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### Document

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# 122)11-1-400
Docket Number: 

# A-83-2 2

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Sheet 122 of 162P. 2 

# •12^33 * 

# flj B 

# » mm

n \

Assessin g th e Risk

s t o Youn g Childre n o f Thre e Effect

s Associate d wit h Elevate d Blood-Lea d Level s (. \



# v. ^

T . S. Wallste n an d R

. G . Whitfiel d

Operate d b

y 

### TH E UNIVERSIT

Y O F CHICAG O lo r U . S . DEPARTMENT O F ENERG Y unde r Contrac

t W-31-10»-€ng-3 8P. 3

Argonne Nationa

l LaMmimy. vnnh fasiiEJe s in th e states o f

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d Idaho , is owned b y th e United States gevemmm , md operated b

y Th e Univenity o f

Chicago , unde rth e provisions @

f aesatrae tmih the Departmen to f Energy .



### = DISCLAIME

R This repor

twa s prepare d as s aaee@ua

to f wor k sponsored by a

n agenc y o f Eh e Uaste d Ssaig s Government. Neitherth e Unite d States Governmeu

anm am y agenc y thereof , noran y o f their employees , make

s an y warranty

0 express o rimplied , o rassumes an y lega l liabilit y 9 ? mponsibilit y forth e accuracy , com * pktenesSo o rusefulnes s @ f aay Information , apparatus , produa , o rproces s disclosed , o rrepresent s tha tit s use woul d no tinfringe privatel y owned rights. -Referenc e herei n t o an y specifi c com * mercia l produc e process , <as servic e by trade name , trademark, manufacturer, o ratherwist , doe s no tnecessarily constitute o r imply its endorsemen trecommendation , o rfavoring by th e Unite d States Govemmea

a@ ? an y agenc y thereof . Th e views an

d opinion s o f

author s expresse d herei n d o no tnecessaril

y state o r reflec tshos e @ f is g United States Governmen to ran y agenc y thereof .

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l taEfe e MJMiisi StoEe

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ANL/AA-3 2
ASSESSIN

G TH E RISK S T O YOUN G CHILDRE

N O F THRE E EFFECT S ASSOCIATE D WIT H ELEVATE

D BLOOD-LEAD LEVEL S

b y Thoma s S . Wallsten * an d Ronal d G . Whitfiel d Energy an

d Environmenta l System s Divisio n Decisio n Analysi s an

d System s Evaluatio n Sectio n

Decembe r198 6

wor k sponsore d b

y U.S . ENVIRONMENTA

L PROTECTION AGENCY Offic e o f Ai rQualit y Plannin g an d Standard s P. 4

• -Vf ""•-•-WTfaT'

*L.L . Thurston e Psychometri c Laboratory , Universit y o f Nort h Carolina , Chape l HillP. 5

CONTENT S
ACRONYM S ix SYMBOLS x ACKNOWLEDGMENTS ." * xi ABSTRAC T 1 1 INTRODUCTION 1 1. 1 Repor tOrganizatio n 2 1. 2 Motivatio n 2 1. 3 Judgmenta l Probabilit y Encodin g 5 1. 4 Dose-Respons e Uncertaint y 6 1. 5 Ris k Assessmen tStrateg y 6 2 PROBABILISTI C DOSE-RESPONS E FUNCTION S FO RLEAD-INDUCED ELEVATE

D E PLEVEL S 7 3 PROBABILISTI C DOSE-RESPONS E FUNCTION S FO RLEAD-INDUCED H b DECREMENT S 1 1 3. 1 Protoco l Developmen t1 1 3. 2 Protoco l Outlin e 1 2 3. 3 Conduc to f

th e Session s 1 3 3. 4 Encodin g th e Judgment s 1 3 3. 5 Representin g th e Judgment s 1 5 3. 6 Th e Expert s 1 7 3. 7 Result s 17 3.7. 1 H b Leve l < 1 1 g/dL , Age s 0- 3 . 1 8 3.7. 2 H b Leve l < 1 1 g/dL , Age s 4- 6 2 0 3.7. 3 H b Leve l < 9. 5 g/dL , Age s 0- 3 2 1 3.7. 4 H b Leve l < 9. 5 g/dL , Age s 4- 6 2 2 3. 8 Discussio n 2 3 4 PROBABILISTI C DOSE-EFFEC T AN D DOSE-RESPONS E FUNCTION S FO R LEAD-INDUCE D I

Q DECREMENT S 27 4. 1 Protoco l Developmen t2 8 4. 2 Protoco l Outlin e 3 0 4. 3 Conduc to f

th e Session s 3 0 4. 4 Encodin g th e Judgment s 3 1 4. 5 Representin g th e Judgment s 3 2 4. 6 The Expert s 3 2 4. 7 Result s 3 3 4.7. 1 Control-Grou p Mea n I Q 3 4 4.7. 2 Within-Group I

Q Standard Deviatio n 3 5 4.7. 3 Mea

n I Q Decrement s fo rth e Low SE S Grou p 3 6 4.7. 4 Mea

n I Q Decrement s fo rth e Hig h SE S Grou p 3 6

mP. 6 CONTENT S (Cont'd )
4.7. 5 Chang e in Percentag e of Low SE S Grou p wit h I Q < 8 5 37 ' 4.7. 6 Chang e i n Percentag e of Hig h SE S Grou p wit h I Q < 8 5 4 0 4. 8 Discussio n 4 1 5 "ESTIMATE

D RISK S O FADVERS E HEALT H EFFECT S VERSU S GEOMETRI C MEA N Pb B LEVE

L 4 3 5. 1 Estimate dPb B Distribution s 4 3 5. 2 Overvie w of

th e Ris k Result s fo r

E P 4 4 5. 3 Overvie w o f

th e Ris k Result s fo r

H b 4 5 5. 4 Overvie w o f

th e Ris k Result s fo r

I Q 4 5 5.4. 1 Ris k

Distribution s ove r

Mean I Q Decremen t

47 5.4. 2 Increase dProbabilit y of Lead-Induce dI Q Level s Bein g < IQ * 4 8 5. 5 Sensitivit y Analysi s 4 9 6 CONCLUDIN G REMARK S 5 1 REFERENCE S 5 2 APPENDI X A : Fittin g Function s t o Dat ao n Lead-Induce dElevate dE P

Level s 5 5 APPENDI X B : Fittin g Function s t o Encode dJudgment s Relatin g t o

Lead-Induce dH

b Decremen t

6 1 APPENDI X C : Fittin g Function s t o Encode dJudgment s Relatin g t o

Lead-Induce dI Q Effect s 10 1 APPENDI X D : Ris k

Distribution s 14 1

TABLE S
1 Probabilit y o f

Sufferin g aSpecifie dHealt h Effec t unde r Alternativ e NAAQS , Give n Complet e Informatio n 4 2 Probabilitie s o f

Sufferin g aSpecifie dHealt h Effec t unde r Alternativ e NAAQS , Give n Incomplet e Informatio n 5 3 Sampl e Size s fo r

th e EP Dat a9 4 Consultant s fo r

th e Hb Protoco l 1 2 5 Expert s Participatin g in th e H b Encoding s 1 7 6 Consultant s fo r

th e I Q Protoco l 2 9 7 Expert s Participatin g i n th e I Q Encoding s 3 3

i vP. 7

TABLE S (Cont'd )
A. l Probabilit y Distribution s an dParameter s fo r E P Level s amon g Ne w Yor k Cit y Childre n 5 8 B.l..Variable s Pertainin g t o th e NOLO Functio n .„ 7 5 B. 2 Encode dJudgment s abou t Populatio n Respons e Rate s fo r Lead-Induce d H b Decrement s 7 8 B. 3 Function s Fi t

t o Judgment s abou t

Populatio n Respons e Rate s fo r Lead-Induce dH

b Decrement s 8 3 B. 4 Compariso n o f

Judgment s an dFitte dFunction s Concernin g Populatio n Respons e Rate s fo r

Lead-Induce dHb Decrement s 8 6 C. l Encode dJudgment s abou t th e Mean I Q o f

Childre n Unexpose dt o Lea d11 6 C. 2 Encode dJudgment s abou t Populatio n Standar dDeviatio n 11 7 C. 3 Encode dJudgment s abou t Mea n I Q Decrement s o f

