Som e of

thes e effects , whic har e no w recognized , includ e enhancemen t

of cel l differentiatio n(maturation) , an d immuno-regulator y capacity
. This , inconsideratio nals o of point s 608 , reasonabl y suggest s tha t adecreas e of

vitami nD hormon e i s likel y t o hav e pervasiv e effect s o nth e functio nof othe r organs .P.5 6
14 8 B.4. 5 Summar

y o f Discussion s with ExpertE Discussion s wit hExper t Efocuse dprimaril y o nFE Peffect s of lead
. 1 . Ther e doe s no t

see mt o b e an y evidenc e tha t elevate dEPi s itsel f a n advers e healt heffect
. However , i t i s possibl e becaus e anytim e th e balanc e of

an essentia l metabolit e i s upset , ther e i s aris k of damag e t o othe r

organ s o r

functions
. Fo r

example :

• Phenylalanin e i s a nessentia l amin o acid , bu t i s toxi c a t

hig h levels
. Thi s i s see ni nth e diseas e phenylketonuria , inwhic h ther e i s a ninabilit y t o metaboliz e exces s phenylalanine
. Thus , (in th e absenc e of

aspecia l diet ) th e phenylalanin e build s up an daffect s th e developin g centra l nervou s system , causin g menta l retardation
.

• Exces s level s of

fluorid e caus e teet ht o becom e brittle , althoug hprope r

level s increas e hardnes s of teeth
. Thus , ther e i s th e chanc e tha t futur e researc hmigh t sho w tha t

elevate d FE Pi s a n advers e healt heffect
. 2 . Elevate dE Pi s avaluabl e inde x of advers e lea deffect s inothe r organs , e.g. , th e centra l nervou s system , th e liver , th e kidney , etc . 3 . Th e bod y ha s th e abilit y t o compensat e fo r lea dinsul t

up t o a point
. Fo r

example , a t

lo w lea dlevel s th e inhibitio nof EPi s compensate dfor , bu t

no t a t slightl y highe r

levels
. Piomellis' s analysi s indicate s athreshol daroun d16-1 7 yg/dL
. ALAD show s n o threshold
. 4 . Regardin g measuremen t of EP , car e mus t

b e take nif

th e hematofloromete r

i s use dbecaus e th e amoun t of EPtha t i s zin c protoporphyri n (ZPP ) decrease s proportionatel y a s tota l EPrises ;P.5 7

14 9 sinc e th e hematofloromete r measure s ZPP , i t may b e underestimatin g tota l EP . Belo w 3 5 yg/d Lther e i s goo d agreemen t

betwee nFE P(extraction ) an dZP P (hemotofluorometer)
. Abov e 3 5 yg/d Lther e appear s t o b e a30 % differenc e betwee n ZP P(lower ) an dFE P(higher)
. 5
. In assessin g th e nee dfo r treatment , bot hEPan dPb B level s shoul db e considere d(a s th e Center s fo r Diseas e Contro l does)
. 6 . Critica l blood-lea dlevel s fo r regulator y purpose s may nee dt o b e les s tha n thos e considere dfo r clinica l purpose s inorde r t o provid e an adequat e margi n of

safet y fo r

th e populatio na t

large
.P.5 8
15 0 APPENDI

X C INTELLIGENC

E QUOTIEN

T Thi s appendi x i s organize dinafashio nsimila r t o App . B fo r

hemoglobin
. Sectio n C l i s th e I Q protocol , an dSec . C. 2 summarize s th e mathematica l formulations
. Sectio n C. 3 tabulate s th e encode djudgments , specification s fo r function s fi t

t o thos e judgments , variou s credibl e intervals , an dcomparison s o f encode djudgment s vs . fitte dfunctions
. Sectio n C. 4 summarize s of th e discussion s wit heac hof th e IQ experts . C l I Q PROTOCOL
Cl. l Introductio n Th e Environmenta l Protectio nAgenc y (EPA ) i s charge db y th e Clea nAi r Ac t wit hsettin g an drevisin g Nationa l Ambien t Ai r Qualit y Standard s (NAAQS ) fo r selecte d pollutants , a t

level s sufficien t

t o protec t

th e publi c healt hwit hanadequat e margi n of safety
. A s yo u know , th e scientifi c base s fo r NAAQ S ar e presente dan dreviewe din criteri adocuments
. I

n suppor t of th e forthcomin g revie w of th e lea dNAAQS , EPA ha s jus t prepare dane w Air

Quality Criteria for

Lead. I t

present s scientifi c evidenc e fro m whic hth e mos t

susceptibl e population s ca nb e determine dan dfro mwhic hvariou s advers e healt heffect s ca n b e identified
. Th e criteri adocumen t summarize s an d evaluate s th e availabl e clinical , epidemiological , an danima l o r toxicologica l laborator y evidenc e wit hregar dt o th e physiologica l an dadvers e healt heffect s of lead , an d therefor e represent s ou r mos t up t o dat e knowledg e o nlea deffects
. A s on e aspec t

of th e revie w process , EPA assesse s healt hrisk s b y identifyin g th e mos t sensitiv e population s fo r eac hpollutant , an destimatin g probabilisticall y th e numbers ' of

peopl e in th e population s wh o ma y suffe r eac hof

variou s well-define d advers e healt heffect s attributabl e t o th e pollutant
. I t i s believe dtha t

informatio nabou tP.5 9 15 1 th e healt hrisk s associate dwit hvariou s potentia l standard s wil l ai dth e EPA administrato r

in selectin g tha t

standar dwhich , inhi s judgment , protect s th e publi c healt hwit ha n adequat e margi n of safety
. Becaus e th e ris k

estimate s tha t

EP A seek s ar e ofte nbase di npar t o ndose

respons e relationship s an dlea dexposur e estimate s whic har e uncertain , i t i s necessar y t o mak e probabilit y judgment s abou t relevan t

dose-respons e function s base do nth e availabl e evidence , an dt o probabilisticall y estimat e lea dexposur e unde r alternativ e NAAQS . Obtainin g th e healt hris k estimate s the ninvolve s combinin g dose-respons e an d exposur e probabilit y estimates
. Th e proble mof

estimatin g dose-respons e relationship s i s simila r t o tha t whic h exist s inclinica l medicin e whe n ther e d o no t exis t dat atha t

bea r precisel y o n th e patient' s problem
. I

n tha t cas e i t i s necessar y t o us e scientifi c judgmen t t o extrapolat e fro mth e dat at o mak e abes t decisio nfo r

th e patient
. Here , too , i t i s necessar y t o us e scientifi c judgmen t

t o extrapolat e fro mth e availabl e data
. Th e extrapolatio ni s no t certai n and , therefore , w e wil l ai dyo u t o represen t you r opinio nprobabilistically
. Furthermore , sinc e th e extrapolatio ndepend s o none' s interpretatio nof th e literature , differen t peopl e wil l hav e differen t judgments
. Fo r

eac hhealt heffec t

w e inten dt o obtai nth e probabilisti c judgment s of abou t fiv e expert s t o sampl e th e rang e of respecte d opinions
. Th e model fo r estimatin g risk s wil l no t merg e thes e judgment s int o asingl e averag e judgment , bu t

rathe r wil l estimat e th e rang e of risk s base do nth e rang e of judgments
. I

f w e a s ris k

analyst s d o ou r

jo b properly , the nno t onl y wil l w e b e abl e t o sho w th e EPA administrato r th e rang e of

estimate s base do nth e rang e of judgments , bu t w e wil l als o b e abl e t o sho w som e of th e source s of

th e disagreements
. Indeed , asid e benefi t of thi s exercis e in whic hw e prob e you r knowledg e inastructure dmanne r may b e t o hel p identif

y source s of

greates t disagreement
. Base donth e evidenc e i nth e lea dcriteri adocument , tw o population s hav e bee n identifie da s bein g mos t susceptibl e t o th e effect s of lea dintoxication
. On e i s childre nP.6 0

15 2 fro mbirt hthroug hth e sevent hbirthday , an dth e othe r i s pregnan t

women , o r

mor e precisely , th e fetuse s bein g carrie db y th e pregnan t women . A numbe r

o f advers e healt h effect s hav e bee n identifie dfo r whic hw e woul dlik e t o estimat e dose-respons e function s includin g th e on e discusse dbelow
. C.1. 2 Lead-Induce d I

Q Decrement s
C.l.2. 1 Centra l Nervou s Syste m and Behaviora l Effect s o f Lead A larg e numbe r

of studie s reviewe dinth e Criteri aDocumen t sugges t tha t ther e ar e numerou s centra l nervou s syste m(CNS ) an dbehaviora l effect s of lea dexposure . Considerabl e uncertaint y surround s al l of thes e effects , however , becaus e of th e enormou s difficult y in definin g an dmeasurin g them , an di nisolatin g the mfro mth e effect s of

covariates
. Sinc e ou r

goa l i s t o obtai nprobabilisti c estimate s abou t th e shap e of adose-respons e curv e fo r aparticula r

well-define deffec t

if asufficien t

amoun t of pertinen t dat acoul db e collected , ou r firs t tas k i s t o selec t

on e CN S o r

behaviora l effec t tha t i s of acknowledge dimportanc e an dtha t ca nb e wel l specified
. Th e searc hfo r

lead-induce deffect s ha s include dstudie s of : EEGeffects ; sensor y motor , perceptual , an dattentiona l deficits ; cognitiv e decrement s of variou s sorts ; hyperactivity ; negativ e classroo mbehaviors ; an dothe r effect s tha t

s o fa r hav e bee n studie donl y in anima l models
. Fro mthi s larg e assortmen t of effects , w e hav e selecte dI Q decremen t

a s th e advers e effec t

upo nwhic ht o focus
. W e ar e no t considerin g I Q t o b e th e onl y no r

necessaril y th e bes t

measur e o f

cognitiv e abilities
. No r i s i t bein g considere da s asurrogat e fo r th e othe r

system s inwhic heffect s hav e bee nexplored
. (Becaus e of

it s multifacete dnatur e i t probabl y involve s man y of them. ) Rather , w e hav e selecte dI Q decremen t

becaus e ther e ar e mor e dat ao nthi s effec t tha no nan y other , an d becaus e it s functiona l o r "clinical " significanc e i s clear
. I t i s quit e conceivabl e tha t a s researc hcontinue s in futur e years , othe r mor e "pure " CN S o r

behaviora l effect s wil lP.6 1
15 3 emerg e tha t

ar e obviousl y advers e an dfo r whic hasubstantia l body of dat aha s developed
. Unti l suc ha n even t occurs , i t

appear s tha t

lead-induce dIQ decremen t i s th e mos t appropriat e effec t

t o consider
. C.l.2. 2 Definitio n o f

I Q Decremen t Becaus e i t

i s generall y though t

tha t CN S effect s of

lea dmay b e cumulative , i t i s necessar y t o specif

y th e children' s age s a t whic hth e IQ decrement s ar e estimated
. I n al l cases , assum e tha t

IQ test s ar e give no nth e children' s sevent hbirthdays
. Assum e furthe r tha t th e WISC- Ri s th e tes t employed
. A lead-induce dI Q chang e canno t b e measure ddirectl y fo r agive nchild , an d therefor e th e chang e woul dhav e t o b e estimate dstatisticall y fro msuitabl e data
. Thus , rathe r tha nas k

yo u directl y abou t

dose-respons e functions , w e wil l encod e you r judgment s abou t

th e outcome s of

hypothetica l idea l experiments
. I f you agre e wit hth e assumption s o n whic hth e hypothetica l experiment s ar e based , the nyou r judgment s abou t th e potentia l outcome s wil l lea dnaturall y t o probabilisti c estimate s abou t dose-respons e function s fo r

IQ decrements
. Ther e ar e difference s of opinion , of

course , a s t o wha t

IQ decrement s shoul db e considere dadverse
. Th e Clea n Ai r Ac t make s i t

clea r tha t EPA shoul dse t

standard s t o protec t agains t advers e healt heffects , bu t th e leve l define da s advers e may b e differen t fo r regulator y tha n fo r

clinica l o r

remedia l purposes . W e wil l no t

focu s o nparticula r magnitude s of

IQ decrements , bu t

rathe r wil l encod e you r

probabilisti c judgment s abou t I Q distribution s give n variou s blood-lea dlevels
. The nw e wil l us e you r judgment s t o deriv e probabilisti c statement s abou t th e percen t

of childre na t

eac hlea dleve l whos e IQ score s ar e belo w an y valu e of interest , suc has , fo r

example , belo w IQ s of 70 , 80 , 90 , o r 100 .15 4

C.1.2. 3 Hypothetica l Ideal Experiment s Assum e tha t

a t conception , subject s ar e randoml y assigne dt o group s differentiate db y bloo dlea dleve l targete dfo r th e thir dbirthday
. Member s o f eac h treatmen t

grou p ar e expose dt o lea dfro mconceptio nunti l thei r sevent hbirthdays , whil e member s of

acontro l grou p ar e sheltere dfro mlea dfro mconceptio nunti l thei r sevent h birthdays
. Th e leve l of environmenta l lea dassigne dt o achil di s roughl y constan t fo r th e seve n years , however , eac hchild' s lea duptak e i s not constant , du e t o th e change s wit h ag e of hi s o r he r physiolog y an dbehavior
. Nevertheless , th e experimenta l condition s ar e suc htha t a t thei r third birthdays , al l th e childre nineac hgrou p hav e essentiall y th e sam e measure dbloo dlead
. Thus , group s diffe r interm s of

mea nbloo dlea do nth e thir d birthday
. Environmenta l lea dlevel s necessar y t o yiel dagive nblood-lea dleve l a t ag e thre e inaparticula r

chil dremai n constan t

throug hth e sevent hbirthday
. Th e experimenta l manipulatio naffect s onl y lea dexposure , an dn o othe r aspec t of th e children' s lives
. The n th e WISC- RIQ tes t i s administere dt o al l childre no n thei r seventh birthdays
. Th e childre n ineac hgrou p hav e adistributio no f IQ score s wit hsom e mea n an dstandar ddeviation
. W e ar e intereste di nyou r probabilisti c judgment s abou t th e IQ distribution s fo r group s of

childre no nthei r

sevent hbirthdays , al l of who mha d specifi c blood-lea dlevel s o n thei r thir dbirthdays
. Not e thre e feature s abou t thi s hypothetica l experiment
. First , i t i s simila r

t o a longitudina l study ; childre n ar e i n agrou p fro mconceptio nunti l thei r sevent hbirthdays
. Second , i t

involve s rando massignmen t of childre nt o groups , makin g i t unnecessar y t o worr y abou t

covariates
. Third , bloo dlea di s measure da t ag e three, an dI Q a t

ag e seven. I f yo u believ e I Q effect s of lea dt o b e differen t

fo r lowe r SE S tha nfo r

middl e an duppe r

SES subpopulation s of childre nunde r

thes e experimenta l conditions , the nw e wil l conside r

separat e hypothetica l experiment s fo r th e tw o subpopulations
. Otherwise , w e wil l conside r

onl y asingl e suc hexperiment
.P.6 3 15 5 SES i s acomple x variable
. Fo r simplicity , i

f w e divid e th e populatio nint o lo w SE S an dmiddl e o r

uppe r SE S categories , le t

u s defin e lo w SE S a s thos e childre ncomin g fro mhousehold s wit hincome s in th e lowes t 1 5 percent . Unles s yo u disagree , w e wil l als o assum e tha t th e distributio nof

IQ score s i s norma l withi n eac hgroup . (Th e WISC- Rwa s develope dt o yiel dnormall y distribute dIQ score s fo r

th e genera l population , wit hmea nI Q equa l t o 100 an dastandar ddeviatio n of 15. ) Furthermore , if w e conside r

onl y asingl e hypothetica l experiment , samplin g fro mth e ful l populatio n of children , then , unles s yo u disagree , w e wil l assum e tha t th e IQ standar ddeviatio n i s 1 5 a t eac hblood-lea dleve l an dw e wil l onl y hav e t o encod e you r probabilisti c judgmen t

abou t th e mea nI Q a t

ag e seve nfo r

eac hof severa l blood-lea d level s a t ag e three
. I f w e conside r

tw o hypothetica l experiments , eac hsamplin g fro madifferen t SE S subpopulation , the n th e IQ standar ddeviatio nwil l possibl y b e les s tha n15
. Assumin g tha t I Q standar ddeviatio n i s th e sam e a t al l blood-lea dlevel s withi nSE S subpopulations , w e wil l hav e t o encod e you r probabilisti c judgmen t abou t th e standar ddeviatio nfo r eac h SES group . Then , separatel y fo r

eac hSE S grou p o r

fo r th e populatio na s awhole , a s appropriate , w e wil l encod e you r probabilisti c judgmen t abou t th e mea nIQ a t

ag e seve n of th e contro l group . Finally , w e wil l encod e you r probabilisti c judgment s abou t th e difference s in mea n I Q a t ag e seve nbetwee nchildre nwit hnegligibl e bloo dlea d(th e contro l group ) an dchildre n a t eac hof severa l elevate dbloo dlead s a t ag e thre e (th e treatmen t

groups) . Th e followin g section s specif y furthe r

th e condition s t o b e assume din thi s hypothetica l experiment
.P.6 4
15 6 C.1. 3 Populatio n a tRis k Base do n th e Criteri aDocument , w e ca nspecif y th e mos t

susceptibl e populatio n a s al l Unite dState s childre n fro mconceptio nthroug hthei r sevent hbirthdays
. W e hav e alread y define dth e effec t a s bein g measure do nth e sevent hbirthday , bu t onth e assump tio ntha t younge r childre n wil l reac hthei r sevent hbirthdays , th e effec t i s well-define d fo r th e whol e population
. However , a s alread y discussed , yo u may conside r IQ effect s of

lea dt o b e dif

feren t fo r lowe r SE S tha n fo r

middl e an duppe r

SE S subpopulation s of

children , resultin g indifferen t

experimenta l outcome s fo r th e tw o groups . I

f so , the nw e wil l elici t you r judgment s separatel y fo r lowe r SE S childre nan dfo r

middl e an duppe r

SE S children
. C.1. 4 Exposure Condition s W e wil l b e askin g you r

judgmen t

abou t mea nI Q value s o nth e sevent hbirthday s a t variou s blood-lea dlevels
. Assum e tha t th e blood-lea dlevel s unde r consideratio nfo r

a give n judgmen t

hav e bee n measure do nth e children' s thir dbirthdays
. Assum e furthe r tha t externa l environmenta l condition s supportin g thos e level s hav e bee nmor e o r les s constan t sinc e birth , an dtha t

in interactin g wit hth e environment , th e childre nexhibite d th e usua l rang e of

behavior s a t

eac hage . Thus , blood-lea dlevel s wer e no t necessaril y constan t fro mbirt ht o ag e seven , bu t exposur e an dbehaviora l factor s wer e suc htha t a t ag e three , bloo dlea dwas a t aspecifi c level
. Finally , assum e tha t th e change s inbloo d lea dlevel s fro mbirt hunti l th e sevent hbirthda y ar e distribute da s yo u believ e the y actuall y are . C.1. 5 Physiologica l and Environmental Condition s Becaus e th e effect s of lea ddepen do nman y parameters , i t i s necessar y t o specif y assumption s abou t