Childre n Expose dt o Lea d11 8 C. 4 Function s Fi t

t o Judgment s abou t

Mean I Q Level s amon g Childre n Unexpose dt o Lea d120 C. 5 Function s Fi t

t o Judgment s abou t

Populatio n Standar dDeviatio n fo r I Q Level s 12 1 C. 6 Function s Fi t

t o Judgment s abou t

Mea n I Q Decrement s amon g Childre n Expose dt o Lea d12 2 C. 7 Compariso n of

Judgment s an dFitte dFunction s Concernin g Lead-Induce d I Q Effect s 12 5 C. 8 Function s fo r

Respons e Rat e fo r

I Q Level s belo w 8 5 an d7 0
.. . 13 1 D. l Ris k Estimate s fo r

Lead-Induce dElevate dEP Levels , U.S
. Childre n Age d0- 6 14 5 D. 2 Ris k Estimate s fo r

Hb Level s < 9. 5 an dsl l g/dL , U.S
. Childre n Age d0- 3 an d4- 6 14 7 D. 3 Ris k Estimate s fo r

I Q Decrement , U.S
. Childre n Age d7 15 1 D. 4 Ris k Estimate s fo r

I Q Level s < 7 0 an d< 85 , U.S
. Childre n Age d 7 15 4

FIGURE S
1 Mea n Respons e Rat e vs . Dos e fo rE P > 3 3 yg/d L an d > 5 3 yg/d L 8P. 8
FIGURE S (Cont'd )
2 Media n Respons e Rat e an d90 % C I vs . Dos e fo r E P > 3 3 yg/d L
... . 9 3 Media n Respons e Rat e an d90> % C I vs . Dos e fo r

E P > 5 3 yg/d L 1 0 4 Dose-Respons e Functions , H b < 1 1 g/dL , Age s 0-3 , Exper t A .'.......
. 1 8 5 Dose-Respons e Functions , Hj b < 1 1 g/dL , Age s 0-3 , Expert s A , C , D , an dE 1 9 6 Compariso n o f

Judgments , H

b < 1 1 g/dL , Age s 0-3 , Expert s A , C , D , an dE 2 0 7 Dose-Respons e Functions , H b < 1 1 g/dL , Age s 4-6 , Expert s A , C , D , an dE 2 1 8 Compariso n of

Judgments , H

b < 1 1 g/dL , Age s 4-6 , Expert s A , C , D , an dE 2 2 9 Dose-Respons e Functions , H b < 9. 5 g/dL , Age s 0-3 , Expert s C , D , an dE 2 3 1 0 Compariso n o f

Judgments , H

b < 9. 5 g/dL , Age s 0-3 , Expert s A , C , D , an dE 2 4 1 1 Dose-Respons e Functions , H b < 9. 5 g/dL , Age s 4-6 , Expert s C , D , an dE 2 5 1 2 Compariso n o f

Judgments , H

b < 9. 5 g/dL , Age s 4-6 , Expert s A , C , D , an dE 2 6 1 3 Median Value s an d90 % CI s fior Function s Fi t

t o Judgment s abou t

th e Mean I Q of th e Contro l Group , Expert s F , G , H , J , an dK 3 4 1 4 Media n Value s an d90%-C l Judgment s abou t a, Q , Expert s F , G , H , J , an dK 3 5 1 5 Judgment s abou t

Lead-Induce dI Q Decrements , Lo w SE S Population , Expert s F , G , H , I , J , an dK 3 7 1 6 Compariso n of

Judgment s abou t

Lead-Induce dI Q Decrements , Lo w SE S Population , Expert s F , G , H , J , J , an dK 3 8 1 7 Judgment s abou t

Lead-Induce dI Q Decrements , Hig h SE S Population , Expert s F , G , H , I , J , an dK
... . 3 9 1 8 Compariso n o f

Judgment s abou t

Lead-Induce dI Q Decrements , Hig h SE S Population , Expert s F , G , H , I , J , an dK 4 0 1 9 Increase dProbabilit y o f Havin g I Q < 85 , Lo w SE S Population , Expert s F , G , H , J , an dK

4 1

v iP. 9 "TT''" ' T^IT *


### FIGURE S (Cont'd ) 2 0 Compariso n o

f Increase dProbability o

f Havin g I Q < 85 , Lo

w SE S Population , Expert s F , G , H , J , andK '.. 4 2 2 1 Ris k Result s fo r

th e Occurrenc e o

f E P Leve l > 5 3 yg/d

L .j
. 4 4 2 2 Risk Result s fo r

th e Occurrenc e o

f H b Leve l < 9. 5 g/dL amon g Childre n Aged0- 3 46 2 3 Risk Result s for

Mea n I Q Decremen t

i n Lo w SE S Childre n 4 7 2 4 Respons e Rate s for

I Q Leve l < 7 0 amon g Lo

w SE S Childre n 4 8

v i iP.1 0


### ACKNOWLEDGMENT

S
Thi s enterpris e ha

d it s origins i

n wor k fo rth e U.S . Environmenta l Protectio n Agenc y b y privat e consultant

s Thoma s Feagans an

d Willia m Biller , an

d thei rsuppor

tan d ideas were ver

y helpful . Joh

n Haine s an d Jef f Cohe n o f th e U.S . Environmenta l Protectio n Agenc

y provide d guidance throughou

tth e project . Theirsupport, as well a s thato f Thoma s McCurdy

, Harve y Richmond, Bruc

e Jordan, an

d others i

n th e Offic e o

f Ai rQualit y Plannin

g an d Standards , wa

s aconstan tsource o

f encouragement . Th

e assistanc e o

f two othe rgroup

s o f people , whose names appea ri n th e report , wa

s essentia l forcompletio n o

f thi s work : reviewers o f th e protocol s an

d th e 1 1 healt

h experts wh

o provide d judgment

s o n lead-induced healt

h effects . Th e author s als o exten d thei rappreciatio n to thos e a tArgonn e Nationa

l Laborator y wh o wer e instrumenta

l i n preparin

g thi s report . Mar

y Warre n greatl y improve d th e repor

ta s aresul tof

herthoroug

h editing . Christine Wegere rwrot e man y o f th e computerprograms . Barbar aSalbeg o prepare d th e manuscriptforpublication ; Mari e Ree d an d Louis e Kickels prepare

d earlie rdrafts . Th

e computer-generate d graphics wer

e th e wor k o f Lind aHaley . Thi s projectwa

s funde d throug h Interagenc

y AgreementDW89930551-01-02 betwee n the U.S . Departmen to f Energ y an d th e U.S . Environmenta

l Protectio n Agency .P.1 1

ACRONYM S

' ALAD 6-aminolevulini c aci ddehydras e ALA S 6-aminolevulini c aci dsynthas e C D criteri adocumen t CD Fcumulativ e distributio n functio n C I credibl e interva l CN S centra l nervou s syste m ECA O Environmenta l Criteri aAssessmen t Offic e EDT A ethylenediaminetetraacetat e EE G electroencephalogra m E P erythrocyt e protoporphyri n EP A U.S
. Environmenta l Protectio n Agenc y FE P fre e erythrocyt e protoporphyri n G M geometri c mea n GS D geometri c standar ddeviatio n H b hemoglobi n HERL Healt h an dEnvironmenta l Researc h Laborator y I Q intelligenc e quotien t NAAQ S Nationa l Ambien t Ai r Qualit y Standard(s ) NHANE S I

I secon dNationa l Healt h an dNutritio n Surve y NOL O normal-on-log-odd s OAQP S Offic e o f Ai r Qualit y Plannin g an dStandard s Pb B bloo dlea d PD Fprobabilit y densit y functio n PM Fprobabilit y mas s functio n SE S socioeconomi c statu s ZP P zin c protoporphyri n

I XP.1 2


### SYMBOL S E[R ] expecte d valu e o f R F : encode d cumulativ e probabilit y valu e F . cumulativ e probabilit y valu e tha tresult s fro m fittin g aregressio n -lin e t o 1 

### ase to f

dat a f(R ) probabilit y distributio n ove rR F(R ) cumulativ e probabilit y distributio n ove rR I Q mea n I

Q o f childre n sheltere d fro m lea d exposur e IQ * specifie d critica l leve l o f I Q L blood-lea d leve l I n natura l logarith m Rrespons e rate , o rpercentag e of apopulatio n experiencin g aspecifie d healt h effec t 2 . . . 

### rregressio n r-squar e statisti c SD[R ] standar d deviatio n o f R X odd s variable , X = R/(10 0 - R) ; i f X i s lognormall y distributed , Ri s normal-on-log-odd s distribute d Y log-odd s variable , Y = ln(X) ; i f Y i s normall y distributed , X i s lognormall y distribute d A-= Q mea n I Q decremen t y mea n o f

Y OJ Q within-grou p I Q standar d deviatio n
o ' estimat e o f o v

### obtaine d b y poolin g dat aacros s severa l blood-lea d level s
o standar d deviatio n o f Y
o varianc e o f Y y 

### •(X ) cumulativ e distributio n functio n fo rth e standardize d norma l rando m

variabl e

### ASSESSIN G TH E RISK S T O YOUN G CHILDRE

N O F THRE E EFFECT

S ASSOCIATE

D WIT H ELEVATE D BLOOD-LEA

D LEVEL S b y Thoma s S . Wallste

n an d Ronal d G . Whitfiel d
ABSTRAC

T
Forma l ris k assessments wer

e conducted a

s par to f th e U.S . Environmenta

l Protectio n Agency' s curren treview o

f th e primar

y Nationa l Ambien tAi rQualit y Standar d fo rlead . Th

e assessments focuse d o n thre e potentiall y advers e effect s o f exposur e t o lea d i

n children fro

m birt h throug h th e sevent

h birthday : erythrocyte protoporphyri

n (EP ) elevation , hemoglobi

n (Hb ) decrement , an

d intelligenc e quotient(IQ ) effect . Th

e same genera

l strateg y wa

s followe d i

n al l thre e cases : fortwo level s o f eac h effect , probabilit

y distributions ove rpopulatio n respons e rate wer

e estimate d ataserie s o f blood-lead (PbB) levels . Thes e distributions wer e estimate d fro

m dat ai n th e cas e o

f E Pelevatio n an

d fro m exper tjudgment

s i n th e case s o f H b decrementan

d I Q effect . Althoug

h o f interes ti

n thei r ow n right , thes e estimate s were combine d wit h Pb B distributions t o yiel d probabilit

y distributions ove rth e estimate d percentage s o f children experiencin g th e particularhealt h effects . 1 INTRODUCTIO

N
Th e Clea n AirActcharges th e U.S . Environmenta l Protectio n Agenc

y (EPA) * wit h settin g an

d reviewin g bot

h primar y an d secondar

y Nationa

l Ambien tAi rQualit y Standard s (NAAQS

) fo rselecte d pollutants . Eac h primar y standar d mus tb e se tataleve l sufficien tt o protec tpublic healt h wit h a n adequat

e margi n of safety . Thi

s repor t presents th e results o

f aris k assessmentperforme

d t o assis ti

n th e revie w o

f th e primar

y NAAQ S fo rlead . Fo reach review , th e scientifi c basi s fo rrevisin g the primar y lead NAAQ

S i s presente d i

n a n update d documen

tentitle d At

rQuality Criteria for

Lead (EPA , 1986a) , hereafte rreferre d t o a s th e criteri adocumen

t(CD) . I

tsummarizes an

d analyze s availabl e scientifi c evidenc e abou tth e advers e healt

h effect s o

f lead . Afte revaluatin g an d interpretin g th e information i n th e CD , adraf

tEP A staf f pape r(EPA , 1986b

) identifie s th e critica l element s thatEP A staf f believ e shoul

d b e considere d i

n th e review an d possibl e revisio n o

f th e lead NAAQS . Particularattentio n i s paid t o thos e subject
•Al l acronyms used i

n thi s repor

tar e liste d alphabetically o

n pp . i x an d x .P.1 4



### areas requiring judgment s based o n careful interpretatio n o f imperfectevidence . Indeed, t o provide th e required adequat e margi n of safety , uncertaint

y mus tb e taken int

o consideratio n a teach ste p o f th e process . Th

e information an

d recommendations in'th e staf f paperguid e th e EP

A Administrato ro

n alternativ e regulator

y approaches for controllin g atmospheri c lea d emissions . Scientifi c uncertaint

y wa s handle d i n ahighl y simplifie d manne

rwhe n th e 197 8 primar y NAAQ S forlea d wa

s set . Instea

d o f quantifying uncertainty , deterministi c assumptions wer

e mad e thatwer

e considere d conservativ e give n qualitativ e assessmen t o f th e uncertaint

y associate d wit

h availabl e evidence . Calculations based o n thes e assumptions resulte d i

n aprimar

y NAAQ S fo rlead o

f 1. 5 yg/ m o f air . Soo n thereafte r EPA' s Offic e o

f AirQualit

y Plannin

g an d Standard

s (OAQPS

) bega n explorin g ris

k assessmen tmethods thatincorporat e uncertaint

y into th e standard-settin g proces s i n a formal , defensible , an

d ope n manner . O f th e man y potentia l advers e healt h effect s associate d wit h exposure to lead , OAQP S selecte d thre e fo rinclusion i n thi s ris k assessment : hemoglobi n (Hb ) decrement , elevate d erythrocyte protoporphyri n (EP ) levels , an

d intelligenc e quotient(IQ ) effect . Th e population a

tris k fo rthi s ris

k assessmen twa

s limite d t o all U.S . children fro m birt h throug h thei rsevent

h birthdays . Constitutin g aforma l ris k assessmentregarding thes e thre e advers e healt

h effect s o

f lead , thi s repor

tshoul d aid i n th e curren

trevie w o

f th e primar y NAAQ S forlead . 1. 1 REPOR

T ORGANIZATIO

N T o th e exten tpossible , detail s o f th e methods an

d results o

f th e thre e ris

k assessments ar

e presente d i

n th e appendixes . Nevertheless , reader s wil l gai n agood understandin

g o f th e risk assessments fro m th e mai

n text . Sectio n 1.

2 presents th e reasons fo rchoosing th e particularfor m o f th e ris k assessments ; Sec . 1.

3 discusse s th e rol e o f judgmenta

l probabilit

y encoding i

n th e ris k assessments ; Sec . 1.

4 discusse s dose revwns e uncertainty ; an

d Sec. 1. 5 summarizes th e overal l ris k assessmentstrategy . Sectio n 2 treat s th e dose-respons e uncertaint y fo rlead-induce d elevate d E P levels . Becaus e relativel y complete datawere available , judgmenta l probabilit

y encoding wa s unnecessary . Section s 3 an d 4 focu s o

n th e dose-respons e uncertaint y fo rlead induce d H b decrements an

d I Q effects , respectively . Judgmenta l probabilit

y encoding wa s require d i n thes e cases . Sectio n 5 presents th e results o f combining dose-respons e uncertaint

y wit h blood-lead (PbB) distribution s i n th e specifie d population . Th e results ar e probabilit

y distributions ove rrespons e rat e as afunctio n o f geometri c mea

n Pb B level . Sectio n 6 summarize s th e mai n findings . Th

e repor tconclude s wit

h fou r appendixes . 1.2 MOTIVATIO

N Assessin g th e healt

h risk s associate d wit

h exposin g youn

g children to lead requires estimatin g th e probabilitie s of certai n fraction s of

th e population atris

k sufferin g well-define d healt h effect s unde

ralternativ e primar

y NAAQ S fo rlead . Th

eP.1 5

probabilitie s mus tb e estimate d i n aformal , defensibl e manne rtha ti s ope n t o publi c scrutiny . The y wil l generall y reflec ttw o source s o f uncertaint y —on e derivin g fro m th e characteristic s of