thos e parameter s inth e population(s)
.P.6 5
15 7 C.l.5. 1 Physiologica l Condition s Th e effec t

of lea din th e syste mdepend s o nth e person' s nutritiona l an dmeta boli c status . Assum e tha t th e level s of

iron , zinc , copper , vitamin s A , C , D , an dE , calcium , phosphorus , an dmagnesiu mar e distribute dwithi nth e populatio no r withi n eac h o f th e tw o SE S group s a s yo u believ e the y i nfac t are , takin g int o accoun t th e wid e rang e of diet s an dnutritiona l level s of childre nwithi nth e populatio no r withi neac hof

th e tw o SE S groups . C.1.5. 2 Environmenta l Condition s Th e effec t

of lea do n IQ als o may depen do nnumerou s environmenta l an dcare givin g factor s tha t

var y withi n SES level , suc ha s thos e assesse dinth e HOM Escal e (Hom e Observatio n for
. Measuremen t of th e Environment) , parenta l IQ , an ds o forth
. Assum e tha t

thes e factor s ar e distribute dwithi nth e populatio no r withi neac hof

th e tw o SE S group s a s yo u believ e the y in fac t are . C.1. 6 Factor s t o Conside r I norde r t o hel p yo u brin g t o min dth e relevan t evidenc e s o tha t

yo u ma y conside r i t systematically , an dals o in orde r t o hel p u s t o interpre t you r judgments , w e woul dlik e t o as k yo u t o discus s briefl y you r interpretation s of

variou s aspect s of

th e literature
. How d o yo u evaluat e th e researc hconcernin g th e effect s of low leve l lea dexposur e o n cognitiv e an dbehaviora l development ? I s i t you r feelin g tha t

lea dha s adeleteriou s effec t o n thi s developmen t

ove r an dabov e tha t

whic hca nb e explaine db y othe r factor s frequentl y associate dwit hlea dexposure ? I f so , d o yo u believ e tha t th e effect s of

lea d simpl y ad dt o th e effect s of othe r factors , o r

tha t th e effect s of

lea ddepen do n th e level s of othe r factors ? I

n th e latte r

case , wha t

ar e th e variable s tha t lea dexposur e interact s with ? A relate dquestio nconcern s you r opinio nabou t

th e relationshi p betwee n exposur e an dsusceptibility
. Tha t is , d o yo u thin k

tha t thos e childre nwh o ar e a t greates t15 8

ris k of exposur e du e t o thei r livin g i ndeterioratin g pre-195 0 housin g o r inurba n area s wit hlarg e amount s of

vehicula r

traffi c o r

du e t o othe r

reasons , ar e als o mos t

susceptibl e t o th e effect s of

lead ? Fo r

example , thes e may b e th e sam e childre nwh o als o hav e poore r diets , les s acces s t o medica l care , poore r care-givin g environments , an dles s intellectua l resource s t o fal l bac k on . What i s you r opinio n abou t

th e tim e cours e of

lea dexposur e an dof

lea deffect s o nCNS , cognitiv e an dbehaviora l development ? What ar e th e relativ e effect s of cumula

tiv e versu s curren t

exposure . Ar e th e effect s reversible ? I s ther e athreshol dfo r th e effects ? Wha

t ar e th e implication s of th e anima l model research , bot hth e behaviora l an dth e morphological , fo r huma nCNS , cognitive , an dbehaviora l effect s o f lead ? Ar e ther e othe r

factor s t o conside r

inthinkin g abou t

th e dose-respons e function s fo r lead

induce dIQ effect s tha t

w e shoul ddiscus s now ?
C.1. 7 Factor s t o Kee p in Min d Whe n Making Probability Judgment s Ther e i s usuall y uncertaint y associate dwit hconclusion s tha t w e dra w fro m research , an dmor e generall y in ou r everyda y thinking
. However , no t everyon e i s awar e of al l th e source s tha t

shoul dcontribut e t o thei r uncertainty , no r

ar e mos t

peopl e familia r wit hth e proces s of

actuall y expressin g thei r uncertaint y inprobabilisti c terms . Whe nanexper t

i s aske dt o mak e probabilit y judgment s o nsociall y importan t matters , i t i s particularl y importan t tha t h e o r sh e conside r

th e relevan t

evidenc e inasystemati c an deffectiv e manne r

an dprovid e judgment s tha t represen t

hi s o r he r opinion s well
. Experimenta l psychologist s an ddecisio nanalyst s hav e amasse daconsiderabl e amoun t of dat aconcernin g th e way peopl e forman dexpres s probabilisti c judgments
. Th e evidenc e suggest s tha t whe n considerin g larg e amount s of comple x information , mos t peopl e emplo y simplifyin g heuristic s an ddemonstrat e certai nsystemati c distortion s of thought , i.e. , cognitiv e biases , whic hadversel y affec t thei r judgments
. Th e purpos e of thi s sectio n i s t o mak e yo u awar e of thes e biase s an dheuristic s s o that , a s muc ha sP.6 7
15 9 possible , yo u ca n avoi dthe min makin g probabilit y judgments
. W e wil l firs t

revie w th e mos t widesprea dbiase s an dheuristics , an dthe noffe r som e suggestion s t o hel p yo u mitigat e thei r

effects
. C.1.7. 1 Sequentia l Consideratio n o f Informatio n Generally , th e orde r

i n whic hevidenc e i s considere dinfluence s th e fina l judgment , althoug hlogicall y tha t shoul dno t

b e th e case . O

f necessity , piece s o f informatio nar e considere don e b y on e inasequentia l fashion
. However , thos e considere dfirs t

an dlas t ten dt o dominat e judgment
. I npart , initia l informatio nha s it s undu e influenc e becaus e i t provide s th e framewor k tha t subsequen t

informatio ni s the n tailore dt o fit
. Fo r

example , peopl e usuall y searc hfo r evidenc e t o confirm thei r initia l hypotheses ; the y rarel y loo k fo r evidenc e tha t

weighs against

them
. Th e late r

evidenc e ha s it s undu e effec t

simpl y becaus e i t

i s freshe r

inmemory . Relate dt o thes e sequentia l effect s i s th e phenomeno nof anchoring and adjustment. Base do n earl y partia l information , on e form s a ninitia l probabilit y estimat e regardin g th e even t

in question
. Thi s ancho r judgmen t

i s the nadjuste da s subsequen t informatio ni s considered
. Unfortunately , suc hadjustment s ten dt o b e to o conservative
. I

n othe r words , to o littl e weigh t i s attache dt o informatio nconsidere d subsequen t

t o th e formatio n of

th e initia l judgment
. C.l.7. 2 Effect s o f

Memor y o n Judgmen t I t i s difficul t

fo r mos t peopl e t o conceptualiz e an dmak e judgment s abou t large , abstrac t universe s o r

populations
. A natura l tendenc y i s t o recal l specifi c member s an d the n t o conside r

the mrepresentativ e of th e populatio na s awhole
. However , th e specifi c instance s ofte n ar e recalle dprecisel y becaus e the y stan dou t insom e way , suc ha s bein g familiar , unusual , especiall y concrete , o r of persona l significance
. Unfortunately , th e specifi c characteristic s of thes e singula r

example s ar e the nattributed , ofte nincorrectly ,P.6 8
160 t o al l th e member s of

th e populatio no

f interest
. Moreover , thes e memor y effect s ar e ofte n combine dwit hth e sequentia l phenomen adiscusse dearlier
. Fo r example , in considerin g th e evidenc e regardin g th e dose-respons e curv e of aparticula r

pollutant , yo u migh t naturall y firs t

thin k of astud y you o r

apersona l frien drecentl y completed
. O r yo u migh t

thin k o f astud y yo u recentl y read , o r on e tha t

was unusua l an dtherefor e stand s out . Th e tendenc y migh t the nb e t o trea t

th e recalle dstudie s a s typica l of th e populatio no f

relevan t

research , ignorin g importan t difference s amon g studies
. Subsequen t

attempt s t o recal l informatio ncoul dresul t inthinkin g primaril y of evidenc e consisten t

wit hth e initia l item s yo u though t of
. C.l.7. 3 Estimatin g Reliabilit y o f Informatio n Peopl e ten dt o overestimat e th e reliabilit y of information , ignorin g factor s suc h a s samplin g erro r

an dimprecisio n of

measurement . Rathe r the y summariz e evidenc e in term s of simpl e an ddefinit e conclusions , causin g the mt o b e overconfiden t i nthei r judgments
. Thi s tendenc y i s stronge r whe non e ha s aconsiderabl e amoun t of intellectua l and/o r persona l involvemen t

in aparticula r

field
. I

nsuc hcases , informatio ni s ofte n interprete din away whic hi s consisten t wit hone' s belief s an dexpectations , result s ar e over-generalized , an dcontradictor y evidenc e i s ignore do r underestimated
. C 1.7. 4 Relatio n Betwee n Even tImportanc e and Probability Sometime s th e importanc e of events , o r

thei r possibl e cost s o r

benefits , influenc e judgment s abou t th e certaint y of

th e event s when , rationally , importanc e shoul dno t

affec t probability
. I

n othe r words , one' s attitude s toward s ris k ten dt o affec t one' s abilit y t o mak e accurat e probabilit y judgments
. Fo r example , man y physician s ten d t o overestimat e th e probabilit y of ver y sever e diseases , becaus e the y fee l i t i s importan t t o detec t an dtrea t

them ; an dsimilarly , man y smoker s underestimat e th e probabilit y of advers e consequence s of smoking , becaus e the y fee l tha t th e odd s d o no t

appl y t o themselve s personally
.P.6 9
16 1 C.l.7. 5 Estimatio n o f

Probabilitie s Anothe r limitatio n i s relate dt o one' s abilit y t o discriminat e betwee nlevel s of uncertainty , an dt o us e appropriat e criteri aof discriminatio nfo r

differen t

range s of probability
. On e resul t of thi s fac t

i s tha t peopl e ten dt o estimat e bot hextrem e an d mid-rang e probabilitie s in th e sam e fashion , usuall y doin g apoo r jo b inth e extremes . I t help s her e t o thin k

in term s of

odd s a s wel l a s probabilities
. Thus , fo r example , changin g aprobabilit y estimat e fro m0.51 0 t o 0.50 1 i s equivalen t t o achang e i

nodd s fro m1.041: 1 t o 1.004:1 , bu t

achang e fro man estimat e of 0.99 9 t o 0.99 0 change s th e odd s b y afacto r of abou t 1 0 fro m999: 1 t o 99: 1 Th e close r t o th e extreme s (eithe r 0 o r 1 ) tha t on e i s estimatin g probabilities , th e greate r th e impac t

of smal l changes
. C.1.7. 6 Recommendation s Althoug hextensiv e an dcarefu l trainin g woul db e necessar y t o eliminat e al l th e problem s mentione dabove , som e relativel y simpl e suggestion s ca nhel p minimiz e them
. Mos t importan t

i s t o b e awar e of

one' s natura l cognitiv e biases , an dt o tr y consciousl y t o avoi dthem
. T o avoi dsequential

effects kee p inmin dtha t th e orde r

inwhic hyo u thin k

of informatio nshoul dno t

influenc e you r

fina l judgment
. I t

may b e helpfu l t o actuall y not e o npape r th e importan t

fact s yo u ar e considerin g an dthe nt o reconside r the mintw o o r mor e sequences , checkin g th e consistenc y of you r judgments
. Tr y t o kee p anope n min d unti l yo u hav e gon e throug hal l th e evidence , an ddon' t le t th e earl y informatio nyo u conside r swa y yo u mor e tha n i s appropriate
. T o avoi dadvers e memory effects, defin e variou s classe s of informatio ntha t

yo u dee mrelevant , an dthe n searc hyou r memor y fo r

example s of

each
. Don' t

restric t you r thinkin g onl y t o item s tha t stan dou t

fo r specifi c reasons . Make aspecia l attemp t t o conside r conflictin g evidence , an dt o thin k of dat atha t

may b e inconsisten t

wit ha particula r

theory
. Also , b e carefu l t o concentrat e o nth e give nprobabilit y judgmen t an dP.7 0
162 do no t le t you r ow n value s (how yo u woul dmak e th e decisio nyourself ) affec t thos e judgments
. T o accuratel y estimate the reliability of information, pa y attentio nt o suc h matter s a s sampl e siz e an dpowe r of th e statistica l tests . Kee p i nmin dtha t dat aar e probabilisti c in nature , subjec t t o element s of

rando merror , imprecis e measurements , an dsubjectiv e evaluatio n an dinterpretation
. I naddition , th e furthe r on e mus t extrapolate , o r

generalize , fro maparticula r stud y t o asituatio no f interest , th e les s reliabl e i s th e conclusio n an dth e les s certaint y shoul db e attribute dt o it
. Rel y mor e heavil y o n informatio n whic hyou conside r mor e reliable , bu t

do no t trea t i t a s "absolut e truth. " Kee p in min dtha t the importance of

an event or an outcome should

not influence its judged

probability. I t

i s rationa l t o le t

th e costlines s o r

severit y of

a noutcom e influenc e th e poin t

a t whic hactio ni s take nwit hrespec t t o it , bu t

no t th e judgmen t

tha t i s mad e abou t

th e outcome' s likelihood
. Finally , in makin g probabilit y judgments , thin k primaril y interm s of

th e measur e (probabilit y o r

odds ) wit hwhic hyo u fee l mor e comfortable , bu t sometime s translat e t o th e alternativ e scale , o r eve n t o measure s of

othe r event s (e.g. , th e probabilit y of th e even t no t happening)
. Whe

n estimatin g ver y smal l o r ver y larg e likelihoods , i t i s usuall y bes t t o thin k i n term s of

odds , whic har e unbounded , instea dof probabilities , whic har e bounded
. Fo r

example , on e ca nmor e easil y conceptualiz e odd s of 1:20 0 tha n a probabilit y of

.005
. C.1. 8 Final Preparatio n fo rElicitatio n o f Probability Judgment s Th e outcome s of

th e idea l experiment s describe dabov e ar e uncertain
. Existin g dat aar e relevant , bu t

do no t allo w exac t

predictions
. Our

goa l i s t o hav e yo u represen t probabilisticall y you r

own uncertaint y abou t th e experimenta l outcome s base do n you r expertis e an dth e availabl e knowledge
. I nrespondin g t o th e question s w e wil l as k you ,P.7 1 16 3 pleas e thin k

carefull y abou t

th e relevan t

informatio nreviewe dinth e criteri adocument , an dconsul t

i t a s wel l a s th e literatur e o r you r file s a s yo u dee mappropriate
. Th e previou s sectio n suggest s way s t o thin k abou t th e relevan t

data
. Th e purpos e o f tha t sectio n i s t o hel p minimiz e th e biasin g effect s tha t frequentl y accompan y th e informatio n overloa dnaturall y resultin g fro mrapi dconsideratio nof larg e amount s of comple x evidence
. You ma y fin di t helpfu l t o revie w th e sectio no r rais e question s abou t th e point s mad e i n i t

befor e w e begin
. Uncertaint y abou t

th e effect s of

lea dexposur e o nmea ndecremen t in I Q (relativ e t o mea n IQ a t zer o bloo dlead ) ca nb e represente dprobabilisticall y in tw o differen t ways . 1 . Uncertaint y abou t

th e mea nIQ decremen t tha t woul dresul t

whe n th e expose dgrou p ha s agiven blood-lead concentration. 2 . Uncertaint y abou t th e blood-lea dconcentratio ntha t woul db e require dt o cause a given mean IQ decrement
. W e wil l concentrat e o n on e way a t atime , focusin g primaril y o nth e firs t one . Fo r thes e purpose s recal l tha t everyon e i nth e expose dpopulatio nha s aspecifie d blood-lea dleve l whil e everyon e inth e zer o blood-lea dpopulatio nha s negligibl e bloo d lead , a s describe dabov e unde r Exposur e Conditions
. Then , i norde r fo r u s t o determin e you r uncertaint y abou t

th e mea n IQ decremen t of th e expose dgrou p wit hagiven bloodlead level relativ e t o th e negligibl e blood-lea dgroup , w e mus t introduc e adefinition
. Le t Lb e th e give n blood-lea dconcentratio ninquestion
. Definition: D(L) i s th e mea nI Q decremen t of th e expose dgrou p wit h blood-lea dleve l Lrelativ e t o th e negligibl e group . Th e valu e of

D(L) fo r

agive nLi s uncertain , an dw e woul dlik e t o obtai n probabilit y judgment s fro myo u abou t it s possibl e values
. W e wil l elici t

you r judgment s abou t th e possibl e value s of D(L) b y specifyin g aparticula r mea nI Q decremen t

dan d havin g yo u conside r

ho w likel y i t

i s tha t D(L ) i s les s tha ntha t

value
. T o hel p yo u mak eP.7 2
16 4 you r probabilit y judgments , we wil l mak e us e of adevic e calle daprobabilit y wheel , whic hha s adjustabl e sector s of blu e an dorange . W

e ca nrea do nth e bac k

of th e whee l th e percentag e of

th e whee l tha t

i s eac hcolor
. Inmakin g you r judgment s yo u ar e t o imagin e tha t

th e whee l i s aperfectl y fai r rando mdevice , an dtha t therefor e th e probabilit y of

it s stoppin g wit hth e pointe r o nblu e i s exactl y represente db y th e relativ e are atha t i s blue
. W e wil l the n procee da s follows
. Fo r eac hbloo dlea dconcentratio nL , w e wil l specif y aparticula r

mea n IQ decremen t

d , an dals o se t

th e probabilit y whee l t o hav e a specifi c relativ e are aof blue
. The nyou ar e t o conside r carefull y th e question: D o you conside r

i t mor e probabl e tha t

D(L) i s les s tha ndor tha t th e whee l woul dsto p wit hth e pointe r o nblu e (onarando mspin) ? You ca n giv e on e of

thre e responses : 1 . Yo u judg e i t

t o b e mor e probabl e tha t D(L) i s les s tha nd ; 2 . Yo u judg e i t

t o b e mor e probabl e tha t th e whee l woul dsto p wit h th e pointe r

o n blue ; 3 . Yo u canno t judg e eithe r

even t a s mor e probabl e tha nth e other
. Fo r aparticula r

concentratio nLan dmea nIQ decremen t d , som e whee l setting s wil l hav e asmal l enoug hrelativ e are ao f blu e tha t

yo u wil l fee l confiden t makin g respons e (1) . Othe r

whee l setting s wil l hav e alarg e enoug hrelativ e are aof blu e tha t

yo u wil l fee l confiden t

makin g respons e (2) . Th e intermediat e setting s wil l b e mor e difficul t t o judge
. However , fo r afixe dbloo dlea dL , an dmea nIQ decremen t d , w e wil l manipulat e th e whee l setting s t o fin dth e on e fo r whic hyou fee l mos t

comfortabl e makin g respons e (3) . Onc e w e hav e determine dth e poin t a t whic hyo u ar e mos t

comfortabl e wit h respons e (3) , an dstil l focusin g o n th e give nbloo dlea dL , w e wil l specif y ane w mea n IQ decremen t

d' , rese t th e whee l t o ane w relativ e are aof blue , an dprocee dt o obtai nyou r judgment s regardin g th e probabilisti c relatio nbetwee nd ' an dD(L) . Thi s wil l continu e fo rP.7 3 16 5 th e give n Lunti l w e hav e obtaine dcomparison s o f variou s mea nvalue s t o D(L) . The n w e wil l hav e elicite dth e probabilisti c representatio nof you r uncertaint y abou t

th e mea n IQ decremen t

fo r on e blood-lea dlevel
. W e wil l obtai nth e probabilisti c representatio n of you r uncertaint y fp r

th e outcom e of

anothe r experimen t

b y specifyin g ane w Lan d continuin g a s before
. W e wil l d o thi s fo r

anumbe r

of value s of

L . I t frequentl y happen s tha t a nexpert' s judgment s alte r somewha t

ove r th e cours e of asessio n suc ha s this , a s h e o r sh e consider s th e evidenc e fro mvariou s perspective s an dthink s abou t

th e variou s response s calle dfor
. Hence , w e wil l grap hyou r response s and , a t appropriat e times , sho w the mt o yo u fo r you r consideratio nan dcomparison
. A t thes e time s yo u may wis ht o chang e som e of th e judgment s yo u giv e earlier
. Also , althoug hth e probabilit y judgment s ar e entirel y you r own , w e mus t introduc e on e logica l constraint : namely , tha t you r final judgment s ar e coheren t in a sens e tha t

w e ca n explai n a s w e g o along
. I t i s quit e commo nfo r

initia l judgment s t o exhibi t som e incoherencies
. Tha t i s anothe r

reaso nw e wil l conside r togethe r

th e graph s of you r judgments
. Ou r

objectiv e i s t o obtai nacoheren t se t of judgment s tha t

represen t you r opinion s wel l b y th e en do f thi s elicitatio nprocess . You ar e no t expecte dt o giv e u s suc hase t

immediately
. Al l of

thi s wil l becom e cleare r a s w e g o along
. W e shoul demphasiz e tha t th e judgment s w e ar e askin g yo u t o mak e ar e no t simpl e ones , no r

of cours e ar e ther e know ncorrec t answers . Rather , w e wan t you r bes t an dmos t

considere djudgmen t inligh t

of th e availabl e relevan t scientifi c data
. Therefore , pleas e reflec t o n th e availabl e dat acarefully , feelin g fre e t o consul t th e lea d criteri adocumen t

o r othe r source s a s yo u wis ha s yo u formulat e you r judgments
. (Encod e judgment s fo r tw o blood-lea dconcentrations , the ncontinu e wit h instructions. ) Recal l tha t

uncertaint y abou t

th e experimenta l outcome s ca nals o b e expresse d interm s of

th e blood-lea dconcentratio nnecessar y t o produc e agive nmea n I Q decremen t

D , i f th e entir e expose dpopulatio nha dth e sam e blood-lea dconcentration ,P.7 4
16 6 establishe din th e manne r discusse dearlier
. Mor e specifically , proceedin g a s before , le t u s introduc e adefinition : Definition: L(D ) i s th e blood-lea dleve l tha t woul dcaus e amea nIQ decremen t

D in a n expose dgrou p relativ e t o th e negligibl e group . Th e valu e of

L(D ) i s uncertai nfo r agive nD , an dw e wan t t o obtai n you r judgment s abou t

it s possibl e values
. Analogousl y t o wha t w e hav e alread y don e i n obtainin g th e D(L

) judgments , fo r

agive nD w e wil l specif y concentration s 2

, an das k yo u t o conside r

ho w likel y i t

i s tha t th e L(D ) i s les s tha nth e specifie d£ . Mor e specifically , utilizin g th e whee l a s before , w e wil l as k you th e question: D o yo u conside r

i t mor e likel y tha t

L(D ) i s les s tha nI

or tha t th e whee l woul dsto p wit hth e pointe r onblu e (onarando mspin) ? Yo u ca ngiv e on e o f

thre e responses : 1 . You judg e i t

mor e probabl e tha t

L(D ) i s les s tha n8, ; 2 . You judg e i t

mor e probabl e tha t

th e whee l woul dsto p wit hth e pointe r o n blue ; 3 . You canno t

judg e eithe r

even t a s mor e probabl e tha nth e other
. Afte r determinin g th e whee l settin g a t whic hyo u fee l mos t

comfortabl e wit h respons e (3) , w e wil l specif y ane w aan drepea t

th e process . A s before , fo r eac hD w e wil l elici t you r comparativ e judgment s fo r variou s value s of

2, . W e mus t encod e you r

probabilisti c judgmen t

abou t th e mea nI Q of

childre nin th e population , o r

in th e tw o SE S groups , wh o hav e negligibl e blood-leve l unde r th e exposur e condition s describe dpreviously
. W e star t wit hadefinition : Definition: Le t

y b e th e tru e populatio nmea nI Q fo r childre nwit hnegligibl e bloo dlead
. (Or , le t

y : b e th e tru e populatio nmea nI Q fo r childre nwit hnegligibl e bloo d lea di nSE S grou p i. ) Th e valu e o f

y o r y • i s uncertain , an dw e wil l obtai nyou r judgmen t

abou t it s possibl e values
. Analogousl y t o wha t w e hav e alread y done , w e wil l specif y amea ny an dP.7 5 167

* * as k yo u t o conside r

ho w likel y i t

i s tha t y o r y • i s les s tha ny . W e wil l elici t

you r judgment s abou t

variou s value s of

y wit hth e ai dof

th e probabilit y wheel , inth e sam e manne r a s was don e previously
. I f yo u fel t

i t necessar y t o conside r separat e experiment s fo r tw o SE S groups , the n yo u ma y believ e tha t th e within-grou p I Q standar ddeviatio ni s differen t fro m15
. I f so , w e mus t

encod e you r

probabilisti c judgmen t

abou t tha t value
. I f yo u agree , w e wil l assum e tha t

th e standar ddeviatio ni s unaffecte db y lead-level
. However , yo u ma y fee l tha t th e standar ddeviatio n i s differen t fo r th e tw o SE S groups . I f so , w e mus t

encod e you r opinio nseparatel y abou t eac hcase . A s before , w e star t

wit hadefinition : Definition: Le t

oj * b e th e tru e I Q standar ddeviatio nfo r SE S grou p i
. Th e valu e of

ar*i s uncertain , an dw e wil l obtai nyou r judgmen t

abou t it s possibl e values
. Analogousl y t o wha t w e hav e alread y done , w e wil l specif y astandar ddeviatio n o an das k yo u t o conside r

ho w likel y i t

i s tha t o-*i s les s tha no . W e wil l elici t

you r judgment s abou t

variou s value s of

o wit hth e ai dof

th e probabilit y wheel , inth e sam e manne r a s was don e previously
. C. 2 SUMMAR

Y O FFUNCTION S FI T T O I Q JUDGMENT S Normal-on-log-odd s (NOLO ) probabilit y function s wer e fi t t o al l of th e judgment s of th e hemoglobi n experts . Becaus e of th e divers e natur e of th e judgment s obtaine d fro mth e IQ experts , i t was necessar y t o choos e amon g normal , lognormal , an dNOL O probabilit y function s t o adequatel y represen t thos e judgments
. Fittin g norma l an d lognorma l distribution s t o judgment s ar e intermediat e step s inth e proces s of fittin g a NOLO distribution , s o i t i s unnecessar y t o repea t thos e detail s here
. Th e reade r ca n refe r t o Sec . B. 2 fo r

al l of th e necessar y information
. I n fittin g lognorma l distribution s t o judgments , th e variabl e of interes t i s tha t designate dX in Sec . B.2.2 ; fo r fittin g norma l distributions , th e variabl e of interes t i sP.7 6
16 8 tha t designate dY . Lognorma l distribution s wer e foun dt o b e particularl y usefu l i nfittin g function s t o judgment s abou t mea nIQ level s of

childre nsheltere dfro mlea dexposure , an dnorma l distribution s wer e particularl y usefu l infittin g function s t o judgment s abou t populatio n standar ddeviation
. C. 3 RESULT S Result s ar e presente di n seve ntable s whic hcover :

• Encode djudgment s fo r th e mea nIQ , E[I Q ] of th e distributio nove r IQ of childre n sheltere dfro mlea d(Tabl e Cl) ,
• Encode djudgment s fo r within-grou p standar ddeviation , o (Tabl e C2) ,
• Encode djudgment s fo r mea nIQ decrements , A— , fo r expose d childre nrelativ e t o unexpose dchildre n(Tabl e C.3) ,
• Specification s (form , parameters , moments ) fo r function s fi t

t o th e judgment s fo r

A

—(Tabl e C4) , ^ o

• Specification s fo r

function s fi t

t o judgment s fo r

o (Tabl e C5) ,
• Specification s fo r

function s fi t

t o judgment s fo r

A

—(Tabl e C.6) , an d

• Comparison s of

median s an dcredibl e interval s fo r encode d judgment s vs . fitte dfunction s (Tabl e C.7) . C.3. 1 ExpertF Exper t Fdi dno t

fee l tha t

SE S leve l wa s asignifican t facto r influencin g th e effect s of

lea do n IQ . Thus , onl y on e se t of judgment s was obtaine dfro mExper t F . I n addition , Exper t

Fdi dno t

fee l tha t

i t was necessar y t o us e aprobabilit y distributio n t o characteriz e populatio n standar ddeviatio nan dsimpl y gav e apoin t estimat e fo r

tha t quantity
.P.7 7 169 TABLE C l Encode d Judgment s abou tth e Mea n I Q o f Childre n Sheltere d from Lea d Exposure
Exper t F

Bot h SE S Level s

^ 10 0 10 0 10 1 10 1 10 2

• F 0.0 1 0.0 1 0.4 2 0.8 0 0.9 9 Exper t G

*% 9 0 9 3 9 4 9 6 9 8 10 0



## W Q 10 0 10 4 10 6 10 8 11 0 F 0.0 1 0.2 5 0.5 0 0.7 6 0.9 2 0.9 9

F 0.0 1 0.1 5 0.5 0 0.8 5 0.9 9 Exper t H

Lowe r SE S
W 0F 9 2 0.0 1 9 4 0.2 0 9 8 0.5 0 9 9 0.6 5 10 2 0.9 9 Exper t J

Level s

*% 90. 0 93. 5 95. 0 96. 0 98. 0 F 0.0 1 0.2 5 0.5 0 0.7 5 0.9 0

Highe r SE S Level s
W Q F 10 0 0.0 2 10 2 0.1 1 10 4 0.3 0 10 6 0.4 9 10 8 0.7 5 11 0 0.9 6 ^ 0

10 0 10 2 10 4 10 6 10 8 11 0 F 0.00 1 0. 1 0.7 7 0.9 0 0.9 9 0.99 9 Exp e

*% 7 8 8 3 8 5 8 8 9 1

**~o 10 0 10 2 10 4 10 6 10 8 11 0 r t K

F 0.0 1 0.2 5 0.5 0 0.7 5 0.9 9

F 0.0 1 0.1 7 0.4 2 0.6 0 0.8 5 0.9 9P.7 8

170 TABL E C. 2 Encode d Judgment s abou tPopulatio n Standard Deviatio n
Exper t F

Bot h SE S Level s

°I Q F 1 5 1 Exper t G



### ^ Q 1 4

1 4 F 1

1 Exp e



### ^ Q 1 0 1 1 1 2 1 3 1 4 1 5

1 3 13. 5 1 4 14. 3 1 5 15. 5 r t H

Lowe r

F 0.0 4 0. 1 0.3 5 0. 5 0.8 5 0.99 9 Exper t J

SE S Level s



### °^ Q 1 1 1 2 1 3 1 4 1 5

Highe r SE S 0.0 4 0.0 7 0.27 5 0. 5 0. 9 0.9 9 1 1

1 2 1 3 1 4 1 5 F 0.00 1 0.12 5 0. 5 0.87 5 0.99 9

Level s 0.00 1 0.12 5 0. 5 0.87 5 0.99 9 Ex

p



## °? Q 1 0 1 1 1 2 1 3 1 4 1 5

1 2 1 3 13. 5 1 4 1 5 ar t K

F 0.0 1 0.0 5 0.1 4 0.5 3 0.9 3 0.99 9

0. 2 0.2 5 0. 5 0.7 5 0.9 9P.7 9 17 1

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m moesocooo o O—IrHCSCSCOtfv OTABL EC. 3 (Cont'd )
Blood-Lea dLeve l

-I Q A I Q F ki Q 'I Q 1 I Q *I Q Exper t K , Highe r SE S Level s 1 5 yg/d L 2 5 yg/d L

0. 5 1. 0 1. 5 2. 0 0.0 1

0.3 5 0. 5 0.9 9 3 5 yg/dL 4 5 yg/dL 5 5 yg/d L 6 5 yg/d L

1. 0 1. 5 2. 0 2. 5 3. 0 0.0 1

0.1 1 0. 5 0. 9 0.9 9 2. 0

3. 0 3. 5 4. 0 5. 0 0.0 1 0. 2 0. 5 0.7 5 0.9 9 3. 0

4. 0 4. 5 5. 0 6. 0 0.0 2 0.2 5 0. 5 0.7 8 0.9 8 4. 0 0.01 0

5. 0 0.17 0 6. 0 0.50 0 7. 0 0.82 0 8. 0 0.99 0 s l O N *Aj 0 denote s the mea n I Q decremen t among childre n wit h the specifie d blood-lead levels , rererence d t o unexpose d children . F denote s cumulativ e probability .TABL E C. 4 Parameter s o f

Function s Fi tt o th e Probabilisti c Judgment s o f Expert s Regardin g Mea

n I Q Level s amon g Childre n Sheltere d fro m Lea d Exposure

Exper tSE

S Cas e Functiona l

For m Parameter s o f Normal-on-L n (IQ Q ) Distributio n Mea n SD d Moment s o f Distributio n Ove r IQ Q E[I Q J bSD[I Q 1 ( r 2 o f F o n F Combine d Lognorma l 4.614 0 0.004 6 100. 9 0.4 7 0.93 1
G H J K
G H J K Lowe r Lowe r Lowe r Lowe r Highe r Highe r Highe r Highe r Lognorma l

Lognorma l Norma l Norma l Lognorma l Lognorma l Lognorma l Norma l 4.549 5

4.576 3

-

- 4.659 1 4.659 6 4.645 4

- 0.023 2 0.024 9

-

- 0.020 6 0.026 5 0.015 8

- 94. 6

97. 2 94. 8 85. 0 105. 6 105. 6 104. 1 104. 9 2.2 0

2.4 2 1.9 3 2.9 2 2.1 7 2.8 0 1.6 5 2.3 6 0.99 4

0.96 6 0.99 6 0.99 3 0.98 7 0.99 2 0.96 0 0.98 8

a S D denote s standard deviation . E[I Q ] denote s the mean o f the distributio n fo r IQ_ . s l s l

'SD[I Q ] denote s the standard deviatio n o f th e distributio n fo r IQ Q .TABL E C. 5 Summary o f

Function s Fi tt o th e Probabilisti c Judgment s o f Expert s Regardin g Populatio n Standar d Deviatio n fo rI Q Level s

Exper t Functiona l

SE S Cas e For

m Parameter s o f Normal-on-L n (°TQ ) Distributio n Mean SD e Moment s o f Distributio n Ove r OJ Q E[o IQ ] SD[o IQ ] c r 2 o f F o n F Combine d Poin t 15. 0
G H J K
G H J K Lowe r Lowe r Lowe r Lowe r Highe r Highe r Highe r Highe r Poin t

Lognorma l Norma l Norma l Poin t Lognorma l Lognorma l Norma l —

2.505 6

-

-

- 2.654 1 2.559 0

- —

0.091 5

-

-

- 0.041 6 0.053 1

- 14. 0

12. 3 13. 0 12. 6 14. 0 14. 2 12. 9 13. 5 —

1.1 3 0.6 8 0.9 3

- 0.5 9 0.6 9 0.6 9 —

0.99 9 0.99 9 0.99 9

- 0.99 9 0.99 9 0.99 9 s l oo

a S D denote s standar d deviation . E[OJQ ] denote s th e mea n o f th e distributio n o f OJQ .
C SD[OJQ ] denote s th e standar d deviatio n o f th e distributio n fo r OTA
-P.8 7 

### 17 9 TABL E C. 6 Summar

y of Function Fi tt o th e Probabilisti cJudgment s of Expert s Regardin g Mea n I Q Decrement

s amon g Childre n Expose d t o Lea d

Blood-Lea

d Leve l (yg/dL ) Functiona l For m Parameter s of

Norma l o

n L N (ATM ) Distributio

n
Mea n SD

e Moment s of

Distributio

n Over A ^ E[^iQ] b SD[AJQ] C r 2 of F o nF Expert F , Bot

hSE S Level s 2 5 3 5 4 5 5 5 6 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l -1.405 9

-0.712 7 -0.032 9 0.335 0 0.557 4 0.462 8

0.462 8 0.462 8 0.462 8 0.462 8 0.272 9

0.545 7 1.077 0 1.555 9 1.943 4 0.133 4

0.266 7 0.526 4 0.760 4 0.949 8 0.999 0

0.999 0 0.998 6 0.998 4 0.988 5 Expert G , Lower SE S Level s 5 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l -0.481 6

0.331 6 0.977 5 1.354 8 1.735 9 1.990 5 0.642 2

0.542 9 0.522 9 0.380 7 0.301 1 0.317 4 0.759 3

1.614 5 3.047 1 4.167 5 5.936 9 7.697 0 0.542 5

0.945 2 1.708 9 1.645 9 1.828 7 2.506 0 0.978 9

0.978 9 0.968 9 0.982 5 0.970 1 0.978 2 Expert H , Lower SE S Level s 5 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l 0.826 8

1.248 1 1.586 0 2.032 3 2.242 2 2.404 5 0.408 7

0.398 9 0.374 9 0.308 7 0.236 6 0.188 7 2.485 1

3.772 4 5.239 7 8.004 0 9.680 7 11.271 4 1.059 6

1.566 9 2.035 6 2.530 7 2.322 4 2.145 8 0.971 5

0.976 5 0.87 7 0.987 9 0.989 8 0.988 8 Expert I , Lower SE S Level s 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l -0.327 6