th e dat aan

d th e othe rfrom alac k o f knowledge . Th e forme rtyp e of uncertaint y reflect s measuremen tan d samplin g error , an

d probabilitie s ar e generall y calculate d by mean s o f standar d statistica l procedures . Althoug h thi s typ e of uncertaint y ca n b e reduce d through experimenta l manipulation , i tcanno tb e eliminate d completel y in any finit e study . Th e latte rtyp e o f

uncertaint y reflect s th e paucity , incompleteness , and indirec t natur e o f

muc h of th e availabl e data . Forexample , i ti s frequentl y necessar y t o dra w inference s abou tahealt h effec tin aspecifie d populatio n on th e basi s o f epidemiologica l o rclinica l dat aon differen tpopulation s undervaryin g o rdifferen texposur e conditions , o ron th e basi s o f

laborator y dat aon othe rspecie s o ron in vitr o preparations . Statistica l technique s canno tquantif y this typ e of

uncertaint y becaus e i ti s judgmental . Uncertaint y can , however , b e quantifie d usin g appropriat e procedure s t o encod e subjectiv e probabilities . Differen texpert s wil l asses s th e uncertaint y differently , dependin g on thei rfait h i n th e implici to rexplici ttheorie s underlyin g thei r extrapolation s from th e dat at o th e effec ti n questio n an

d on thei rperceptio n o f th e distanc e ove rwhich th e extrapolatio n mustb e made . Therefore , th e procedure s mus t accommodat e an

d represen tapossibl e divergenc e o f judgments . The leve l o f thi s typ e o f uncertainty , a s wel l a s th e degre e o f divergenc e amon g experts , ca n b e reduced , an d conceivabl y eve n eliminated , by increasin g th e availabl e knowledge . Conductin g aris k assessmen tin whic h thes e tw o type s o f uncertaint y ar e accommodate d respond s t o th e followin g challeng e issue d by Willia m Ruckleshau s i

n a speec h a tPrinceto n Universit y when h e heade d EP A (Ruckleshaus , 1984 , p . 158) . ...I f I a m goin g t o propos e control s tha tma y hav e seriou s economi c an d socia l effects , I nee d t o hav e som e ide ahow muc h confidenc e shoul d b e place d i n th e estimate s o f

ris k tha tprompte d thos e controls . I n th e sam e talk , h e wen ton t o propos e som e principle s fo rreasonabl e discussio n abou t ris k (p . 161) : First , w e mus tinsis ton risk calculation s bein g expresse d a s distribution s o f

estimate s an

d no ta s magi c numbers tha tca n b e manipulate d withou tregar d t o whatthe y reall y mean . W e mus ttr y t o displa y more realisti c estimate s o f ris k t o sho w arang e o f probabilities . T o hel p do this w e nee d ne w tool s fo rquantifyin g and orderin g source s o f

uncertaint y an

d fo rputtin g the m i

n perspective . Second , w e mus texpos e t o publi c scrutin y th e assumption s tha t underlie ] ou ranalysi s in managemen to f risk . I f complet e informatio n relevan tt o agive n healt h effec tin apopulatio n wer e available , the n th e statistica l uncertaint y coul d b e represente d by asingl e probability distributio n fo reac h alternativ e NAAQ S underconsideration . Tabl e 1 illustrate s arisk assessmen toutpu to f

thi s type . Fo rNAAQ S alternativ e 1 , th e probabilit y i s 0.0 1 tha t fewe rtha n 0.5 % o f

th e populatio n wil l suffe rth e healt h effect , th e probabilit y i s 0.0 5P.1 6



### tha t fewe r tha n 1 % o

f th e populatio n will TABL E 1 Probabilit

y of Suffering a suffer it , ands o forth
. (Equivadently , th e Specifie d Healt h Effec tunde

rAlternativ e probability i s 0.9 9 tha t

more tha n 99.5 % o

f NAAQS , Give

n Complete Informatio

n th e populatio n wil l no t suffe r th e healt h effect , 0.9 5 tha t

more tha n 99 % wil l no t
_ _ suffe r it , ands o forth. ) NAAQ S alternativ e „..., :

. _. . .. . . . , » . ' . Probabilit y unde r 

### 4 provide s th e greates t

degre e o f protectio n _UAA^ P » I 

### -• . •

. . _B e



### . \ Respons e NAAQ S Alternative s i n tha t agreate r

chanc e exist s tha t

fewe r

Rat e 

### < R3 

### peopl e will suffe r

th e health effect
. (Z ) ° 1 2 3 4 Outpu t o f th e sor t

illustrate di

n Tabl e 1 wouldpresumabl y b e helpfu l t o EP A 0. 5 0.0 1 0.0 6 0.1 9 0.3 8 i n selectin g astandar dtha t i n it s judgmen t

1. 0 0.0 5 0.1 1 0.2 3 0.6 0 wouldprotec t

publi c healt h with a n 1. 5 0.4 1 0.5 3 0.6 4 0.7 5 adequat e margi n o

f safety
. Fo r

example , i

f
... . EP A determine dtha t

th e inten t

o f th e Clea n Ai r Ac t wouldb e me t

by protectin g 99.5 % o f th e populatio n a t

ris k wit h : 

### probability 0.99 , the n NAAQ S alternativ e 1 » wouldb e selected
. I

f th e inten t

wouldb e met b y protectin g 99.5 % o

f th e populatio n wit

h probabilit y 0.95 , then NAAQ S alternativ e 2 woul db e appropriate
. O

f course , thi s exampl e i s highl y simplifie dbecaus e multipl e healt h effect s will generall y b e a t issue , an dpopulation s can b e define di n variou s ways . However , i t

illustrate s th e rol e tha t

forma l ris k

analysi s can play i

n settin g standards
. Generally , th e informatio n relevan t t o aparticula r

healt h effec t

associate dwit

h a n environmenta l agen t

will b e indirec t

an dincomplete , andexpert s will diffe r wit h respec t t o th e associate djudgmenta l uncertainty
. Th e degre e o f agreemen t

amon g th e expert s will b e ameasur e o f ho w fir mth e probabilit y estimate s ar e an dwill provid e usefu l informatio n i

n settin g th e standard
. On e wa y o f representing'th e degre e o f agreemen t

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

f eac h exper t

throug h th e entir e analysis , whic h result s i n afamil y o

f probability distribution s under etc h alternativ e NAAQS
. Tabl e 2 illustrate s thi s case . Unde r NAAQ S alternativ e 1 , for

example , ther e i s a0.0 1 t o 0.02 probabilit y rang e base d o n th e judgment s o

f severa l expert s tha t

fewe r tha n 0.5 % o

f th e populatio n wil l suffe r th e healt h effect
. Th e close r togethe r ar e th e distribution s fo r aparticula r

NAAQS , th e mor e fir mar e th e correspondin g probabilit y estimates
. I n settin g th e NAAQS , th e degre e o f firmnes s i

n th e estimate s can b e take n int o accoun t i n anumbe r

o f ways . One possibility i s t o plac e requirement s o n th e probabilitie s base don th e judgment s o f expert s (e.g. , tha t

a t leas t 99.5 % o

f th e populatio n b e protected)
. Fo r thi s leve l o

f protection , i t

ma y b e decide dtha t

th e smalles t probabilit y shoul db e a t leas t 0.01 , o r tha t th e probabilit y b e greate r tha n or equal t o 0.0 2 i

n a t leas t 75 % o f th e ris k distributions
. The secon dapproac h help s t o ensur e tha t

individual expert s d

o -no t exer t undu e influence
. The probabilit y encodin g session s with eac h exper t can includ e informal discussion s o

f th e relevan t

data
. Summarie s o

f thes e discussion s can supplemen t th eP.1 7



### TABL E 2 Probabilitie s o

f Sufferin g aSpecifie dHealt h Effec t unde rAlternativ e NAAQS , Given Incomplet e Informatio n

Respons e Rat e < R 0 (Z )
0. 5 1. 0 1. 5 Probabi l

1

0.01-0.0 2 0.01-0.0 5 0.29-0.4 1 .t

y Range s fo

t 2

0.02-0.0 6 0.04-0.1 1 0.40-0.5 3 • NAAQ S Alternative s

3 4
0.11-0.1 9 0.26-0.3 8 0.15-0.2 3 0.49-0.6 0 0.53-0.6 4 0.68-0.7 5



### probability distribution s andcan provid e guidanc e o n thei r use . Th e thre e ris k assessment s presente di

n thi s repor t

includ e output s similar

t o thos e i

n Table s 1 and2 andsummarie s o

f th e associate ddiscussions
. Whil e endeavorin g t o mak

e th e ris k assessment s fully interpretable , we d o no t presum e t o sugges t

th e criteri atha t

shoul d gover n thei r us e i n th e standard-settin g process . 1. 3 JUDGMENTA

L PROBABILIT

Y ENCODIN

G W e wish t o emphasiz e tha t judgmenta l probability encodin g i s unnecessary whenever adequat e direc t

dat aar e available
. However , more ofte n tha n not , suc h dat a ar e unavailable , andth e only alternative s t o encodin g judgmenta l probabilitie s ar e t o trea t th e adde duncertaint y qualitatively , which currentl y canno t b e don e i

n arigorou s manner , o r

t o ignore i t

altogether , which i s indefensible
. Fo r encode djudgmenta l probabilitie s t o b e useful , the y mus t satisf y tw o importan t criteria
. The firs t

criterio n i s tha t

judgment s mus t

b e obtaine dfro

mexpert s wh o spa n th e rang e o

f respecte dopinion
. The problemo f establishin g th e rang e o f opinio n andselectin g appropriat e expert s appear s t o b e difficul t andjudgmenta l i

n nature ; however , th e relevan t issue s ten dt o b e debate dfrequentl y an dpublicl y enough tha t suc h decision s ar e possible
. Fo r th e H b andI Q ris k assessments , EPA' s OAQPS selecte dth e expert s whos e judgment s wer e t o b e encoded
. Althoug h thei r name s ar e give n i n th e report , thei r

individual judgment s anddiscussio n summarie s ar e identifie db y cod e lette r

only
. I n thi s way , user s o

f th e ris k assessment s can decid e whethe r th e full rang e o f opinion i s represented , andth e individua l expert s can 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 or discussion s wit

h thos e wh

o ma y disagree
. The secon dcriterio n i s tha t a n individual' s encode dprobabilit y judgment s mus t b e stabl e (barrin g ne

w information) , b e coheren t i n awell-define dway , an daccuratel y represen t hi s o r he r uncertainty
. Researc h relatin g t o thes e issue s ha s bee n reviewe dbyP.1 8



### Wallste n an d Budesc u (1983) , an

d a n experimentspecificall y addressing the m i n the presentcontex twa

s performe

d b y Wallste n e tal . (1983) . Th

e technique s use

d i n th e presentwor

k wer e based o n thi s foundatio

n bu tals o relie d o

n pilo twor

k described i

n Whitfield an

d Wallste n (1984) . 1.4 DOSE-RESPONS

E UNCERTAINT

Y Tw o type s o

f uncertaint

y wer e discussed i

n Sec . 1.2 . Ambiguit

y als o exist s regardin g th e leve l o

f a n effec ttha

tshoul d b e considered advers e an d fo rwhic

h adose respons e functio n woul

d be o f interest . W

e deal twit

h thi s issu e b

y specifyin g two level s o f th e relevantvariabl e foreach healt h effec tan

d estimatin g adose-respons e function foreach . A dose-respons e function exist s fo raparticularpopulation an d effec tunde

r specifie d conditions . Relativel y complete dat awer e availabl e regarding th e dose response functions fo rE

Peffects , althoug

h th e dat awer e somewha

tuncertai n becaus e o

f samplin g an d mesuremen

terrors . I

n the H b an d I Q assessments , th e dat

aregarding th e dose-respons e function s wer e incomplet

e o rindirect , an

d th e need t o extrapolat e resulte d i

n judgmenta

l uncertaint

y (se e Sec. 1.3) . Becaus e uniqu e factor s were associate d wit

h eac h of

thes e latte rassessments , th e procedures an d models used fo r quantifying uncertaint

y wer e different . 1.5 RIS KASSESSMEN

T STRATEG

Y Ou rris k assessmen tstrateg y i s mos teasil y understood b

y firs tassuming thatn

o uncertaint

y i s involved . I

n thi s case , dose-respons e function s are determine d fo reac h selecte d lead-induced healt h effect . Th

e dose-respons e curve s plo tth e percentag e of th e specifie d population exhibitin g th e particularphysiologica l o rbehaviora

l effec tas a function o

f Pb B level . Th

e actual distribution o

f Pb B level s i

n th e population wil l b e affecte d b

y th e particularNAAQ

S scenario . Th

e dose-respons e functio n fo raspecifie d healt h effec ti s the

n combined wit

h th e estimate d Pb

B (dose) distributio n unde reac h alternativ e scenari o t o yiel d th e percentag e o f th e population tha twoul d suffe rth e effec tunde

rthatscenario . I

n reality , however , uncertaint y i s presen ta teac h ste p an d mus tbe incorporated into th e analysi s i n amanne

rproviding fina

l output s o f th e forms show n i n Tables 1 an

d 2 . Fo rthi s assessment , w

e produce d risk results thatare afunctio n of geometri c mea n Pb B level . Whe

n a n exposur e mode l linking alternativ e NAAQ S t o Pb B level s i n th e population i s available , i twill be possibl e an d straightforward t o achiev e th e ultimate goal of relatin g alternativ e NAAQ S to overal l ris

k measures .P.1 9



### 2 PROBABILISTI

C DOSE-RESPONS

E FUNCTION

S FO R LEAD-INDUCE

D ELEVATE

D E PLEVEL S
Piomelli e tal . (1982) examined PbB * an d E Plevel s fro

m 2004 Ne

w Yor k Cit y childre n aged 2-12 , wh

o ha d been screene d t o accountfo rth e effect s of iro n deficienc y an d otherconfoundin

g variables . Empirica

l dose-respons e curve s were presente d fo rtwo level s o f E Pelevation ; i

n each case , th e percentag e o f th e sampl e wit

h EP s above th e critica l leve l wa

s plotte d a

s afunction o

f Pb B level . W

e use d th e dat adirectl y becaus e ou rconsultant

s believe d thatth e populatio n fro m whic h th e sampl e wa

s draw n wa s sufficientl y clos e t o the populatio n o f interes t(childre

n u p to thei rseventh birthdays) t o mak e extrapolatio n unnecessary . Becaus e o

f th e ver y careful procedures use d b y Piomelli e tal . (1982) , sampling bu tno tmeasuremen

terro rneeded to be considered . Eac h o f th e point

s o n adose response function i s base d o n anumbe

ro f observations (N) , i

n whic h X exhibi tth e healt

h effec tan d th e remainde

r( N - X ) d o not . These dat

aprovid e a n estimat e Po

f th e true proportio n Po f the population suffering th e healt h effec ta

tth e Pb B leve l i n question . Uncertaint

y i s associate d wit

h th e estimat e becaus e o f sampling error . I

n classica l probabilit y theory , thi s uncertaint y i s handle

d b y usin g th e binomia

l distributio n wit

h parameters P, X

, an d N to calculat e confidence interval s aroun d P as a n estimat e o

f P , o rmor e generally t o calculat e aprobabilit y distribution ove rP . Thus , th e outpu tis a probabilit y distribution ove rth e percentag e o f th e populatio

n affecte d ateach observed Pb B level . Th e Bayesia n approac h i s to calculat e aposterio rprobabilit y distribution ove rP