0.849 5 1.336 1 1.700 9 1.904 1 0.535 1

0.411 0 0.328 2 0.308 8 0.284 5 0.831 6

2.544 5 4.014 8 5.746 5 6.990 8 0.478 9

1.091 5 1.354 0 1.817 8 2.029 8 0.998 4

0.994 5 0.992 6 0.998 0 0.994 9TABL E C. 6 (Cont'd ) 18 0 P.8 8

Blood-Lea d Leve l (yg/dL ) Functiona l For m Parameter s o f

Norma l o n L N(ATM ) Distributio n
Mea n SD

a Moment s o f

Distributio n Ove r A ^

—i b E[AJQ ] SD[AJQ] C r 2 o f F o n F Exper t J , Lowe r SE S Level s 5 1 5 2 5 3 5 4 5 5 5 Norma l

Norma l Norma l Norma l Norma l Norma l 2.387 4 3.470 4 4.774 7 6.826 4 8.835 7 10.741 2 0.895 6

1.187 8 1.487 2 1.502 5 1.564 2 1.600 7 0.960 8

0.990 7 0.992 7 0.994 9 0.988 9 0.979 1 Exper t K , Lowe r SE S Level s 1 5 2 5 3 5 4 5 5 5 6 5 Norma l

Norma l Norma l Norma l Norma l Norma l 1.276 4 2.891 0 3.766 8 6.434 9 7.760 8 10.369 4 0.442 6

1.102 7 1.081 6 1.220 1 1.307 1 1.585 5 0.954 0

0.991 3 0.990 0 0.980 0 0.988 9 0.992 0 Exper t G , Highe r SE S Level s 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l -0.343 0

0.205 9 0.957 5 1.354 8 1.749 7 0.567 1

0.504 5 0.484 7 0.380 7 0.306 8 0.833 5

1.395 4 2.929 9 4.167 5 6.029 8 0.513 3

0.751 2 1.507 9 1.645 9 1.894 2 0.954 6

0.966 8 0.985 4 0.982 5 0.961 3 Exper t H , Highe r SE S Level s 5 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l -0.576 7

0.896 0 1.478 5 1.687 3 1.885 9 2.068 8 0.520 7

0.449 8 0.260 7 0.195 5 0.129 7 0.110 3 0.643 3

2.710 6 4.538 2 5.509 0 6.648 a 7.963 5 0.359 0

1.283 7 1.203 5 1.087 3 0.866 1 0.880 9 0.996 1

0.983 3 0.989 9 0.996 8 0.984 2 0.996 7TABL E C. 6 (Cont'd ) 18 1 P.8 9

Blood-Lead Leve l (yg/dL ) Functiona l For m Parameter s o f

Norma l o n L N(L-) Distributio n
Mea n SD

e Moment s o f

Distributio n Ove r ATQ " E[Ajp] b SD[AJQ] C r 2 o f F o n F Exper t I , Highe r SE S Level s 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l -1.1800 1

0.063 7 0.849 5 1.319 8 1.471 9 0.619 1

0.602 2 0.411 0 0.319 3 0.383 9 0.372 2

1.277 6 2.544 5 3.938 3 4.690 9 0.254 4

0.844 8 1.091 5 1.290 2 1.869 2 0.998 7

0.990 3 0.994 5 0.997 0 0.997 4 Exper t J , Highe r SE S Level s 1 5 • 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l 0.454 2

1.006 9 1.298 2 1.618 0 1.948 9 0.450 2

0.364 0 0.276 2 0.199 1 0.146 6 1.742 9

2.924 6 3.805 3 5.144 2 7.097 0 0.826 2

1.100 7 1.071 3 1.034 4 1.046 3 0.962 0

0.941 0 0.959 0 0.997 9 0.992 3 Exper t K , Highe r SE S Level s 2 5 3 5 4 5 5. 5 6 5 Norma l

Norma l Norma l Norma l Norma l 1.283 6 1.995 3 3.521 6 4.485 8 6.007 0 0.348 5

0.423 2 0.646 1 0.726 2 0.894 8 0.932 2

0.999 3 0.998 9 0.999 2 0.997 6TABL E C. 7 Summar

y and Compariso n o f

Judgment s and Fitte d Function s Concernin g Lead-Induce d I Q Effect s
Exper t F , Bot hSE S Group s
AI Q Blood-Lea d Leve l

. 9 ( - , 1.5 ) ( - , 2 ) 1. 5

(1.1 , 1.9 ) ( - , 3 ) 2

(1.3 , 2.6 ) (-- , 4 ) Inde x IQ Q o 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L 6 5 yg/d L Encode d Judgment s Media n 100. 5 1 5 .2 5 . 5 50 % C.I. a (100.2 , 101.3 ) —( — , .62 ) (-- , 1.2 ) 90 % C.I . (100.1 , 101.9 ) —( — , .92 ) (— , 1.9 ) Fitte dRepresentation s ° > Media n 100. 9 1 5 .2 5 .4 9 .9 7 1. 4 1. 7 50 % C.I . (100.6 , 101.2 ) —(.12 , .34 ) (.36 , .67 ) (.71 , 1.32 ) (1.02 , 1.91 ) (1.28 , 2.39 ) 90 % C.I . (100.1 , 101.7 ) —(.11 , .52 ) (.23 , 1.05 ) (.45 , 2.07 ) (.65 , 2.99 ) (.81 , 3.74 ) 98 % C.I . (99.8 , 102 ) —(.08 , .72 ) (.17 , 1.4 ) (.33 , 2.84 ) (.48 , 4.10 ) (.59 , 5.12 )

a C.I . denote s credibl e interval .

T l C OTABLE C. 7 (Cont'd ) Exper tG, Lowe rSE S Grou p AI Q Blood-Lea

d Leve l Inde x IQ Q o 5 yg/d L 1 5 yg/d

L 2 5 yg/d

L 3 5 yg/d

L 4 5 yg/d

L 5 5 yg/d

L Encode d Judgment s 1 4 0. 5 1. 5 3. 0 3. 5 5. 0 7. 0 (5 , 10 ) Media n 50 % C.I . 90 % C.I . 9 4

(93 , 96 ) (91 , 99 ) 0. 5

(.3 , 1 ) (.2 , 3 ) 1. 5

(.7 , 2 ) (.5 , 5 ) 3. 0

(1.3 , 4 ) ( 1 , 8.5 ) 3. 5

(2.5 , 5 ) ( 2 , 10 ) 5. 0

( 4 , 7 ) (3.5 , 12 ) (4 , 15 ) Fitte d Representation s o o CO Media n 94. 6 1 4 0. 6 1. 4 2. 7 3. 9 5. 7 7. 3 50 % C. I (93 , 96 ) —(.4 , .9 ) (1 , 2 ) (1.9 , 3.8 ) (3 , 5 ) (4.6 , 7 ) (5.9 , 9.1 ) 90 % C. I (91 , 98 ) —(.2 , 1.8 ) (.6 , 3.5 ) (1.1 , 6.3 ) (2.1 , 7.3 ) (3.5 , 9.3 ) (4.3 , 12.3 ) 98 % C.I . (90 , 100 ) —(.1 , 2.8 ) (.4 , 4.9 ) (.8 , 9 ) (1.6 , 9.4 ) (2.8 , 11.4 ) (3.5 , 15.3 )

T J C OTABL

E C. 7 (Cont'd )
Exper tG , Highe rSE S Group s AIQ Blood-Lead Leve l Index IQ Q o 5 yg/dL 1 5 yg/dL 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L Encode d Judgment s Media n 10 6 1 4 — 0. 5 50 % C.I . (105 , 107 ) ——(.4 , 1 ) 90 % C.I . (103 , 109 ) ——(.3 , 3 ) Fitte dRepresentation s oo Media n 105. 6 1 4 ~ 0. 7 1. 2 2. 6 3. 9 5. 8 50 % C.I . (104 , 107 ) ——(.5 , 1 ) (.9 , 1.7 ) (1.9 , 3.6 ) (3 , 5 ) (4.7 , 7.1 ) 90 % C.I . (102 , 109 ) ——(.3 , 1.8 ) (.5 , 2.8 ) (1.2 , 5.8 ) (2.1 , 7.3 ) (3.5 , 9.5 ) 98 % C.I . (101 , 111 ) ——(.2 , 2.7 ) (.4 , 4 ) (.8 , 8 ) (1.6 , 9.4 ) (2.8 , 11.7 ) 1. 0 (.7 , 2 ) (.5 , 4 ) 2. 5

(1.5 , 4 ) ( 1 , 8 ) 3. 5

(2.5 , 5 ) ( 2 , 10 ) 5. 0

( 4 , 7.5 ) (3.5 , 12 )TABL E C. 7 (Cont'd )
Exper tH , Lowe rSE S Grou p AI Q Blood-Lea dLeve l Inde x IQ Qo 5 yg/d L1 5 yg/d L2 5 yg/d L3 5 yg/d L. 4 5 yg/d L5 5 yg/d L Encode d Judgment s Median 50 % C.I . 90 % C.I .

Median 50 % C.I . 90 % C.I . 98 % C.I . 9 8

(95 , 100 ) (92 , 102 )

97. 2 (96 , 99 ) (93 , 100 ) (92 , 103 ) 1 3

(12,14 ) (10 , 15 )

12. 4 (12 , 13 ) (11 , 14 ) (10 , 15 ) 2. 6 3. 0 5. 2

(1.6 , 3.4 ) (2.6 , 5 ) (3.4 , 7.2 ) (1.1 , 4.5 ) (1.9 , 6.1 ) (2.4 , 9.2 )

Fitte d Representation s 2. 3 3. 5 4. 9 (1.7 , 3 ) (2.7 , 4.6 ) (3.8 , 6.3 ) (1.2 , 4.5 ) (1.8 , 6.7 ) (2.6 , 9 ) (.9 , 5.9 ) (1.4 , 8.8 ) (2 , 11.7 ) 8. 2 (6 , 9.7 ) (4.2 , 12 )

7. 6 (6.2 , 9.4 ) (4.6 , 12.7 ) (3.7 , 15.7 ) 9. 5

(7.4 , 11.3 ) (6.2 , 14 )

9. 4 (8,11 ) (6.4 , 13.9 ) (5.4 , 16.3 ) 10. 5

(9.7 , 11.8 ) (8.2 , 16 )

11. 1 (9.7 , 12.6 ) (8.1 , 15.1 ) (7.1 , 17.2 )185TABL E C. 7 (Cont'd ) Exper tH , Highe rSE S Grou p AI

Q Blood-Lead Leve l Index IQ Q o 5 yg/dL 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L Encode d Judgment s Median 10 6 14. 3 0. 6 2. 5 4. 5 5. 5 6. 5 8. 0 50 % C.I . (104 , 108 ) (13.8 , 14.7 ) (-- , .9 ) (1.8 , 3.5 ) (3.8 , 5.6 ) (4.4 , 6.4 ) (6.1 , 7.1 ) (7.4 , 8.7 ) 90 % C.I . (101 , 110 ) (13.2 , 15.2 ) ( — , 1.3 ) (1.2 , 4.1 ) (2.7 , 6.7 ) (3.9 , 7.8 ) (5.3 , 8.4 ) (6.4 , 9.6 ) Fitte d Representation s Median 105. 6 14. 3 0. 6 2. 4 4. 4 5. 4 6. 6 7. 9 50 % C.I . (104 , 108 ) (13.8 , 14.6 ) (.4 , .8 ) (1.8 , 3.3 ) (3.7 , 5.2 ) (4.7 , 6.2 ) (6 , 7.2 ) (7.3 , 8.5 ) 90 % C.I . (101 , 110 ) (13.3 , 15.2 ) (.2 , 1.3 ) (1.2 , 5.1 ) (2.9 , 6.7 ) (3.9 , 7.5 ) (5.3 , 8.2 ) (6.6 , 9.5 ) 98 % C.I . (99 , 112 ) (12.9 , 15.6 ) (.2 , 1.9 ) (.9 , 7 ) (2.4 , 8 ) (3.4 , 8.5 ) (4.9 , 8.9 ) (6.1 , 10.2 ) o o O NTABL E C. 7 (Cont'd )

Media n 5 0 % C.I . 9 0 % C.I . Exper t I , Lowe r SE S Group s
AI Q Blood-Lea d Leve l Inde x IQ Q a 5 yg/d L 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L Encode dJudgment s 0. 7 (0.5 , 1.1 ) ( 0 , 2 ) 2. 3

(1.9 , 3.2 ) ( 1 , 5 ) 3. 6

(3.1 , 5.1 ) ( 2 , 7 ) 5. 3

(4.5 , 6.9 ) ( 3 , 10 ) 6. 3

(5.5 , 8.2 ) ( 4 , 12 ) Fitte dRepresentation s oo Media n ———. 7 2. 3 3. 8 5. 5 6. 7 5 0 % C.I . —- - - - (.5 , 1.0 ) (1.7 , 3.1 ) (3.0 , 4.7 ) (4.4 , 6.7 ) (5.5 , 8.1 ) 90 % C.I . - - —- - (.3 , 1.7 ) (1.2 , 4.6 ) (2.2 , 6.5 ) (3.3 , 9.1 ) (4.2 , 10.7 ) 98 % C.I . —- - —(.2 , 2.5 ) (.9 , 6.1 ) (1.8 , 8.2 ) (2.7 , 11.3 ) (3.5 , 13.1 ) s jTABL E C. 7 (Cont'd )

Median 50 % C.I . 90 % C.I . Exper t I , Higher SE S Grou p
AI Q Blood-Lead Leve l Index IQ Q o 5 yg/dL 1 5 yg/d L 2 5 yg/dL 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L Encode d Judgment s 0. 3 (.2 , .5 ) ( 0 , 1 ) 1. 0

(.7 , 2 ) ( 0 , 3 ) 2. 3

(1.9 , 3.2 ) ( 1 , 5 ) 3. 6

(3.1 , 4.7 ) ( 2 , 7 ) 4. 3

(3.5 , 5.8 ) ( 2 , 9 ) Fitte dRepresentation s 5 5 Media n—

— ~ 0. 4 1. 1 2. 4 3. 8 4. 5 50 % C.I . ~ —

— (.2 , .5 ) (.6 , 1.7 ) (1.8 , 3.2 ) (3.1 , 4.7 ) (3.4 , 5.7 ) 90 % C.I . —

— —

(.0 , .9 ) (.1 , 2.8 ) (1.2 , 4.5 ) (2.2 , 6.3 ) (2.3 , 8.0 ) 98 % C.I . - - —

- - (0.7 , 1.3 ) (.3 , 4.3 ) (.9 , 6.1 ) (1.8 , 7.9 ) (1.8 , 10.6 )TABL

E C. 7 (Cont'd ) Exper tJ , Lowe rSES Grou p AI Q Blood-Lead Leve l Index IQ Q o 5 yg/d L 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L Encode d Judgment s Median 50 % C.I . 90 % C.I .
Median 50 % C.I . 90 % C.I . 98 % C.I . 9 5

(94 , 96 ) (91 , 99 )

94. 8 (94 , 96 ) (92 , 9 8 (90 , 99 ) 1 3

(12 , 14 ) (11 , 15 )

1 3 (13 , 14 ) (12 , 14 ) (12 , 14 ) 2

(1 , 3 ) (.2 , 5 )

2. 4 (1.8 , 3.0 ) (0.9 , 3.9 ) (0.3 , 4.5 ) 3. 5 5

(2.3 , 4.5 ) (4 , 5.8 ) (.4 , 6.4 ) (1 , 8 ) Fitte d Representation s 3. 5 4. 8 (2.7 , 4.3 ) (3.8 , 5.8 ) (1.5 , 5.4 ) (2.3 , 7.2 ) (0.7 , 6.2 ) (1.3 , 8.2 ) 7 (6 , 8 ) (3 , 9.6 )

6. 8 (5.8 , 7.8 ) (4.4 , 9.3 ) (3.3 , 10.3 ) 9

(7.5 , 10.5 ) (5 , 11.7 )

8. 8 (7.8 , 9.9 ) (6.3 , 11.4 ) (5.2 , 12.5 ) 1 1

(9 , 12.5 ) (6.6 , 13.7 )

10. 7 (9.7 , 11.8 ) (8.1 , 13.4 ) (7.0 , 14.5 ) o

oTABL E C. 7 (Cont'd )
Exper t J , Highe r SE S Grou p

Index IQ , AI Q Blood-Lead Leve l
o 5 yg/d L 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L Encode d Judgment s Median 50 % C. I 90 % C.I . 9 4

(93 , 96 ) (91 , 99 ) 1 4 (1.3 , 2.3 ) (.7 , 3 ) (2.8 , 3.5 )

(1.4 , 6.4 ) Fitte d Representation s (3.5 , 5 ) (2 , 6.7 ) (4.5 , 5.8 )

(3.3 , 7.6 ) (6.5 , 7.5 )

(5.3 , 9.7 )
V O

o Median 50 % C.I . 90 % C.I . 98 % C.I . 94. 6

(93 , 96 ) (91 , 98 ) (90 , 100 ) 1 4 1. 6 (1.2 , 2.2 ) (.7 , 3.4 ) (.5 , 4.6 ) 2. 9

(2.2 , 3.8 ) (1.5 , 5.7 ) (1.1 , 7.6 ) 3. 8

(3.1 , 4.7 ) (2.2 , 6.4 ) (1.8 , 8.0 ) 5. 0

(4.4 , 5.8 ) (3.6 , 7.0 ) (3.2 , 8.0 ) 7. 0

(6.4 , 7.8 ) (5.5 , 8.9 ) (5.0 , 9.9 )

C OTABL E C. 7 (Cont'd ) Exper tK, Lowe rSES Grou p AIQ Blood-Lea d Leve l Index IQ Q o 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yg/d L 6 5 yg/d L Encode d Judgment s Media n 50 % C.I . 90% C.I . 8 5

(83 , 88 ) (79 , 90.4 ) 1 3

(12.2 , 13.5 ) (11 , 14 ) 1. 5

(0.8 , 1.7 ) (0.3 , 2 ) 3. 1

( 2 , 3.8 ) ( 1 , 4.8 ) 4

(3.2 , 4.7 ) ( 2 , 5.8 ) 6

(5.4 , 7.5 ) (4.5 , 8.8 ) 8. 1

(6.8 , 8.6 ) (5.5 , 9.8 ) 1 0

(8.8 , 11.8 ) (7.5 , 13.7 ) Fitte d Representation s Median 8 5 12. 6 1. 3 2. 9 3. 8 6. 4 7. 8 10. 4 50 % C.I . (83 , 87 ) (11.9 , 13.2 ) (0.7 , 1.6 ) (2.1 , 3.6 ) (3 , 4.5 ) (5.6 , 7.3 ) (6.9 , 8.6 ) (9.3 , 11.4 ) 90 % C.I . (80 , 90 ) (11 , 14.1 ) (0.5 , 1.8 ) (1.1 , 4.7 ) (2 , 5.5 ) (4.4 , 8.4 ) (5.6 , 9.9 ) (7.8 , 13 ) 98 % C.I . (78 , 92 ) (10.4 , 14.7 ) (0.2 , 2.3 ) (0.3 , 5.5 ) (1.3 , 6.3 ) (3.6 , 9.3 ) (4.7 , 10.8 ) (6.7 , 14 )TABL E C. 7 (Cont'd ) Exper tK , Highe rSE

S Grou p AI Q Blood-Lea d Leve l Inde x IQ Q o 2 5 yg/d L 3 5 yg/d L 4 5 yg/d L 5 5 yig/d L 6 5 yg/d L Encode dJudgment s Media n 104. 9 13. 5 1. 5 2 3. 5 4. 5 6 50 % C.I . (102.6 , 107.2 ) (13 , 14 ) (.8 , 1.7 ) (1.6 , 2.3 ) (3.1 , 4 ) (4 , 4.8 ) (5.2 , 6.8 ) 90 % C.I . (100.6 , 109.4 ) (12.2 , 14.8 ) (.6 , 1.9 ) (1.2 , 2.9 ) (2.2 , 4.8 ) (3.1 , 5.9 ) (4.3 , 7.8 ) Fitte dRepresentation s N > Media n 104. 9 13. 5 1. 3 2 3. 5 4. 5 6 50 % C.I . (103.3 , 106.5 ) (13 , 14 ) (1 , 1.5 ) (1.7 , 2.3 ) (3.1 , 4 ) (4 , 5 ) (5.4 , 6.6 ) 90 % C.I . (101 , 108.8 ) (12.3 , 14.6 ) (.7 , 1.9 ) (1.3 , 2.7 ) (2.5 , 4.6 ) (3.3 , 5.7 ) (4.5 , 7.5 ) 98 % C.I . (99.A , 110.4 ) (11.9 , 15.1 ) (.5 , 2.1 ) (1 , 3 ) (2 , 5 ) (2.8 , 6.2 ) (3.9 , 8.1 )_E2
_ 19 3 Thus , Exper t

Fjudge daprobabilit y of 0. 5 tha t th e mea nIQ of

th e unexpose d grou p woul db e < 100.5 , 0. 8 probabilit y tha t i t woul db e <_101.5 , an ds o on . Thes e an d othe r judgment s abou t

mea n IQ of

a nunexpose dgrou p of childre nar e liste dinTabl e C.l
. Exper t

Fprovide dapoin t

valu e of 15.2 5 fo r

o , whic happear s inTabl e C.2 . Exper t Fprovide djudgment s o nI Q difference s a t fiv e Pb B levels : 25 , 3 5 ,45 , 55 , an d6 5 yg/dL
. Thes e judgment s ar e liste dinTabl e C.3 . Fo r example , a t

aPb B leve l of

6 5 yg/dL , Exper t

Fjudge daprobabilit y of 0. 9 tha t I Q differenc e woul db e _ < 3 . Figur e 4. 3 show s tha t

Exper t Fi s increasingl y uncertai nabou t th e magnitud e of

I Q difference s a s Pb B leve l increases
. Tabl e C. l indicate s tha t judgment s o nIQ difference s havin g cumulativ e probabilitie s les s tha n 0. 5 wer e no t provide da t

th e lowe r

thre e Pb B levels
. Exper t Fcite ddifficult y i n providin g judgment s o nwha t woul db e ver y smal l IQ differences
. Fo r th e reason s presente dinSec . 1 , mathematica l function s wer e fi t t o th e judgment s of

Exper t F . Fo r Exper t F , th e mathematica l representation s of th e CDF s fo r IQ difference s conditiona l o n Pb B leve l ar e guarantee dneve r t o cross . The y wer e obtaine db y fittin g regressio n line s t o transformation s of th e judgments
. Th e transformatio n use dwa s th e lo g (ln ) transformation
. Simila r t o th e hemoglobi ncase , thi s transformatio n lead s t o distribution s tha t ar e norma l distributions , wit hahig hdegre e of accuracy . Thus , th e fitte ddistribution s ar e lognorma l distributions
. The y ar e uniquel y define db y th e mea n an dvarianc e of th e underlyin g norma l distributions , an dth e transformatio n function
. Propertie s o f th e lognorma l distributio nar e summarize din Tabl e B.l
. A variet y of distribution s wer e fi t

t o th e judgments , an dth e one s reporte d her e wer e determine d(withinpu t fro mth e experts ) t o b e best
. Table s C.4-C. 6 summariz e relevan t informatio nabou t

th e distribution s fi t

t o th e judgment s of

th e experts . I

n Tabl e C.4 , column s identif y th e functiona l form , mea n an d standar ddeviatio n of

a n underlyin g norma l distributio n(if atransformatio ni s used) ,P. 3
19 4
mea n(E[I Q ] ) an dstandar ddeviatio n (SD[OJQ] ) o f th e I Q distribution , an dr of th e regressio nof

fitte dcumulativ e probabilit y value s Fversu s encode dvalue s (F) . Simila r colum n heading s appea r inTable s C. 5 an dC.6 . I nTabl e C.5 , E[OTQ ] denote s th e mean , an dSD[CJJQ ] denote s th e standar ddeviatio no f th e distributio n fo r populatio n standar ddeviation
. Ldenote s Pb B level , an dE[A—] an dSD[A— ] denot e th e mean s an dstandar ddeviation s of probabilit y distribution s fo r I Q decrement s inTabl e C.6 . Fo r

Exper t F , th e fitte ddistributio nof th e uncertai nmea nIQ of th e unexpose d grou p ha s amea n valu e of
. 100.9 ; i t i s alognorma l distributio nan dth e r valu e of

th e regressio nof

th e Fvalue s vs . th e Fvalue s i s 0.93 . Th e standar ddeviatio nof th e distributio n i s 0.47 . Th e mea n an dstandar ddeviatio nof th e underlyin g norma l distributio n (whic hresult s afte r takin g th e natura l lo g of th e encode dmea nIQ values ) ar e 4. 6 an d0.0046 . Thes e value s ar e neede dt o calculat e point s o nacumulativ e probabilit y functio n fo r th e mea n IQ variable
. Fo r populatio nstandar ddeviation , apoin t estimat e of

1 5 was given
. Lognorma l distribution s provide dth e bes t fit s of Exper t F' s judgment s abou t

I Q differences
. Thus , al l of th e column s hav e entries
. Th e mea nvalue s of th e distribution s ove r IQ decremen t

var y fro mabou t

0. 3 a t aPb B leve l o f

2 5 yg/d Lt o abou t

1. 9 a t 6 5 yg/dL
. I n general , th e fitte dfunction s represen t thes e judgment s quit e well , havin g r value s aroun d0.9 9 o r

higher
. C.3. 2 Exper tG Exper t Gprovide dprobabilisti c judgment s abou t mea nIQ fo r

anunexpose dgrou p an dI Q decrement s fo r population s expose dt o varyin g level s o f lea dfo r

bot hSE S categories
. A poin t

estimat e fo r

populatio nstandar ddeviatio n (OJQ=14 ) wa s mad e fo r bot hSES catetories
. Lognorma l distribution s provide dth e bes t fit s fo r th e res t of th e judgments
. Th e mea n value s of th e IQ distribution s wer e 94. 6 an d105. 6 fo r th e lowe rP. 4 19 5

an dhighe r

SE S cases , respectively
. Averagin g acros s SE S leve l result s i na naverag e valu e of abou t 104 fo r th e mea nIQ fo r

unexpose dchildren
. Meanvalue s of th e distribution s fo r

I Q decrement s rang e fro m0. 8 (a t 5 yg/dL ) t o 7. 7 (a t

5 5 yg/dL ) fo r

th e lowe r SES category , an dfro m0. 5 (a t 1 5 yg/dL ) t o 6. 0 (a t

5 5 yg/dL ) fo r

th e highe r

SE S category . Th e r

value s of

th e regression s of

th e fitte ddistribution s versu s th e encode d distribution s wer e quit e good
. Th e lowes t valu e wa s 0.95
. C.3. 3 ExpertH Thi s exper t

provide dprobabilisti c judgment s abou t al l of th e variable s fo r

bot h SE S categories
. Lognorma l distribution s agai nprovide dexcellen t fit s t o al l of

th e encode djudgments
. Th e mea n value s o f th e fitte dI Q distribution s wer e 97. 2 an d105.6 , an dth e mea n value s of th e fitte dstandar ddeviatio ndistribution s wer e 12. 3 an d14.2 . Th e standar ddeviation s of th e fitte dIQ distribution s wer e 2. 4 an d2.8 . Meanvalue s of th e fitte ddistribution s fo r I Q decrement s range dfro m2. 5 (a t 5 yg/dL ) t o 11. 3 (a t

5 5 9 yg/dL) , an dfro m0. 6 (a t 5 yg/dL ) t o 8 (a t

5 5 yg/dL)
. Again , th e r value s o f

th e regression s ar e quit e goo d(0.9 8 o r higher)
. (I

nal l cases , th e value s fo r th e lowe r

SE S case s ar e first , an dth e value s fo r th e highe r

SE S case s ar e second. ) C.3. 4 ExpertI Exper t I onl y provide dprobabilisti c judgment s fo r IQ decrement
. Thi s individua l wa s no t comfortabl e abou t

providin g judgments , reasondin g tha t i t shoul db e possibl e t o solv e fo r

th e othe r

variables , give nwha t i s currentl y know nan dpublishe dabou t populatio n I Q distributions
. However , w e foun dtha t i t wa s no t

possibl e t o d o thi s withou t makin g stron g assumption s abou t Exper t l' s probabilit y judgments
. I nparticular , w e woul deithe r

hav e t o assum e tha t

judgment s of

I Q effect s a t

eac hlea dleve l ar e independen t

of eac hother , o r

assum e aparticula r

patter nof

dependencies
. Sinc e w e wer e certai n tha t

a n assumptio n of

independenc e woul db e wrong , an dha dn o basi s fo r an y othe r specifi c assumptions , w e simpl y accepte dth e judgment s a s provided
.P. 5
19 6 Lognorma l distribution s provide dth e bes t fit s t o thes e judgments
. Judgment s wer e provide da t

fiv e Pb B level s (15-55 yg/dL)
. Meanvalue s of th e fitte ddistribution s on IQ decremen t

range dfro m0. 8 t o 7 fo r th e lowe r

SE S group , an dfro m0. 4 t o 4. 7 fo r th e highe r SE S group . Th e r

value s fo r

th e regression s of

th e fitte ddistribution s ( Fvalues ) vs . th e encode ddistribution s ( Fvalues ) wer e al l greate r tha n0.99 . C.3. 5 Exper tJ Exper t J provide dprobabilisti c judgment s o nal l thre e IQ variables
. Lognorma l distribution s wer e use dt o represen t thes e judgments
. Th e mea nvalue s of th e fitte dIQ distribution s wer e 94. 7 an d104.1 , an dth e mea nvalue s of th e fitte dstandar ddeviatio n distribution s wer e 1 3 an d12.9 . Meanvalue s of th e distribution s fitte dt o th e judgment s on I Q decrement s range dfro m2. 4 t o 10. 7 fo r th e lowe r

SE S case , an dfro m1. 7 t o 7. 1 fo r 9 th e highe r

SE S case . Th e r

value s fo r

regression s of

fitte dvalue s versu s encode dvalue s wer e generall y aroun d0.9 9 fo r th e lowe r

SE S case , an dslightl y les s tha n0.9 9 fo r th e highe r SE S case . C.3. 6 Exper tK Exper t K provide dprobabilisti c judgment s o nal l thre e I Q variables
. Norma l distribution s provide dth e bes t fit s t o al l of

th e judgments
. Th e mea nvalue s of th e fitte d IQ distribution s wer e 85. 0 an d104.9 , an dth e mea nvalue s of th e fi t standar ddeviatio n distribution s wer e 12. 6 an d13.5
. Meanvalue s of th e distribution s fi t

t o th e judgment s o n IQ decrement s range dfro m1. 3 t o 10. 4 fo r th e lowe r

SE S case , an dfro m1. 3 t o 6 fo r th e highe r SE S case . Th e r

value s fo r

regression s of

fitte dvalue s versu s encode dvalue s wer e generall y aroun d0.9 9 fo r bot hof th e SE S cases .P. 6 19 7 C.3. 7 Compariso n o f

Judgment s and Fitte d Function s Tabl e C. 7 summarize s an dcompare s encode djudgment s an dcorrespondin g point s o n th e function s fi t

t o th e judgment s of

eac hof th e experts . Th e tabl e ca nb e furthe r use dt o compar e an dcontras t th e judgment s o f

th e differen t

experts . Many table s lik e thi s on e (on e pe r

cas e pe r

expert ) wer e use dt o hel p th e expert s understan dth e implication s of

thei r judgment s an dchoos e mathematica l function s tha t bes t represente d thos e judgments
. Th e mai npoin t

of th e tabl e i s tha t

th e fitte dfunction s matc hth e judgment s quit e well
. Th e fitte dmedia n value s generall y ar e quit e clos e t o th e assesse dmedia n values
. Thi s i s als o th e cas e fo r th e 50 % an d90 % credibl e intervals
. Fo r example , conside r th e judgment s of

Exper t G . Th e media njudgmen t fo r th e mea nT

Q leve l fo r unexpose dchildre n in th e lowe r SE S categor y i s 94 , an dth e media nof th e fitte d distributio ni s 94.6 . Th e encode dmedian s fo r I Q decremen t

ar e 0.5 , 1.5 , 3.0 , 3.5 , 5.0 , an d 7. 0 fo r Pb B level s of

5 , 15 , 25 , 35 , 45 , an d5 5 yg/dL , respectively
. Th e respectiv e median s o

f th e fitte ddistribution s ar e 0.6 , 1.4 , 2.7 , 3.9 , 5.7 , an d7.3 . Th e lowe r end s of th e 50 % credibl e interval s (th e 0.2 5 point s o nth e cumulativ e probabilit y curves ) ar e 0.3 , 0.7 , 1.3 , 2.5 , 4 , an d5 fo r th e encode djudgments , an d0.4 , 1 , 1.9 , 3 , 4.6 , an d5. 9 fo r th e fitte dfunctions
. Th e uppe r end s of th e 50 % credibl e interval s (th e 0.7 5 point s o n th e cumulativ e probabilit y curves ) ar e 1 , 2 , 4 , 5 , 7 , an d1 0 fo r th e judgments , an d0.9 , 2 , 3 , 8 , 5 , 7 , an d9. 1 fo r

th e fitte dfunctions
. Exper t Fjudge dtha t

th e mea nIQ of

childre nsheltere dfro mlea dshoul db e aroun d10 1 wit hahig hdegre e of certaint y (indicate db y astandar ddeviatio nof abou t 0.5)
. Th e othe r

expert s judge dtha t

th e mea nIQ woul db e on e t o thre e point s higher , o n th e average , bu t

wit hmuc hles s certaint y a s indicate db y standar ddeviation s fo r th e mea n IQ distributio n tha t range dfro m1. 5 t o 3.0 . Similarly , Exper t Fjudge dmuc h smalle r IQ decrement s attributabl e t o lea dexposur e tha ndi dth e othe r experts . Firs t judgment s wer e a t

Pb B level s of

2 5 yg/d Lfo r

Exper t F , 1 5 yg/d Lfo r

Exper t K, an d5 yg/d Lfo r th e othe r

experts .P. 7
19 8 Whil e thes e judgment s ar e interestin g inan dof themselves , the y tak e o nadde d meanin g whe n include din ahealt hris k assessment . Thus , th e result s of Sec . 5 provid e furthe r insigh t int o th e significanc e of th e difference s injudgment s amon g th e experts . C. 4 SUMMAR

Y DISCUSSIONS
C.4. 1 Summar

y o f Discussion s with ExpertF 1 . Low lea dlevel s (belo w 3 0 yg/d Lo r 4 0 yg/dL ) do no t

hav e a discernable , deleteriou s effec t o nIQ . Studie s tha t purpor t t o sho w suc ha n effec t

hav e methodologica l an dbia s problems
. 2 . Althoug hlo w lea dlevel s d o no t hav e independen t

effect s o nIQ , on e canno t

currentl y rul e ou t

th e possibilit y tha t

lea da t highe r level s interact s wit hothe r variable s t o affec t

IQ . Nor

ca nw e rul e ou t completel y th e possibilit y tha t IQ influence s lea dlevel
. Thes e variable s coul drelat e t o genera l healt hstatus , menta l healt hstatus , o r

othe r environmenta l factors
. 3 . Numerou s covariate s ar e associate dwit hlea dexposure , man y o f whic har e know n t o b e negativel y relate dt o IQ . I t i s difficul t

t o us e regressio n technique s t o determin e whic hof th e variable s ar e "causative. " 4 . Behavioral , social , an dcognitiv e measure s hav e som e degree s of unreliabilit y tha t

ad duncertaint y t o an y conclusions
. 5
. Cor dbloo dlea dmay b e relate dt o afe w negativ e birt houtcomes , bu t on e canno t

infe r directio nof

causalit y fro msuc hdata
. Perhap s adistresse dfetu s accumulate s lead
. 6 . Ther e i s afairl y stron g correlatio n(aroun d0.8 ) betwee nmaterna l bloo dlea dan dcor dbloo dlead
.P. 8 19 9 7 . Childre n ar e robus t an dca nrecove r

fro mmino r

disruption s in thei r cognitiv e development
. I t i s no t clea r t o wha t degre e the y ca nrecove r

fro mlarge r

disruptions
. Middle-clas s children , i n particular , migh t

b e abl e t o compensate . 8 . Th e availabl e evidenc e doe s no t indicat e wha t

i s th e threshol d leve l fo r I Q effect s of

lead
. 9 . Th e assumptio n of

norma l IQ distribution s withi nexposur e group s in ou r hypothetica l experimen t i s reasonable , excep t

tha t a t hig h lea dlevels , th e I Q distributio nma y b e skewe dnegatively , s o tha t th e percentag e of

childre nbelo w aspecifie dI Q leve l woul db e underestimated
. C.4. 2 Summar

y o f Discussion s with ExpertG 1 . IQ effect s of

lea do nlowe r

SE S childre nmay b e les s inEuropea n countrie s tha n in th e U.S. , becaus e th e educationa l an dhealt h disparitie s betwee n th e SES level s ar e probabl y les s inthes e countrie s tha n in th e U.S . 2 . Ther e ar e n o dat at o sugges t tha t physiologica l respons e t o lea d varie s a s afunctio n of