, given the dat

aan d aprio rdistribution ove rP. Whe n the prio rdistributio n i s represente d a s abet adistribution wit

h parameter

s aan d b , the n the posterio rdistribution i s als o beta , bu twit h parameter

s a+ X an

d b + ( N - X) . A conservativ e strateg y i s to assume a diffus e prio

rstat e o f information characterize d b y a= b = 0 (Winkler

, 1972) . I n thi s case , th e resultin g probabilit

y distribution overthe fractio n o f th e population affecte d ata given Pb B leve l i s ver

y clos e t o tha

tcalculate d i

n th e classica l manner

. Technically , however , th e interpretatio n i s different , an d the Bayesia

n approac

h use d i s th e one mos

t suitabl e forou

rpurposes . Furthe

rdetail s ar

e provide d i n App . A .
*Blood-lea

d leve l i s generall y use

d as th e inde

x o f lead exposur

e i n healt h studie s an

d i s s o use d i n thi s report . Simila rdat awer e collecte d b

y Hammon

d e tal . (1985 ) o

n asampl e fro

m adifferen t populatio n o f children . Th

e dose-respons e functions wer e ver y simila rt o thos e obtained b y Piomelli e tal . (1982) , bu tcertai n nonindependencie s i n th e dat

acaused b

y thei r longitudina

l natur e mad e the m unsuitable forthe presentpurpose . Neithe ro f thes e studie s directl y controlle d forinteraction s between iro n statu s an

d lea d i n determining E Plevels . Recen treanalyse s o f dat afro m the second Nationa

l Healt h an d Nutrition Surve y (NHANE

S II ) (Anneste tal. , 1982

) indicat e somewha

tdifferen tdose-respons e relationship s betwee n Pb B an d E Pwhe n adjustment

s ar e mad e fo riro n statu s (Schwartz , 1986) .P.2 0



### Figur e 1 present s th e dose-respons e dat afo r tw o E P level s (Piomell i e t

al. , 1982) , an dTabl e 3 present s th e sample-siz e data
. Eac h o f th e tw o E

P level s ( > 3 3 yg/d L and > 5 3 yg/dL ) wa s considere dadverse
. Expression s can b e determine dfo r th e mea n dose

respons e curve s shown (se e App
. A)
. Thes e expression s ar e function s o f Pb B level , and what Piomell i e t

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

f E P level s > 3 3 yg/d

L an d> 5 3 yg/dL an dinvolv e th e normal probability distributio n function
. A natura l frequenc y i s th e frequenc y of occurrenc e o

f elevate dE

P level s amon g childre n havin g Pb B level s belo w th e threshol dleve l a t which lead-induce dE

P effect s begi n t o occur . I n Fig
. 1 , athreshol do

f abou t 16. 5 yg/d

L for lead-induce dE

P effect s i s indicate dby th e "hockey-stick"-shape dfunctions
. As discusse dabove , th e bet adistributio n i s th e prope r distributio n t o us e t o describ e uncertaint y abou t th e tru e populatio n proportio n sufferin g fro melevate dE P levels
. However , fo r

Pb B level s below 4 1 yg/dL , sampl e size s ar e larg e enough tha t th e norma l distributio n can b e use dt o closel y approximat e bet adistribution s for both E P levels
. I n thos e cases , th e mea

n i s a t leas t 2. 5 standar ddeviation s greate r tha n zero . Tabl e A. 1 i

n App
. A summarize s th e probabilisti c dose-respons e function s tha t wer e derived
. Figure s 2 an d3 show media n dose-respons e relationship s an d90 % credibl e interval s (CIs ) fo r

E P level s > 3 3 yg/d

L and> 5 3 yg/dL , respectively
. Fo r case s in which

99

-
fl) O Q£ V C O C o Q

. ff] « OC c o 0 ) 2 9 5 9 0 75 5 0 2 5 1 0 5 - 1 - —r1 0 3 0

2 0 3 0 4 0 

### Pb B Leve l (jug/dL ) 5 0


### FIGUR E 1 Mea n Respons e Rat e vs . Dos e fo r EP 2 3 3 yg/d L an d > 5 3 yg/dL (Source : Adapte dfro mPiomell i e t aL , 1982 )P.2 1

anorma l approximatio n i s adequate , th e media n an dmea n respons e rate s ar e identical , an dth e CI s ar e symmetrica l abou t th e media n values
. Th e media n valu e i s tha t respons e rat e a t

whic h i 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 n respons e rat e i s belo w th e C I rang e an daprobabilit y o f 0.0 5 tha t

i t i s abov e it
. Th e 90 % CI s ar e fairl y smal l a t Pb B
= 1 5 yg/d L (9-12 % an d2-3 % fo r E P > 3 3 ug/d L an d> 5 3 yg/dL , respectively ) becaus e o f

th e larg e numbe r

of childre n wit h Pb B level s i n th e 10

- t o 20-yg/d L range . Th e 90 % CI s ar e larger , a s expected , a t

Pb B = 3 5 ug/d L (66-80 % an d 37-52 % fo r

E P > 3 3 ug/d L an d> 5 3 yg/dL , respectively ) becaus e ther e wer e fewe r children
. TABL E 3 Sampl e Size s fo rth e E P Dat a

Pb B Leve l (yg/dL )
2-1 7 17-2 1 21-3 1 31-4 1 41-9 8 Number- o f

Childre n
82 9 47 9 54 4 10 9 4 3

Source : Base

d o n dat a fro

m Piomell i e t al. , 198 2 (Seaman , 1985) .

99 - 95

- & 90 4
o cc 0 ) ff) c o Q . ff) O OC 7 5 5 0
2 b 1 0 5
1 - 90 % C l

Media n

1 0 — I —

2 0 3 0 4 0 5 0 

### Pb B Leve l (/J.g/dl) FIGUR E 2 Media n Respons e Rat e an d90 % C I vs . Dos e fo rE P > 3 3 yg/d LP.2 2

99 T

, - s 95 ~ ^ 90 - 0 ) I 

# 1 7 

# H S 

## 50- 1 a! a > 25- ! a! i 10- T

1 0 10

I 2 0 3 0 4 0 Pb B Leve l (yug/dL ) 90 % C l

Media n

5 0
FIGUR E 3 Median Respons e Rat e an d 90 % C I vs . Dos e fo rE

P > 5 3 yg/d LP.2 3 

### 1 1 PROBABILISTI

C DOSE-RESPONS

E FUNCTION

S FO RLEAD-INDUCE

D H b DECREMENT

S
Dat aar e very incomplet e regardin g dose-respons e function s fo rlead-induce dH b decrement s i

n th e ful l populatio n o f U.S
. childre n prio r

t o thei r sevent h birthdays
. Therefore , i t

wa s necessar y t o encod e exper t judgmenta l probabilitie s abou t th e populatio n respons e rate s a t aserie s o

f Pb B levels
. Encode dprobabilitie s mus t satisf y tw o requirements
. They mus t b e internall y consisten t a s determine dby criteri at o b e specifie dshortly , andthe y mus t b e .satisfactor y t o th e expert s i n th e sens e tha t

th e expert s agre e tha t

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

o f PbB level s can b e presente dt o th e expert s fo r encoding ; i n thi s study th e number wa s abou t

six
. T o us e th e judgment s i

n th e ris k

assessments , interpolatio n betwee n encode dvalue s wa s necessary . Suc h interpolation s wer e accomplishe db

y fittin g asuitabl e probability distributio n t o th e encode dvalues
. The distributio n mus t

fi t th e judgment s by areasonabl e mathematica l criterion , bu t i t i s equall y importan t

tha t th e exper t

agre e tha t

th e functio n i s accurate
. To mee t thes e requirement s an dt o follow th e recommendation s i n Wallste n e t

al
. (1983) , w e develope daprotoco l fo r th e probability encoding s andthe n me t wit h eac h exper t o n tw o occasion s abou t

amont h apart
. Judgment s wer e encode ddurin g th e firs t session , andfunction s wer e fi t t o the mbefor e th e nex t visit
. Th e judgment s andfunc

tion s were reviewe ddurin g th e secon dsession , andan y change s deeme dnecessar y b y th e exper t were made
. Additional follow-up by mai l andtelephon e wa s sometime s required
. Sectio n 3. 1 describe s th e developmen t o f th e protocol , andSec
. 3. 2 outline s th e protocol
. Th e manner

in which th e encodin g session s wer e conducted , th e probability encodin g methods , andth e procedure s for fittin g function s t o th e encode djudgment s ar e presente di

n Sees
. 3.3 , 3.4 , an d3.5 , respectively
. Sectio n 3. 6 indicate s whos e judgment s wer e encoded , Sec
. 3. 7 summarize s th e result s fo r th e variou s PbB level s an dages , an d Sec
. 3. 8 provide s some summary discussion
. 3. 1 PROTOCO