SE S level
. 3 . Th e effect s o f

lea do nth e developin g centra l nervou s syste mar e probabl y lon g lastin g an dno t reversible
. 4 . I f ther e i s athreshol dfo r I Q effect s of

lead , i t i s ver y low
. 5
. Anima l model s fo r ris k assessmen t

ar e limite dinusefulness , becaus e of

th e difficult y inextrapolatin g t o human s i na quantitativ e manner . Thei r importanc e i s instudyin g mechanism s of lea deffect s an dothe r importan t

topic s (e.g. , reversibilit y of effect s an dvulnerabl e period s o f development) , no t

inP. 9
20 0 establishin g dose-respons e relationship s directl y applicabl e t o humans
. 6 . Specifi c neurobehaviora l effect s o f lead , suc ha s attentiona l deficits , shoul dno t

b e overlooked
. 7 . Th e assumptio n of

normall y distribute dI Q score s withi nexposur e group s in ou r

hypothetica l experimen t i s reasonable
. C.4. 3 Summar

y o f Discussion s wit h ExpertH 1 . Lea dinteract s wit hothe r factor s init s effec t

o nIQ . Thes e factor s includ e SES , materna l stimulation , an dnutrition
. 2 . Th e concep t

of critica l developmenta l period s i s crucia l i n understandin g th e effect s of lead
. Whe

nopportunitie s fo r intellectua l developmen t ar e lost , i t

i s ver y har dt o compensat e later
. Thi s i s especiall y tru e inlowe r SE S children
. Furthermore , th e effec t

ca n snowball , i ntha t skill s generall y buil do neac h other
. 3 . Childre n wh o ar e expose dt o lea dals o ten dt o ge t mor e cadmium , pesticides , etc . Thi s i s especiall y tru e amon g lowe r SES children
. 4 . Ther e ar e n o dat ao nth e minimu mexposur e tim e necessar y t o produc e a n effect
. 5
. A t agive n dos e level , th e cumulativ e ar e wors e tha nth e immediat e effects
. Exposure s earlie r inlif e hav e mor e impac t tha n do exposure s late r

inlife
. 6 . Som e lea deffect s ar e reversibl e an dother s ar e not . 7 . Th e half-lif

e of lea dinth e brai ni s ver y long , base do nra t studie s b y Gar y Goldstei n a t

UCLA .P.1 0 20 1 8 . Som e recen t

researc hsuggest s tha t lea dma y b e involve din senility
. Specifically , th e amoun t of bon e lea dgoe s dow nwit h aging
. Th e questio n is , wher e doe s th e lea dgo ? I s i t eliminated , o r i s L t recirculate d(i nwhic hcas e i t may hav e neurobehaviora l effects) ? 9 . I t i s reasonabl e t o assum e tha t I Q score s ar e normall y distribute d withi n exposur e group s inou r hypothetica l experiment
. 10 . Ther e i s importan t an drelevan t

work b y Bernar dWeis s an db y Ket z tha t involve s behaviora l toxicology
. C.4. 4 Summar

y o f Discussion s wit h ExpertI 1 . Th e meta-analyse s occasionall y don e wit hth e studie s o nIQ effect s o f

lea dar e inappropriat e becaus e th e studie s diffe r i ns o man y ways , includin g differen t age s of

th e subjects , differen t sort s of contro l groups , differen t methods , an ddifferen t exposur e conditions
. 2 . I t i s reasonabl y certai ntha t ther e i s a nIQ effec t

of lea dabov e 3 0 yg/dL , bu t

les s clea r

abou t whethe r ther e i s a neffec t

a t lowe r levels
. 3 . Ther e i s a n exposure-sensitivit y interaction , intha t childre nwh o suffe r th e greates t

exposure s ten dt o b e thos e wh o ar e mos t susceptibl e t o th e effect s of lead
. 4 . Excep t

fo r hig hacut e exposures , neurobehaviora l effect s ar e mor e likel y t o resul t

fro mchroni c tha nfro macut e exposures . 5
. On e shoul ddistinguis hbetwee nbiologica l an dfunctiona l effect s of lead , bu t

i n eithe r

cas e ther e ar e n o dat asuggestin g tha t th e effect s ar e necessaril y irreversible
.P.1 1

20 2 6 . Th e dat aar e no t

clea r eithe r way wit hregar dt o th e questio nof whethe r ther e i s athreshol dfo r th e I Q effect s o f

lead
. C.4. 5 Summar

y o f Discussion s wit h Exper tJ 1 . Lea ddoe s hav e adeleteriou s effec t o nneurobehaviora l development
. I

n thi s regard , lea dinteract s wit hdie t an dSE S factors
. 2 . Middle-clas s childre nar e somewha t buffere dagains t

th e negativ e effect s of

lea db y virtu e of

thei r bette r diet , genera l healt h status , an driche r

intellectua l resources . 3 . Lea dcrosse s th e blood-brai nbarrier , an donc e i nth e cell s stay s there
. Thi s lea dcanno t b e chelate dou t

an daffect s th e neurotransmitters
. Th e effect s ar e irreversible
. 4 . Researc hwit hanimal s suggest s tha t lea dcause s demyelination
. I t i s no t clea r whethe r thi s effec t

woul doccu r

inchildren
. 5
. Th e implication s of th e EEGdat aar e no t clea r becaus e ther e i s uncertaint y a s t o wha t th e measure s refe r

an dbecaus e finding s ar e somewha t

inconsistent
. 6 . Althoug hsom e functiona l effect s o f lea dma y b e reversible , morphologica l effect s ar e not . 7 . Ther e i s probabl y n o threshol dfo r lea deffects ; i

f ther e i s one , i t i s ver y low
. Th e Germa nstudie s o nprimate s sugges t th e absenc e of athreshold
. 8 . Ther e may b e racia l difference s interm s of th e effect s of

lead
. However , thi s i s aver y complicate dissu e tha t remain s t o b e untangled
. 9 . Th e assumptio n tha t IQ score s ar e normall y distribute dwithi nP.1 2
20 3 exposur e group s i n ou r

hypothetica l experimen t i s reasonabl e wit h th e possibl e exceptio nof th e 55-yg/d Lgroup . C.4. 6 Summar

y o f Discussion s wit h ExpertK 1 . Childre n of

al l genotype s ar e vulnerabl e t o th e effect s of lead
. 2 . Som e neurobehaviora l effect s of lead , suc ha s th e effec t o n attentio n span , ar e reversible
. Thes e ar e generall y associate d wit hlo w level s of

exposure . Eve nsom e perinata l effect s ca nb e reverse dgive n prope r

treatment . 3 . Othe r

neurobehaviora l effect s ar e irreversible
. Thes e includ e morphologica l changes , a s wel l a s effect s o nsom e behavior s tha t depen do n critica l developmenta l periods
. (I s ther e evidenc e o r theor y tha t

allow s specificit y a s t o whic hbehavior s migh t b e irreversibl y affected , o r i s thi s t o b e take na s ageneralize d statemen t

tha t som e behavior s migh t

b e irreversibl y altered? ) 4 . Lea din th e rang e of 5-5 5 yg/d Lha s adeleteriou s effec t inth e presenc e of

othe r factors
. I

ntha t sense , lea dinteract s wit hothe r factors
. However , th e interactio ni s onl y inon e direction , s o tha t ausua l MANOV

A (multivariat e analysi s of variance ) woul dsho w bot ha n interactio n an damai neffect
. 5
. Som e of

th e factor s tha t

lea dinteract s wit har e physica l an d psychologica l hygiene , physiologica l status , parenta l IQ , nutritiona l an dhealt hstatus , organophosphates , an dpesticides
. 6 . Early , long-ter mexposur e t o lea dca nlea dt o long-ter meffects , whil e eposodi c exposur e i s mor e likel y t o lea dt o reversibl e effects , i f th e exposur e i s no t

to o great . 7 . Ther e i s athreshol dfo r I Q effect s o f

lead
.P.1 3

20 4 8 . Th e assumptio n tha t I Q score s ar e normall y distribute dwithi n exposur e group s in th e hypothetica l experimen t i s reasonable
.P. M
20 5 APPENDI

X D RIS KESTIMATE

S Thi s appendi x consist s mainl y of table s tha t

lis t th e function s an dth e parameter s tha t describ e th e ris k

estimate s fo r

lead-induce dEP , hemoglobin , an dI Q healt heffects
. Som e discussio n i s als o provide dt o explai nth e format s of th e tables
. Th e tabula r materia l ca n b e use dt o generat e dat afo r th e figure s presente dan ddiscusse di nSec . 5 , an dt o perfor madditiona l analyses
. Pb B distribution s ar e assume dt o b e lognorma l wit hgeometri c standar ddeviatio n (GSD ) 1.42 an dth e geometri c mea n(GM) value s liste dinTabl e D.l
. G M value s ar e tabulate dfo r

si x air-lea dscenario s a t eac hof 5 poin t source s of

lea demissions
. Th e si x air-lea dscenario s resul t fro m3 tim e period s (baseline , precontrol , an dpostcontro l periods) , eac hof

whic hhav e upper - an dlower-boun destimate s fo r th e GM . D. l ESTIMATE

S FORTH

E RISK S OF LEAD-INDUCED ERYTHROCYTE PROTOPORPHYRI

N EFFECT S AMON

G U.S . CHILDRE

N AGE D 0- 6 YEARS Probabilisti c dose-respons e function s fo r 2 E Plevel s considere dt o b e advers e (3 3 yxA< H av4 > 5 3 yg/dL ) wer e considere dinSec . 2 an dApp . A . W e calculate dth e overal l respons e rate s fo r

population s o f

childre nb y combinin g th e dose-respons e function s (whic har e specifie da t particula r

Pb B levels ) wit hPb B distributions
. I nth e simples t

of cases , th e probabilisti c dose-respons e function s wer e norma l probabilit y distribution s an d th e overal l ris k

resul t wa s als o norma l wit hmea n



### v = I 

### P^ i

an dstandar ddeviatio n

2 2-.1/ 2 

## a 

## - ( I 

## P^ )TABL E D. l Upper - and Lower-Boun d Estimate s o f th e Geometri c Mea

n Blood-Lea d Level s Childre n Livin g around Selecte d U.S . Source s o f Lea d Emissions 8

Sourc e 1 Sourc e 2 Sourc e 3 Sourc e 4 Sourc e 5 Ag e Lowe rUppe rLowe rUppe rLowe rUppe rLowe rUppe rLowe rUppe r

0- 3 y r 4- 6 y r 0- 6 y r 36t h month
0- 3 y r 4- 6 y r 0- 6 y r 36t h month 4. 8

2. 2 3. 7 3. 8 9. 5

5. 4 7. 7 9. 1 Baselin e Perio d 19. 1 14. 0 16. 9 18. 8 26. 6

20. 8 24. 1 26. 7 19. 9

14. 3 17. 2 19. 2 27. 0

21. 2 24. 5 27. 1 18. 7

13. 7 16. 6 18. 4 26. 2

20. 4 23. 7 26. 2 18. 7

13. 7 16. 6 18. 5 26. 2

20. 4 23. 7 26. 3 8. 6

6. 4 7. 7 7. 7 13. 9 11. 5 12. 9 13. 4

5. 2 2. 4 4. 0 4. 4 Precontro l Perio d 9. 9 5. 9 8. 2 9. 7 4. 7

2. 1 3. 6 3. 6 9. 1

5. 0 7. 3 8. 6 4. 6

2. 1 3. 5 3. 8 8. 6

4. 8 7. 0 8. 2 3. 3

2. 0 2. 7 2. 9 6. 7 5. 5 6. 2 6. 5 t o o

Postcontro l Perio

d 0- 3 y r 4- 6 y r 0- 6 y r 36t h mont h 1. 4

1. 0 1. 2 1. 3 3. 4

3. 2 3. 3 3. 4 1. 4

1. 1 1. 3 1. 3 3. 6

3. 4 3. 7 3. 7 1. 4

1.0 . 1. 3 1. 3 3. 4

3. 1 3. 4 3. 3 1. 4

1. 0 1. 2 1. 2 3. 1

2. 8 3. 0 3. 1 1. 4

1. 1 1. 3 1. 3 3. 7 3. 6 3. 7 3. 7

a Th e Pb B distributio n i s assume d t o be lognorma l wit h GS D = 1.4 2 an d the tabulate d G M values .P.1 6

20 7 wher e i denote s aPb B level , P j i s th e probabilit y of

Pb B leve l i , an dy

- an da- ar e th e mea n an dvarianc e of

th e EPdistributio na t

Pb B leve l i
. Thes e calculation s implicitl y assum e statistica l independence , anecessar y assumptio ntha t

w e wer e unabl e t o verify
. I nsom e cases , i t

was necessar y t o us e bet a distribution s in th e calculations
. Fortunately , inthos e case s th e fina l resul t wa s nearl y identica l t o th e dose-respons e functio na t aPb B o f

5 yg/dL
. Thi s occurre di nal l o f th e postcontro l scenario s an dmos t of th e precontro l scenario s becaus e modele dPb B level s wer e quit e low , (<1 0 yg/dL)
. Ris k result s fo r

EPar e tabulate dinTabl e D.2 . I nth e table , th e for m(eithe r norma l o r

beta) , th e expecte dvalue , an dth e standar ddeviatio nof eac hris k

distributio n ar e liste dfo r

th e tw o critica l E Plevel s specifie dabove
. Whenth e for mo f th e distributio n i s beta , th e value s o f th e parameter s ar e alway s a= 3 an db = 128 , whic h resul t in amea n of

2.3 % an dastandar ddeviatio nof 1.3% . D. 3 ESTIMATE

S OF TH E RISK S OF LEAD-INDUCED HEMOGLOBI N EFFECT S AMON G U.S . CHILDRE

N AGE D 0- 3 YEARS Calculatio n of

ris k estimate s fo r

lead-induce dhemoglobi neffect s i s inprincipl e identica l t o tha t

fo r EPrisks
. Th e onl y differenc e i s tha t normal-on-log-odd s (NOLO ) distribution s wer e foun dt o bes t represen t

th e judgment s of

th e expert s w e consulted , s o acomputatio n analogou s t o aconvolutio nintegra l ha dt o b e employed
. Numerica l method s wer e use dt o perfor mth e calculations , an di t wa s necessar y t o assum e statistica l independence
. Result s ar e liste di n Tabl e D.3 . Include dar e th e for m(norma l o r NOLO) , parameters , mean , an dstandar ddeviatio nof th e ris k distributions
. Al l of

thes e item s ar e provide dfo r

NOLO distribution s fo r th e reason s discusse dinApp . B . Th e parameter s of th e norma l distributio n ar e th e mea nan dstandar ddeviation , s o onl y th e latte r ar e liste dfo r norma l distributions
. Th e function s wer e determine dapplyin g linea r regressio nP.1 7 20 8 

### TABL E D.2 Specificatio n of

Distributions fo rth e Risk s o f Elevated E

PLevel s amon

g Childre n Age s 0- 6 Years

Seen ,

Lowe r Uppe r Lowe r Uppe r Lowe r Uppe r

Lowe r Uppe r Lowe r Uppe r Lowe r Uppe r

Lowe r Uppe r Lowe r Uppe r Lowe r Uppe r

Lowe r Uppe r Lowe r Uppe r Lowe r Uppe r iri o

Bas e Bas e Pr e Pr e Pos t Pos t

Bas e Bas e Pr e Pr e Pos t Pos t

Bas e Bas e Pr e Pr e Pos t Pos t

Bas e Bas e Pr e Pr e Pos t Pos t EP *

For m

Norma l Norma l Norma l Norma l Norma l Norma l

Norma l Norma l Norma l Norma l Norma l Norma l

Norma l Norma l Norma l Norma l Norma l Norma l

Norma l Norma l Norma l Norma l Norma l Norma l = 3 3 yg/d L

Mea n S.D. a
Sourc e 1 20.1 0 38.6 9 10.7 0 10.7 8 10.7 0 10.7 0 0.8 2

1.2 4 2.6 9 2.0 9 2.7 0 2.7 0 Sourc e 2 20.7 5 39.7 8 10.7 0 10.8 3 10.7 0 10.7 0 0.8 3

1.2 6 2.6 9 1.9 5 2.7 0 2.6 9 Sourc e 3 19.4 6 37.6 0 10.7 0 10.7 5 10.7 0 10.7 0 0.8 1

1.2 2 2.7 0 2.2 1 2.7 0 2.7 0 Sourc e 4 19.4 6 37.6 0 10.7 0 10.7 3 10.7 0 10.7 0 0.8 1

1.2 2 2.7 0 2.2 9 2.7 0 2.7 0 EP *

For m

Norma l Norma l Beta b Norma l Bet a Bet a

Norma l Norma l Bet a Norma l Bet a Bet a

Norma l Norma l Bet a Bet a Bet a Bet a

Norma l Norma l Bet a Bet a Bet a Bet a = 5 3 y

g Mea n

7.5 2 21.1 4 2.3 4 2.4 3 2.3 4 2.3 4

7.9 2 22.0 7 2.3 4 2.4 6 2.3 4 2.3 4

7.1 3 20.2 2 2.3 4 2.3 4 2.3 4 2.3 4

7.1 3 20.2 2 2.3 4 2.3 4 2.3 4 2.3 4 /dL S.D .

0.5 2 1.1 5 1.3 0 1.0 4 1.3 0 1.3 0

0.5 4 1.1 9 1.3 0 0.9 6 1.3 0 1.3 0

0.5 0 1.1 1 1.3 0 1.3 0 1.3 0 1.3 0

0.5 0 1.1 1 1.3 0 1.3 0 1.3 0 1.3 0P.1 8

20 9
TABL E D. 2 (Cont'd )

Scenari o

Lowe r Bas e Uppe r Bas e Lowe r Pr e Uppe r Pr e Lowe r Pos t Uppe r Pos t EP *

For m

Norma l Norma l Norma l Norma l Norma l Norma l = 3 3 yg/d L

Mea n S.D. a
Sourc e 5 10.7 8 13.4 5 10.7 0 10.7 1 10.7 0 10.7 0 2.0 9

0.8 9 2.7 0 2.4 7 2.7 0 2.6 9 EP *

For m

Norma l Norma l Bet a Bet a Bet a Bet a = 5 3 yg/d L

Mea n

2.4 3 3.7 4 2.3 4 2.3 4 2.3 4 2.3 4 S.D .

1.0 4 0.4 5 1.3 0 1.3 0 1.3 0 1.3 0

a Standar d Deviation . 'Fo r ever ybet a distribution , the parameter s value s ar e a = 3 an

d b = 128 , whic h result s i n the tabulate d mea n an d S.D . values .21 0

TABL E D. 3 Summar

y o f Hemoglobi n RiskDistribution s fo rChildre n Age d 0- 3 Year s P.1 9

Sourc e 1 , Hb * =9. 5
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PRE

LOWE R POS T
UPPE R POS T EXPERT

C D E C D E C D E C D E C ' E C E g/dL

M U Y -3.180 0 -3.694 5 -2.023 9 -2.974 1 -2.926 6 -1.721 4 -3.925 4 -8.745 7 -3.397 5 -3.638 5 -4.462 0 -2.741 5 -3.999 5 -3.782 0 -4.000 4 -3.782 9 SI G Y

0.156 7 0.167 1 0.475 2 0.143 3 0.187 9 0.428 3 0.223 7 0.351 8 0.736 3 0.177 0 0.284 5 0.555 9 0.276 4 0.960 0 0.276 4 0.960 0 MU R

0.040 4 0.024 6 0.125 2 0.049 0 0.051 6 0.159 4 0.019 8 0.000 2 0.040 8 0.026 0 0.011 9 0.068 3 0.018 7 0.033 1 0.018 6 0.033 0 SI G R

0.006 1 0.004 0 0.056 5 0.006 7 0.009 3 0.061 5 0.004 4 0.000 1 0.034 2 0.004 5 0.003 4 0.039 2 0.005 2 0.041 4 0.005 2 0.041 3 R SQ

R 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 1 P.2 0

Sourc e 2 , Hb * = 9. 5
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PRE

LOWE R POS T
UPPE R POS T EXPERT

C D E
C D E C D E C D E C E C E g/dL

M U Y -3.171 8 -3.663 0 -2.012 8
-2.967 1 -2.893 8 -1.707 8 -3.917 2 -8.192 6 -3.382 4 -3.611 8 -4.455 1 -2.688 0 -3.999 5 -3.782 0 -4.001 0 -3.783 6 SI G Y

0.157 0 0.167 5 0.474 1 0.144 4 0.189 0 0.429 0 0.223 6 0.351 9 0.735 7 0.180 2 0.284 4 0.560 0 0.276 4 0.960 0 0.276 4 0.960 0 MU R

0.040 7 0.025 3 0.126 4
0.049 4 0.053 3 0.161 2 0.020 0 0.000 3 0.041 4 0.026 7 0.011 9 0.071 8 0.018 7 0.033 1 0.018 6 0.033 0 SI G R

0.006 2 0.004 2 0.056 8
0.006 8 0.009 6 0.062 2 0.004 4 0.000 1 0.034 6 0.004 7 0.003 4 0.041 4 0.005 2 0.041 4 0.005 2 0.041 3 R SQ

R 1.000 0 1.000 0 1.000 0
1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABLE D. 3 (Cont'd ) 21 2 P.2 1

Sourc e 3 , Hb * = 9. 5
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PRE

LOWE R POS T
UPPE R POS T EXPERT

C D E C D E C D E C D E C E C E g/dL

M U Y -3.191 2 -3.737 6 -2.037 3 -2.982 3 -2.959 6 -1.733 7 -3.927 0 -8.898 0 -3.400 4 -3.664 2 -4.467 7 -2.795 9 -3.999 5 -3.782 0 -4.000 4 -3.782 9 SI G Y

0.156 8 0.166 9 0.476 1 0.143 0 0.186 8 0.427 6 0.223 7 0.351 8 0.736 5 0.174 3 0.284 5 0.552 8 0.276 4 0.960 0 0.276 4 0.960 0 MU R

0.039 9 0.023 6 0.123 8 0.048 7 0.050 0 0.157 7 0.019 8 0.000 1 0.040 7 0.025 3 0.011 8 0.064 9 0.018 7 0.033 1 0.018 6 0.033 0 SI G R

0.006 1 0.003 9 0.056 1 0.006 7 0.009 0 0.060 9 0.004 4 0.000 1 0.034 1 0.004 3 0.003 4 0.037 1 0.005 2 0.041 4 0.005 2 0.041 3 R SQ

R 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 3 P.2 2

Sourc e 4 , Hb * = 9. 5
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PRE

LOWE R POS T
UPPE R POS T EXPERT

C D E C D E C D E C D E C E C E g/dL

M U Y -3.191 2 -3.737 6 -2.037 3 -2.982 3 -2.959 6 -1.733 7 -3.928 3 -9.053 4 -3.403 0 -3.747 2 -5.780 3 -3.107 1 -3.999 5 -3.782 0 -3.999 9 -3.782 4 SI G Y

0.156 8 0.166 9 0.476 1 0.143 0 0.186 8 0.427 6 0.223 7 0.351 8 0.736 6 0.208 3 0.353 0 0.705 0 0.276 4 0.960 0 0.276 4 0.960 0 M

U R 0.039 9 0.023 6 0.123 8 0.048 7 0.050 0 0.157 7 0.019 8 0.000 1 0.040 6 0.023 5 0.003 3 0.052 5 0.018 7 0.033 1 0.018 6 0.033 1 SI G R

0.006 1 0.003 9 0.056 1 0.006 7 0.009 0 0.060 9 0.004 4 0.000 0 0.034 0 0.004 8 0.001 2 0.041 2 0.005 2 0.041 4 0.005 2 0.041 4 R SQ

R 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 4 P.2 3

Sourc e 5 , Hb * = 9. 5
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E
UPPE R PR E

LOWE R POS T
UPPE R POS T EXPERT

C D E C D E C E C D E C E C E g/d L

M U Y -3.747 2 -5.780 3 -3.107 1 -3.397 0 -4.232 6 -2.339 2 -4.000 2 -3.782 7 -3.862 8 -6.764 3 -3.302 6 -3.999 5 -3.782 0 -4.001 5 -3.784 0 SI G Y

0.208 3 0.353 0 0.705 0 0.198 1 0.223 0 0.576 2 0.276 4 0.960 0 0.218 6 0.352 2 0.713 8 0.276 4 0.960 0 0.276 4 0.959 9 M

U R 0.023 5 0.003 3 0.052 5 0.033 0 0.014 7 0.098 5 0.018 6 0.033 1 0.021 0 0.001 2 0.044 0 0.018 7 0.033 1 0.018 6 0.033 0 SI G R

0.004 8 0.001 2 0.041 2 0.006 4 0.003 3 0.057 6 0.005 2 0.041 4 0.004 6 0.000 4 0.035 3 0.005 2 0.041 4 0.005 2 0.041 3 R SQ

R 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 5 P.2 4

Sourc e 1 , Hb * = 11. 0
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PRE

LOWE R POS T

UPPE R POS T EXPER T

A C D E A C D E C D E C D E C D E C D E g/d L

MU Y -7.763 3 -2.019 1 -1.972 6 -1.721 6 -3.062 1 -1.793 2 -1.549 2 -1.536 1 -2.452 7 -3.027 4 -2.170 8 -2.309 0 -2.735 6 -1.998 2 -2.516 2 -3.174 7 -2.346 3 -2.517 1 -3.175 6 -2.347 3 SI G Y

0.653 0 0.155 0 0.262 5 0.318 4 0.508 7 0.140 9 0.249 3 0.288 5 0.221 1 0.388 8 0.471 6 0.171 7 0.297 6 0.358 7 0.272 0 0.491 9 0.599 1 0.272 0 0.491 9 0.599 1 MU R

0.000 5 0.118 2 0.124 9 0.156 1 0.049 8 0.143 5 0.178 0 0.180 9 0.080 7 0.049 3 0.110 3 0.091 4 0.063 1 0.124 4 0.076 9 0.044 5 0.098 7 0.076 8 0.044 5 0.098 6 SI G R

0.000 4 0.016 3 0.029 4 0.043 5 0.026 1 0.017 4 0.037 3 0.044 1 0.016 7 0.019 1 0.050 1 0.014 4 0.018 1 0.040 9 0.019 8 0.022 5 0.060 6 0.019 8 0.022 5 0.060 5 R SQR

0.999 7 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 6 P.2 5

Sourc e 2 , Hb * = 11. (
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PRE

LOWE R POS T

UPPE R POS T EXPERT

A C D E A C D E C D E C D E C D E C D E 3 g/dL

M U Y -7.674 5 -2.012 3 -1.952 8 -1.715 3 -3.060 2 -1.782 9 -1.534 4 -1.527 6 -2.449 3 -3.021 0 -2.168 1 -2.297 7 -2.704 8 -1.986 4 -2.516 2 -3.174 7 -2.346 3 -2.517 8 -3.176 3 -2.348 0 SI G Y

0.653 0 0.155 1 0.263 5 0.317 3 0.508 5 0.141 5 0.249 5 0.289 4 0.221 1 0.388 7 0.471 6 0.174 2 0.299 1 0.359 8 0.272 0 0.491 9 0.599 1 0.272 0 0.491 9 0.599 0 M

U R 0.000 6 0.118 9 0.127 0 0.156 8 0.049 9 0.144 8 0.180 2 0.182 1 0.081 0 0.049 6 0.110 5 0.092 3 0.065 0 0.125 7 0.076 9 0.044 5 0.098 7 0.076 8 0.044 5 0.098 5 SI G R

0.000 4 0.016 4 0.029 9 0.043 5 0.026 1 0.017 7 0.037 7 0.044 5 0.016 7 0.019 2 0.050 2 0.014 7 0.018 7 0.041 4 0.019 8 0.022 5 0.060 6 0.019 7 0.022 5 0.060 5 R SQ

R 0.999 7 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 7 P.2 6

Sourc e 3 , Hb * = 11. 0 g/d L
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PRE

LOWE R POS T

UPPE R POS T EXPERT

A C D E A C D E C D E C D E C D E C D E M

U Y -7.909 1 -2.028 6 -1.996 9 -1.729 5 -3.066 0 -1.803 8 -1.564 9 -1.543 9 -2.453 3 -3.028 6 -2.171 3 -2.320 6 -2.763 7 -2.008 1 -2.516 2 -3.174 7 -2.346 3 -2.517 1 -3.175 6 -2.347 3 SI G Y

0.652 9 0.155 0 0.261 0 0.319 4 0.509 1 0.140 5 0.248 9 0.287 4 0.221 1 0.388 8 0.471 6 0.170 1 0.296 4 0.358 3 0.272 0 0.491 9 0.599 1 0.272 0 0.491 9 0.599 1 MU R

0.000 5 0.117 2 0.122 2 0.155 1 0.049 7 0.142 2 0.175 8 0.179 7 0.080 7 0.049 2 0.110 2 0.090 4 0.061 5 0.123 3 0.076 9 0.044 5 0.098 7 0.076 8 0.044 5 0.098 6 SI G R

0.000 3 0.016 2 0.028 7 0.043 4 0.026 0 0.017 3 0.036 9 0.043 7 0.016 7 0.019 0 0.050 0 0.014 1 0.017 6 0.040 5 0.019 8 0.022 5 0.060 6 0.019 8 0.022 5 0.060 5 R SQ

R 0.999 7 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 3 (Cont'd ) 21 8

Sourc e 4 , Hb * = 11. 0 g/d L P.2 7

SCENARI O EXPERT M U Y SI G Y M U R SI G R R SQ R LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PR E

LOWE R POS T

UPPE R POS T A

C D E C D E C D E C D E C D E C D E 7o909 1

2.028 6 1.996 9 1.729 5 1.803 8 1.564 9 1.543 9 2.453 9 3.029 7 2.171 8 2.381 0 2.902 4 2.134 5 2.516 2 3.174 7 2.346 3 2.516 6 3.175 1 2.346 7 0.652 9

0.155 0 0.261 0 0.319 4 0.140 5 0.248 9 0.287 4 0.221 2 0.388 8 0.471 6 0.206 5 0.367 4 0.447 7 0.272 0 0.491 9 0.599 1 0.272 0 0.491 9 0.599 1 0.000 5

0.117 2 0.122 2 0.155 1 0.142 2 0.175 8 0.179 7 0.080 7 0.049 2 0.110 2 0.086 0 0.055 0 0.113 0 0.076 9 0.044 5 0.098 7 0.076 9 0.044 5 0.098 6 0.000 3

0.016 2 0.028 7 0.043 4 0.017 3 0.036 9 0.043 7 0.016 7 0.019 0 0.050 0 0.016 5 0.019 9 0.048 2 0.019 8 0.022 5 0.060 6 0.019 8 0.022 5 0.060 6 0.999 7

1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL E D. 3 (Cont'd ) 21 9

Sourc e 5 , Hb * = 11. 0 g/d L P.2 8

SCENARI O EXPERT M U Y SI G Y MU R SI G R R SQ R LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PRE

LOWE R POS T

UPPE R POS T C

D E C D E C D E C D E C D E C D E 2.381 0

2.902 4 2.134 5 2.183 2 2.420 2 1.901 3 2.516 9 3.175 4 2.347 0 2.425 4 2.982 9 2.150 9 2.516 2 3.174 7 2.346 3 2.518 3 3.176 7 2.348 5 0.206 5

0.367 4 0.447 7 0.193 4 0.322 1 0.401 4 0.272 0 0.491 9 0.599 1 0.219 6 0.381 9 0.468 6 0.272 0 0.491 9 0.599 1 0.272 0 0.491 9 0.599 0 0.086 0

0.055 0 0.113 0 0.102 6 0.084 9 0.136 4 0.076 9 0.044 5 0.098 6 0.082 8 0.051 3 0.112 1 0.076 9 0.044 5 0.098 7 0.076 8 0.044 4 0.098 5 0.016 5

0.019 9 0.048 2 0.018 0 0.025 9 0.050 1 0.019 8 0.022 5 0.060 6 0.016 9 0.019 4 0.050 4 0.019 8 0.022 5 0.060 6 0.019 7 0.022 5 0.060 5 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0P.2 9
22 0 technique s t o th e result s of th e convolutio nstep . Th e regressio nr-squar e value s wer e abou t equa l t o 1 in mos t

cases , s o the y ar e no t liste dinthi s table
. Suc hhig hr-squar e value s resulte dfo r

tw o reasons . First , i nth e cas e of alo w Pb B scenario , th e dose

respons e functio n fo r

Pb B = 5 yg/d Lessentiall y becam e th e overal l result
. I nhighe r Pb B scenarios , th e distribution s ten dt o becom e normal
. D. 4 ESTIMATE

S OF TH E RISK S OF LEAD-INDUCED I Q EFFECT S AMON

G U.S . CHILDRE

N AGED 7 YEARS Tw o I Q healt heffect s wer e considered , I Q decremen t an dth e increase d probabilit y of

havin g IQ value s les s tha nspecifie dcritica l levels
. A critica l leve l i s denote db y IQ* . Calculation s fo r th e ris k of IQ decrement s ar e quit e simpl e an dsimila r t o bot hth e E Pan dhemoglobi n ris k calculations
. The y followe ddirectl y fro mth e encode djudgment s of

th e expert s regardin g IQ decrement
. Calculatio nof risk s of th e secon dtyp e i s muc hmor e complicate dan dinclude s uncertaint y in : th e mea nI Q of population s of

childre n sheltere dfro mlea dexposure , within-grou p standar ddeviation , an dIQ decrement s amon g childre nexpose dt o lead
. Th e probabilisti c judgment s of expert s regardin g thes e quantitie s wer e obtaine dfo r bot hlowe r

an dhighe r

SE S populations
. Th e spiri t

of th e calculatio ni s a s follows
. Numerica l method s wer e use dt o perfor mth e calculations
. Th e firs t ste p wa s t o chang e eac hprobabilit y densit y functio nint o adiscret e probabilit y mas s functio nwit ha reasonabl e numbe r

of points
. Conside r

jus t on e exper t

fo r th e moment . Fo r

ever y combinatio nof

mea n IQ , standar ddeviation , an dI Q decrement , adistributio nfo r th e increase dprobabilit y of havin g IQ value s < IQ * wa s calculate da t eac hPb B leve l fo r whic hIQ decremen t

judgment s wer e obtained
. Distributio nfunction s (eithe r norma l o r NOLO ) wer e fi t

t o th e result s t o facilitat e furthe r calculations
. A t

thi s point , th e calculation s becam e quit e simila r t o thos e fo r

EP , hemoglobin , an dexpecte dIQ decrement
. Thes e distribution s wer e combine dwit haPb B distribution , agai nusin gP.3 0
22 1 numerica l method s analogou s t o aconvolutio nintegral , t o produc e a noveral l ris k distributio nfo r

aparticula r

SE S group . I

f desired , thes e distribution s ca nals o b e combine dacros s SE S t o produc e furthe r ris k distribution s base do nth e judgment s of eac h expert . Tabl e D. 4 list s relevan t informatio nabou t

th e I Q decremen t

ris k distributions , an dTab
. D. 5 list s relevan t informato nabou t

th e increase dprobabilit y of childre nhavin g I Q level s < IQ* .22 2

TABL E D. 4 Summar

y o f Distribution s fo rExpecte d I Q Decremen t a tAg e 7 fo rLowe rSE S Population s o f Childre n P.3 1

Sourc e 1 , Expecte

d IC , SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H I J K G H I J K G H I J K G H I J K G H J G H I J K Decrement

MU R Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l M

U Y

- 0 0

- 6

- 0 0

- 0 0

- 7 .481 6 .826 8 .165 8

.481 6 .826 8 .481 6 .826 8 .264 4 SI G Y

0 0 0

0 0 0 0 0 .642 2 .408 7 .531 5

.642 2 .408 7 .642 2 .408 7 .531 5 M

U A I Q 2.287 5 4.578 6 1.646 0 4.161 0 1.994 0 3.314 5 6.023 8 2.856 6 5.397 4 3.114 3 0.759 3 2.485 1 0.002 1 2.404 5 0.003 2 1.097 4 2.988 5 0.330 7 2.817 5 0.495 3 0.759 3 2.485 1 2.401 8 0.759 3 2.485 1 0.000 7 2.402 7 0.001 1 S D A I Q

0.779 4 1.116 3 0.457 9 0.825 4 0.444 3 0.882 3
• 1.142 4 0.604 6 0.791 7 0.562 9 0.542 5 1.059 6 0.001 2 0.886 5 0.001 1 0.487 6 0.882 5 0.176 4 0.704 9 0.162 3 0.542 5 1.059 6 0.888 7 0.542 5 1.059 6 0.000 4 0.887 9 0.000 4TABL

E D. 4 (Cont'd ) 22 3 P.3 2

Sourc e 2 , Expecte

d
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H I J K G H I J K G H I J K G H I J K G H J G H I J K I Q Decrement

M U R Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l MU Y

-0.481 6 0.826 8

-0.481 6 0.826 8 -0.481 6 0.826 8 -6.437 8 SI G Y

0.642 2 0.408 7

0.642 2 0.408 7 0.642 2 0.408 7 0.531 5 M

U A I Q 2.340 0 4.648 9 1.708 0 4.220 7 2.052 2 3.363 7 6.099 1 2.914 4 5.461 7 3.166 9 0.759 3 2.485 1 0.006 8 2.410 6 0.010 5 1.166 5 3.088 8 0.400 0 2.901 0 0.594 8 0.759 3 2.485 1 2.401 8 0.759 3 2.485 1 0.001 6 2.403 9 0.002 5 S D A I Q

0.787 2 1.114 1 0.467 3 0.821 9 0.454 1 0.879 6 1.142 9 0.608 1 0.787 8 0.562 1 0.542 5 1.059 6 0.004 0 0.881 5 0.003 6 0.509 1 0.900 9 0.207 6 0.709 5 0.191 0 0.542 5 1.059 6 0.888 7 0.542 5 1.059 6 0.000 9 0.887 0 0.000 922 4

TABL E D. 4 (Cont'd )
Sourc e 3 , Expecte

d I Q Decrement P.3 3

SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H I J K G H I J K G H I J K G H I J K G H J G H I J K MU R Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l . Lognorma l Lognorma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l MU Y