L DEVELOPMEN

T Th e consultant s liste din Tabl e 4 aide du s in developin g th e protoco l fo r H b probability encoding
. Thei r assistanc e too k

man y forms , includin g discussin g th e literatur e wit

h us , guidin g u s i

n readin g key studies , andcommentin g o n numerou s draft s o f th e protocol
. Afte r studyin g relevan t

portion s o

f th e CD an ddiscussin g the ma t length wit

h a subse t o f ou r consultants , wh

o fo r th e mos t

par t wer e th e author s o

f thos e portions , w

e prepare dafirs t

draf t o f th e protocol
. Thi s draf t wa s shown t o thos e expert s a s well a s t o other s draw n fromth e populatio n o f peopl e whos e judgment s migh t b e encoded
. W

e worke dwit

h thes e experts , structurin g th e proble mi n th e manner

we woul di

f we wer e goin g t o encod e thei r

judgments
. The protoco l wa s the n revise daccordingly
.P.2 4 

### 1 2 TABL E 4 Consultant

s fo rth e H

b Protocol

Consultan t
Julia n Chisol m Jef f Cohe n Anit a Curra n

Thoma s Feagan s Leste r Gran t John Haine s Pau l Hammond Rober t Kellam Pau l Musha k Affiliatio n

John s Hopkin s Universit y EPA , OAQPS * Westcheste r Count y Departmen t o f Healt h
EPA , OAQP S
EPA , ECAO b
EPA , OAQP S Universit y

o f Cincinnat i
EPA , OAQP S Universit y

o f Nort hCarolina , Chape l Hil l

a 

### Offic e o

f Ai r Qualit y Plannin g andStandards
. Environmenta l Criteri aAssessmen t Office
. I n thi s fashion , th e protoco l wen t throug h severa l drafts
. I f al l th e respondent s viewe dth e proble mi

n th e sam e way , tha t

wa y wa s specifie din th e protocol
. Whe n th e consultant s differed , o r

indicate dtha t

other s might

differ , we modifie dth e protoco l t o allo w th e expert s t o individualiz e th e scenario , subjec t only t o th e constraint s tha t th e obtaine djudgment s coul db e mappe dint o th e res t o f th e model an dtha t

the y coul db e compare dacros s experts
. Th e protoco l wa s ultimatel y structure dsuc h tha t th e consultan t

healt h expert s considere di t reasonabl e an dindicate dtha t the y wouldfee l comfortabl e providin g th e desire dprobability judgments
. Th e protoco l wa s teste dby usin g i t t o encod e th e judgmenta l probabilitie s o f tw o member s o

f th e EP A staf f familiar with th e effect s o

f lead
. Th e tes t

wa s considere d successfu l an di s reporte di n Whitfiel dan dWallste n (1984)
. 3. 2 PROTOCO

L OUTLIN

E Th e complet e protoco l i s presente din Sec
. B. 1 o f App
. B ; onl y a

n outlin e i s provide dhere : Sectio n 1 introduce s wha t we wer e attemptin g t o do an dwhy ; Sees
. 2- 51 3

specif y th e parameter s o f

th e problem , s o tha tth e dose-respons e function s ar e wel l defined ; Sec . 6 raise s variou s point s i n th e literatur e fo rdiscussion ; Sees . 7 an d 9 discus s tti e proces s o f

probability encoding ; an d Sec . 8 deal s peripherall y with H b decremen tan

d raise s issue s concernin g possibl e advers e healt h effect s associate d with elevate d E P levels . Mor

e specifically , Sec . 2 define s advers e H b level s a s < 9. 5 g/d L -an d < 1 1 g/dL , thereb y bracketin g th e rang e o f interest . Thus , judgment s wer e encode d fo rtw o set s o f dose-respons e functions . Sectio n 3 define s th e populatio n a tris k fo rencodin g a s al l Unite d State s childre n from birth through thei rsevent h birthdays . However , th e expert s wer e give n th e optio n o f considerin g tw o ag e group s (0- 3 an d 4-6 ) i f the y though tfo ran

y reaso n tha tth e tw o group s woul d hav e differen tdose-respons e functions . Therefore , expert s who chos e thi s optio n ha d thei rprobabilisti c judgment s encode d fo rfou rdose respons e relationships . Sectio n 6 i s intende d t o stimulat e discussio n wit h th e expert s on relevan t theorie s an

d data . Thi s ste p helpe d ensur e tha tth e proble m wa s structure d properly , tha tth e expert s consciousl y reviewe d thei rknowledg e befor e providin g probabilit y judgments , an

d tha tapossibl e basi s was provide d fo runderstandin g any discrepan t judgments . Section s 7 an

d 9 , whic h cove rth e probabilit y encoding , ar e base d on prio rwor k on encodin g probabilit y judgment s abou tdose-respons e function s (Wallste n e tal. , 1983) . Sectio n 7 provide s suggestion s on ho w t o minimiz e biase s in probabilit y encoding , wherea s Sec . 9 discusse s th e probabilit y encodin g procedure . 3. 3 CONDUC T OF TH E SESSIONS Al l session s wer e conducte d during th e winte ro f 1984-1985 . Section s 1- 8 o f th e protoco l wer e sen tt o eac h exper tbefor e th e encodin g session . Sectio n 9 wa s provide d an d explaine d durin g th e firs tencodin g session . Th e protoco l wa s the n use d t o guid e discussio n and interactio n durin g th e sessions . Approximatel y on e t o thre e hours wer e spen ta tth e beginnin g o f th e firs tsessio n discussin g th e materia l in Sees . 2-6 . The concept s in Sec . 7 wer e the n discusse d an d illustrated , afte rwhic h th e probabilit y encodin g began . (Discussio n o f Sec . 9 wa s delaye d unti l th e secon d encodin g session. ) Th e actua l encodin g too k fou rt o si x hours . Th e secon d sessio n usuall y too k plac e fou rt o si x week s afte rth e firs tsessio n an d laste d from tw o t o fou rhours . I tinclude d revie w o f

th e summarie s o f

th e previou s session , whic h ha

d bee n sen ti

n th e mail ; additiona l probabilit y encodin g a s necessary ; an d discussio n o f

th e materia l in Sec . 8 . 3. 4 ENCODING TH

E JUDGMENT S Probabilit y encodin g bega n in th e firs tsessio n afte rth e relevan tliteratur e an d th e factor s determinin g th e dose-respons e functio n had bee n thoroughl y discusse d wit hP.2 6
„ . , rz » 