- 0 0

- 6

- 0 0

- 0 0

- 7 .481 6 .826 8 .725 4

.481 6 .826 8 .481 6 .826 8 .600 9 S3

0 0 0

0 0 0 0 0 [ G Y

.642 2 .408 7 .531 5

.642 2 .408 7 .642 2 .408 7 .531 5 M

U A I Q 2.235 6 4.509 5 1.584 9 4.102 3 1.935 8 3.258 9 5.943 9 2.791 9 5.327 8 3.053 7 0.759 3 2.485 1 0.001 2 2.403 4 0.001 9 1.038 4 2.902 0 0.272 1 2.745 4 0.409 5 0.759 3 2.485 1 2.401 8 0.759 3 2.485 1 0.000 5 2.402 5 0.000 8 S D A I Q

0.771 3 1.117 7 0.448 6 0.828 2 0.434 4 0.882 0 1.140 8 0.599 6 0.794 1 0.561 6 0.542 5 1.059 6 0.000 7 0.887 4 0.000 7 0.476 0 0.879 6 0.147 8 0.711 3 0.136 0 0.542 5 1.059 6 0.888 7 0.542 5 1.059 6 0.000 3 0.888 1 0.000 3TABL

E D. 4 (Cont'd ) 22 5

Sourc e 4 , Expecte

d
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H It-i K G H It-i K G H I J K G H I J K G H J G H I J K I Q Decremen t

M U R Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l Norma l Norma l Norma l . Norma l Norma l Lognorma l Lognorma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l M

U Y

-0.481 6 0.826 8 -6.165 8

-0.481 6 0.826 8 -0.481 6 0.826 8 -8.111 7 SI G Y

0.642 2 0.408 7 0.531 5

0.642 2 0.408 7 0.642 2 0.408 7 0.531 5 M

U A I Q 2.247 0 4.526 4 1.598 3 4.116 4 1.948 6 3.270 1 5.960 1 2.805 0 5.341 9 3.066 0 0.759 3 2.485 1 0.002 1 2.404 5 0.003 2 0.996 9 2.840 7 0.230 9 2.694 5 0.349 0 0.759 3 2.485 1 2.401 8 0.759 3 2.485 1 0.000 3 2.402 2 0.000 4 S D A I Q

0.771 6 1.117 2 0.449 5 0.827 5 0.435 2 0.882 1 1.141 2 0.600 7 0.793 6 0.561 9 0.542 5 1.059 6 0.001 2 0.886 5 0.001 1 0.472 9 0.886 3 0.127 4 0.722 3 0.117 1 0.542 5 1.059 6 0.888 7 0.542 5 1.059 6 0.000 2 0.888 4 0.000 2TABLE D. 4 (Cont'd ) 22 6 P.3 5

Sourc e 5 , Expecte

d I C
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H I J K G H I J K G Ht-i K G H I J K G H J G H I J K Decrement

MU R Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Norma l Norma l Norma l Norma l Norma l Norma l Norma l Lognorma l Lognorma l Norma l Lognorma l Lognorma l Lognorma l Norma l Norma l MU Y

-0.481 6 0.826 8

-0.481 6 0.826 8 -0.481 6 0.826 8 -6.437 8 SI G Y

0.642 2 0.408 7

0.642 2 0.408 7 0.642 2 0.408 7 0.531 5 M

U & I Q 0.946 4 2.765 7 0.181 1 2.632 3 0.274 7 1.610 3 3.699 1 0.866 4 3.413 9 1.197 7 0.759 3 2.485 1 2.402 0 0.000 2 0.847 7 2.618 2 0.084 5 2.509 9 0.128 8 0.759 3 2.485 1 2.401 8 0.759 3 2.485 1 0.001 6 2.403 9 0.002 5 S D a I Q

0.475 3 0.904 7 0.101 2 0.743 4 0.093 1 0.674 6 1.107 6 0.344 7 0.835 7 0.320 6 0.542 5 1.059 6 0.888 5 0.000 1 0.501 7 0.974 0 0.048 3 0.808 4 0.044 4 0.542 5 1.059 6 0.888 7 0.542 5 1.059 6 0.000 9 0.887 0 0.000 9P.3 6

22 7 TABL E D. 5 Summar

y o f Distribution s fo rIncrease d Probability o f IQ<IQ * a tAg e 7 fo rLowe rSE S Population s o f Childre n
Sourc e 1 , IQ * = 7 0
SCENARI O EXPERT LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T G

Ht_i K G Hti K G Ht_i G H<-> K G Ht_i G H J M

U Y -3.713 7 -3.423 8 -3.319 8 -3.197 9 -3.263 6 -2.982 2 -2.928 2 -2.635 7 -5.414 8 -4.767 0 -4.423 1 -4.616 2 -4.105 8 -3.893 2 -3.798 4 -5.412 3 -4.764 5 -4.420 6 -5.413 2 -4.765 4 -4.421 5 SI G Y

0.346 9 0.382 3 0.295 0 0.368 5 0.300 0 0.336 6 0.244 2 0.274 7 0.760 8 0.770 6 0.665 1 0.434 6 0.456 0 0.376 9 0.465 0 0.760 8 0.770 6 0.665 2 0.760 8 0.770 6 0.665 1 M

U R 0.025 2 0.033 7 0.036 3 0.041 6 0.038 3 0.050 6 0.052 1 0.068 9 0.005 9 0.011 2 0.014 6 0.010 7 0.017 9 0.021 3 0.024 2 0.005 9 0.011 2 0.014 7 0.005 9 0.011 2 0.014 7 SI G R

0.008 8 0.013 0 0.010 6 0.015 3 0.011 4 0.016 7 0.012 3 0.018 1 0.005 2 0.010 1 0.010 8 0.004 9 0.008 5 0.008 2 0.011 7 0.005 2 0.010 1 0.010 9 0.005 2 0.010 1 0.010 9 R SQ

R 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 5 (Cont'd ) 22 8

Sourc e 2 , IQ * = 7 0
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PRE

LOWE R POS T

UPPE R POS T EXPERT

G H J K G H J K G H J G HLj K G H J G H J M

U Y -3.687 7 -3.402 0 -3.299 4 -3.170 9 -3.247 1 -2.962 8 -2.910 5 -2.615 7 -5.420 6 -4.772 8 -4.429 0 -4.543 4 -4.056 0 -3.855 8 -3.785 1 -5.412 3 -4.764 5 -4.420 6 -5.414 3 -4.766 4 -4.422 5 SI G Y

0.345 1 0.381 2 0.292 8 0.367 4 0.299 5 0.336 5 0.243 4 0.272 9 0.760 7 0.770 6 0.665 1 0.437 0 0.460 0 0.377 0 0.466 4 0.760 8 0.770 6 0.665 2 0.760 8 0.770 6 0.665 1 M

U R 0.025 8 0.034 4 0.037 0 0.042 7 0.038 9 0.051 5 0.052 9 0.070 2 0.005 8 0.011 1 0.014 5 0.011 5 0.018 8 0.022 1 0.024 5 0.005 9 0.011 2 0.014 7 0.005 9 0.011 2 0.014 6 SI G R

0.009 0 0.013 2 0.010 7 0.015 6 0.011 5 0.017 0 0.012 4 0.018 2 0.005 2 0.010 0 0.010 8 0.005 2 0.009 0 0.008 5 0.011 9 0.005 2 0.010 1 0.010 9 0.005 2 0.010 1 0.010 8 R SQR

1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 5 (Cont'd ) 22 9 P.3 8

Sourc e 3 , IQ * = 7 0
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H J K G H J K G H J G H J K G H J G H J M

U Y -3.875 5 -3.597 8 -3.446 8 -3.263 3 -3.281 9 -3.003 5 -2.946 7 -2.658 7 -5.413 8 -4.766 0 -4.422 1 -4.864 5 -4.335 4 -4.067 0 -5.229 1 -5.412 3 -4.764 5 -4.420 6 -5.413 0 -4.765 1 -4.421 2 SI G Y

0.438 1 0.482 0 0.370 7 0.386 1 0.299 4 0.336 5 0.244 4 0.275 9 0.760 8 0.770 6 0.665 1 0.550 4 0.577 2 0.478 1 0.580 2 0.760 8 0.770 6 0.665 2 0.760 8 0.770 6 0.665 1 M

U R 0.022 2 0.029 6 0.032 8 0.039 3 0.037 7 0.049 6 0.051 2 0.067 5 0.005 9 0.011 2 0.014 6 0.008 9 0.015 1 0.018 8 0.006 3 0.005 9 0.011 2 0.014 7 0.005 9 0.011 2 0.014 7 SI G R

0.010 0 0.014 8 0.012 2 0.015 2 0.011 1 0.016 4 0.012 1 0.017 8 0.005 2 0.010 1 0.010 8 0.005 2 0.009 4 0.009 4 0.004 0 0.005 2 0.010 1 0.010 9 0.005 2 0.010 1 0.010 9 R SQ

R 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL E D. 5 (Cont'd ) 

### 23 0

Sourc e 4 , IQ * = 7 0 P.3 9

SCENARI O EXPER T MU Y SI G Y MU R SI G R R SQ R
LOWE R

UPPE R

LOWE R

UPPE R

LOWE R

UPPE R BAS E

BAS E

PR E

PR E

POS T

POS T G H J K G H J K G H J G H J K G H J G H J -3.734 7 -3.440 1 -3.333 4 -3.219 6 -3.278 4 -2.999 5 -2.943 1 -2.653 9 -5.414 8 -4.767 0 -4.423 1 -4.902 7 -4.357 3 -4.086 7 -5.378 8 -5.412 3 -4.764 5 -4.420 6 -5.412 7 -4.764 8 -4.420 9 0.348 1

0.383 1 0.296 9 0.368 3 0.299 6 0.336 4 0.244 2 0.275 6 0.760 8 0.770 6 0.665 1 0.550 9 0.575 9 0.481 0 0.579 7 0.760 8 0.770 6 0.665 2 0.760 8 0.770 6 0.665 1 0.024 7

0.033 2 0.035 8 0.040 8 0.037 8 0.049 8 0.051 3 0.067 8 0.005 9 0.011 2 0.014 6 0.008 5 0.014 8 0.018 4 0.005 4 0.005 9 0.011 2 0.014 7 0.005 9 0.011 2 0.014 7 0.008 7

0.012 8 0.010 5 0.015 0 0.011 2 0.016 5 0.012 1 0.017 8 0.005 2 0.010 1 0.010 8 0.005 1 0.009 2 0.009 3 0.003 4 0.005 2 0.010 1 0.010 9 0.005 2 0.010 1 0.010 9 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 5 (Cont'd ) 23 1

Sourc e 5 , IQ * = 7 0 P.4 0

SCENARI O EXPERT M U Y SI G Y M U R SI G R R SQ R
LOWE R

UPPE R

LOWE R

UPPE R

LOWE R

UPPE R BAS E

BAS E

PRE

PRE

POS T

POS T G

H J K G H•-> K G HCj G H J K G H J G H J -4.9*8 1 -4.385 2 -4.113 8 -5.609 2 -4.273 9 -3.841 9 -3.696 2 -3.696 5 -5.412 5 -4.764 6 -4.420 7 -5.045 3 -4.433 0 -4.144 6 -6.352 6 -5.412 3 -4.764 5 -4.420 6 -5.414 3 -4.766 4 -4.422 5 0.553 4

0.576 0 0.485 5 0.579 1 0.480 5 0.489 3 0.411 5 0.460 9 0.760 8 0.770 6 0.665 2 0.567 2 0.585 3 0.505 7 0.577 7 0.760 8 0.770 6 0.665 2 0.760 8 0.770 6 0.665 1 0.008 2

0.014 4 0.018 0 0.004 3 0.015 3 0.023 5 0.026 2 0.026 7 0.005 9 0.011 2 0.014 7 0.007 5 0.013 8 0.017 6 0.002 1 0.005 9 0.011 2 0.014 7 0.005 9 0.011 2 0.014 6 0.004 9

0.009 0 0.009 1 0.002 7 0.007 7 0.012 0 0.011 0 0.012 7 0.005 2 0.010 1 0.010 9 0.004 6 0.008 8 0.009 4 0.001 3 0.005 2 0.010 1 0.010 9 0.005 2 0.010 1 0.010 8 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 5 (Cont'd ) 23 2 P.4 1

Sourc e 1 , IQ * = 8 5
SCENARI O EXPERT LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PR E

LOWE R POS T

UPPE R POS T G

H J K G H J K G H J G H J K G H J G H J M

U Y -2.680 5 -1.874 6

-2.262 5 -1.506 3

-4.235 4 -2.886 0 -3.519 2 -2.448 9

-4.232 8 -2.883 4 -4.233 7 -2.884 3 SI G Y

0.297 7 0.278 6

0.258 1 0.247 1

0.705 8 0.518 2
0.384 0 0.315 5

0.705 8 0.518 2 0.705 8 0.518 2 M

U R 0.066 5 0.136 2 0.111 4 0.060 5 0.096 6 0.184 3 0.147 8 0.094 2 0.018 0 0.058 9 0.061 6 0.030 8 0.082 6 0.073 5 0.015 2 0.018 1 0.059 1 0.061 8 0.018 0 0.059 0 0.061 7 SI G R

0.019 0 0.033 7 0.023 2 0.013 7 0.023 0 0.038 0 0.023 1 0.017 1 0.014 4 0.031 3 0.023 7 0.011 9 0.024 7 0.019 1 0.005 2 0.014 4 0.031 4 0.023 7 0.014 4 0.031 3 0.023 7 R SQ

R 1.000 0 1.000 0

1.000 0 1.000 0

1.000 0 1.000 0
1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 5 (Cont'd ) 23 3

Sourc e 2 , IQ * = 8 5 P.4 2

SCENARI O EXPERT M U Y SI G Y M U R SI G R R SQ R LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T G

H J K G H J K G H J G H J K G H J G H J 2.655 4

1.856 3

2.245 0 1.489 3

4.241 3 2.892 2 3.454 2 2.406 7

4.232 8 2.883 4 4.234 8 2.885 4 0.295 5

0.277 2

0.256 8 0.246 7

0.705 7 0.518 0 0.383 3 0.318 0

0.705 8 0.518 2 0.705 8 0.518 2 0.068 0

0.138 3 0.113 0 0.062 2 0.098 1 0.186 8 0.149 8 0.095 7 0.017 9 0.058 6 0.061 3 0.032 7 0.085 8 0.075 8 0.018 2 0.018 1 0.059 1 0.061 8 0.018 0 0.059 0 0.061 6 0.019 2

0.034 0 0.023 1 0.013 9 0.023 2 0.038 3 0.023 1 0.017 1 0.014 3 0.031 1 0.023 5 0.012 7 0.025 8 0.019 3 0.006 1 0.014 4 0.031 4 0.023 7 0.014 4 0.031 3 0.023 7 1.000 0

1.000 0

1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0TABL E D. 5 (Cont'd ) 23 4

Sourc e 3 , IQ * = 8 5 P.4 3

SCENARI O EXPERT M U Y SI G Y M U R SI G R R SQ R LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T G

H J K G H J K G H J G H J K G H J G H J 2.811 2

1.983 1

2.281 3 1.524 7

4.234 3 2.885 0
3.727 0 2.586 8

4.232 8 2.883 4 4.233 5 2.884 0 0.373 8

0.345 5

0.258 7 0.246 9

0.705 8 0.518 2 0.487 7 0.390 7

0.705 8 0.518 2 0.705 8 0.518 2 0.060 1

0.125 7 0.107 3 0.057 0 0.095 0 0.181 6 0.145 8 0.092 4 0.018 0 0.059 0 0.061 7 0.026 2 0.074 3 0.070 6 0.012 0 0.018 1 0.059 1 0.061 8 0.018 1 0.059 1 0.061 7 0.022 0

0.039 6 0.023 2 0.013 4 0.022 7 0.037 5 0.023 1 0.017 1 0.014 4 0.031 3 0.023 7 0.013 3 0.028 2 0.019 1 0.004 3 0.014 4 0.031 4 0.023 7 0.014 4 0.031 4 0.023 7 1.000 0

1.000 0

1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0TABL

E D. 5 (Cont'd ) 235 P.4 4

Sourc e 4 , IQ * = 8 5
SCENARI O LOWE R BAS E

UPPE R BAS E

LOWE R PRE

UPPE R PR E

LOWE R POS T

UPPE R POS T EXPERT

G H J K G H J K G H J G H J K G H J G H J M

U Y -2.699 0 -1.890 1

-2.277 5 -1.521 0

-4.235 4 -2.886 0 -3.763 1 -2.609 4

-4.232 8 -2.883 4
-4.233 2 -2.883 7 SI G Y

0.299 1 0.279 9

0.258 6 0.247 1

0.705 8 0.518 2 0.491 7 0.391 0

0.705 8 0.518 2
0.705 8 0.518 2 M

U R 0.065 3 0.134 5 0.110 1 0.059 2 0.095 3 0.182 1 0.146 2 0.092 8 0.018 0 0.058 9 0.061 6 0.025 4 0.072 8 0.069 4 0.010 3 0.018 1 0.059 1 0.061 8 0.018 1 0.059 1 0.061 7 SI G R

0.018 8 0.033 5 0.023 2 0.013 4 0.022 8 0.037 6 0.023 1 0.017 1 0.014 4 0.031 3 0.023 7 0.013 0 0.027 7 0.019 4 0.003 7 0.014 4 0.031 4 0.023 7 0.014 4 0.031 4 0.023 7 R SQ

R 1.000 0 1.000 0

1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 023 6

TABL E D. 5 (Cont'd )
Sourc e 5 , IQ * = 8 5 P.4 5

SCENARI O EXPERT M U Y SI G Y M U R SI G R R SQ R LOWE R BAS E

UPPE R BAS E

LOWE R PR E

UPPE R PR E

LOWE R POS T

UPPE R POS T G

H J K G H J K G H J G H J K G H J G H J 3.810 8

2.638 8

3.195 6 2.235 5

4.233 0 2.883 5 3.896 0 2.681 6

4.232 8 2.883 4 4.234 8 2.885 4 0.498 5

0.392 5

0.421 4 0.372 7

0.705 8 0.518 2 0.523 4 0.405 7

0.705 8 0.518 2 0.705 8 0.518 2 0.024 3

0.070 8 0.067 9 0.008 2 0.042 5 0.101 4 0.088 6 0.035 6 0.018 1 0.059 1 0.061 8 0.022 6 0.068 4 0.064 8 0.003 9 0.018 1 0.059 1 0.061 8 0.018 0 0.059 0 0.061 6 0.012 7

0.027 1 0.019 9 0.003 0 0.018 1 0.035 6 0.023 0 0.010 1 0.014 4 0.031 4 0.023 7 0.012 5 0.027 2 0.021 6 0.001 4 0.014 4 0.031 4 . 0.023 7 0.014 4 0.031 3 0.023 7 1.000 0

1.000 0

1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0

1.000 0 1.000 0 1.000 0 1.000 0