### th e expert . Th

e intentio n wa

s to encod e probabilit

y judgment

s fo rpossibl e respons e rate s a tPb

B level s o

f 5 , 15 , 25 , 35 , 45 , an

d 5 5 yg/dL . Highe

rPb B level s wer

e encode d wit h one expert . T o determin e useful point s i n th e dose-respons e spac e fo rencoding probabilities , eac h expertwa

s firs taske

d t o suppl

y broa d 98%-C I ranges forpossibl e respons e rate s at eac h of th e Pb B levels . W

e helped th e expertdetermin e thes e ranges b y posing suitabl e questions . Fo

rexample , afte rarang

e wa s specified , w

e aske d whetherth e expertcould construc taplausibl e explanatio n i f som e da

y i twer e foun d thatth e true valu e fel l outsid e thatrange . Fo rmosto f th e experts , probabilitie s wer e encoded usin

g aprobabilit

y wheel . Fo rthi s purpose , th e rang

e o f possibl e respons e rate s foreach Pb B leve l wa

s divided int

o fiv e equa l interval s fordetaile d encoding a tsix points . Fo rexample , i

f th e response-rate range a taparticularPb

B leve l wa

s 20-70% , encodings were recorded a t20% , 30% , 40% , 50% , 60% , an

d 70% . I f durin g th e encoding proces s i tbecam e apparen tthatothe rpoint

s eithe rinside o routsid e th e rang e were important, they wer e incorporated . Blood-lead level s wer

e presente d forencoding i n rando m order ; foraparticular Pb B level , respons e rate s wer e als o presente d i

n rando m sequence . Probabilitie s were encoded fo ral l respons e rate s a tagive n Pb B leve l before movin

g o n t o th e nex tPb

B level . Th

e probabilit

y wheel use

d fo rencoding i s radially divide d into tw o sector s o

f adjustabl e relativ e areas —on e orange an

d on e blue . Th

e whee l ca n b e spu n s o thati t randoml y stop s wit

h eithe rsecto runde

rapointer . Fo

raparticularrespons e rate Rata give n Pb B leve l L, th e wheel wa s se tatsome relativ e areao f blue , an d th e expertwa

s asked t o conside rth e followin g question : I s i tmor e probabl e thatth e true respons e rate a tL i s les s tha n R , o r thatarando

m spi n o f th e wheel will sto p wit

h th e pointero

n blue ? Thus , th e expertwa

s aske d t o weig h tw o probabilitie s an

d decid e whic

h wa s greater . Th

e expert' s answerdetermined whetherth e proportio n o f blu e wa s increase d ordecreased , an d th e questio n wa

s posed again . Thi

s procedur

e wa s continued unti

l th e wheel wa

s se t suc h thatth e expertconsidered i tequally likel y thatth e whee l woul d randoml

y lan d o n blue as thatth e true respons e rate wa s les s tha n Rfo rPb

B leve l L. Th

e relativ e are ao

f blue wa s then provisionally taken as th e judge d cumulativ e probabilit

y F(R|L) . Th

e procedur e was repeate d fo rth e required respons e rate s unti l a n entir e cumulativ e probabilit y distributio n ove rRha

d been encoded fo raparticularL. I f afte raperiod o

f tim e th e expertdi

d no tbecom e comfortabl e wit h the probabilit y wheel , a

n encoding method based o n successiv e interval s an d hypothetical bet s wa s used . I n thi s case , acumulativ e subjectiv e probabilit y o f F(R|L) = 0.50 wa

s firs t encoded b

y having th e expertspecif y apopulation respons e rate Rfo rth e Pb B leve l L unde rconsideratio n suc

h thati f abe twere mad

e i n whic h th e payof

f depende d o n whethe rth e true respons e rate turne d outt o b e abov

e o rbelo w R , th e expertwoul

d b e indifferen tas t o whic

h be th e held . I

n othe rwords , th e exper tinitiall y specifie d a respons e rate suc

h thati n his judgmen

ti twa s equally likel y thatth e tru e rate woul d b e

### 1 5

abov e or belo w it
. Afte r

discussion , i t

frequentl y turne dou t

tha t th e exper t

wa s no t indifferen t

betwee n th e tw o side s o f th e bet
. Adjustment s were made unti l arespons e rat e wa s founda t

which h e wa s indifferent
. Havin g determine dth e respons e rat e correspondin g t o acumulativ e subjectiv e probability o

f 0.50 , th e exper t

wa s the n aske dt o imagin e tha t th e necessar y researc h ha d bee n done , tha t

th e tru e respons e rat e wa s no w known , an dtha t

i t wa s greate r

than th e valu e h e ha

djus t indicated
. (O

n abou t half o f th e occasion s a t

thi s point , h e wa s t o imagin e tha t

th e tru e respons e rat e wa s les s tha n tha t specifie dearlier. ) Given tha t th e tru e rat e wa s greate r

tha n tha t

indicate dearlier , ane w respons e rat e Rwa s t o b e specifie dfor

ane w be t suc h tha 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 respons e rat e bein g abov e or belo w it
. The resultan t valu e corresponde dt o acumulativ e subjectiv e probability o f F(R|L ) = 0.75
. I

n thi s manner , respons e rate s correspondin g t o probabilities o f 0.25 , 0.50 , and0.7 5 wer e encoded
. Finally , respons e rate s correspondin g t o subjectiv e probabilities o f 0.0 1 an d0.9 9 were determine db

y imaginin g bet s wit

h 1:9 9 an d99: 1 odds
. Afte r th e cumulativ e probability distributio n over respons e rat e wa s encode dfor th e firs t Pb B level , regardles s o

f th e encodin g metho dused , th e distributio n wa s graphe d andshow n t o th e exper t

fo r discussion
. An

y inconsistencie s were pointe dou t and resolved
. Suc

h inconsistencie s appear a s dip s i

n th e graphs , whic h shoul dris e monotonicall y a s th e respons e rat e increase s (Wallsten e t al. , 1983)
. Th e implication s o

f th e encode ddistribution s were als o discussed
. Fo r example , squally wit h thi s or an y o f severa l othe r

implications , adjustment s were 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 wa s selecte dandth e proces s wa s repeated
. fo r R

- > Rj , F(RjlL) = 0.2 5 andF(R-|L ) = 0.7 5 imply tha t th e tru e respons e rat e i s equal ! likel y t o fal l eithe r

inside th e (Rj , R.-

) interva l or

outsid e it
. I

f th e exper t

disagree dwi

l

Afte r th e probability distribution s hadbee n encode dfor al l selecte dPbB levels , the y wer e plotte do

n one grap h anddiscusse dwit h th e expert
. I

f tw o distribution s crosse da t

any point , thi s inconsistenc y wa s resolve d(Wallsten e t al. , 1983)
. Whe

n th e exper t wa s satisfie dtha t

th e entir e se t

o f distributions represente dhi s probabilisti c judgments , th e encodin g wa s finished
. Followin g th e firs t

session , th e encode dprobabilitie s (distributions ) wer e fi t t o function s i

n th e manner

describe di

n Sec
. 3.5
. Summarie s o f th e encode djudgment s and th e respectiv e fits , alon g wit h explanator y text , were sen t t o eac h exper t

befor e th e secon dvisit
. During th e secon dvisit , thes e material s wer e reviewed , th e exper t was aske dt o indicat e whethe r th e fitte ddistribution s correctl y represente dhi s judgments , andadditiona l probability encodin g wa s carrie dou t i f necessary . I

n afew instances , furthe r functio n fittin g wa s necessary , an dsubsequen t discussio n wa s conducte dby lette r an dtelephone
. 3. 5 REPRESENTIN

G TH E JUDGMENT

S Calculatin g ris k

require dfindin g mathematica l function s tha t fi t th e assesse d points
. Becaus e probabilisti c judgment s abou t dose-respons e relationship s generall y for mP.2 8 

### 1 6 S-shaped curve s ove rth e close d [0% , 100% ] interval (Wallste n e tal , 1983 ; Whitfield an d Wallsten , 1984) , i ti s difficul tt o representthe m wit h simpl e mathematical functions . On e particularl y useful functio n tha ti s relativel y eas y t o wor k wit h i s th e normal-on-log odds (NOLO

) distributio n function , whic h i s obtaine d b

y fittin g anorma

l distributio n to th e natura

l lo g of th e odd s implie d b

y th e population respons e rat e R . Thus , the followin g relationship s ca n b e define d
X 

### " lOCrhi ' ^ r0 , X < - an d Y = ln(X) , fo r- » < Y < » 

### where X i s th e odd

s variabl e an

d Y i s th e lo g of

th e odd s variable . I

f Y i s normall

y distribute d (wit

h mea n y an d varianc e o ) , then X i s lognormally distributed , an d th e distributio n induce

d o n Ri s calle d a 7 

### NOL O distribution . Althoug h th e NOL

O distributio n canno tb e expresse d i n aclose d form , al l probabilitie s o f interes tca

n easil y b e derive d fro

m th e norma

l distributio n ove rY (se e App . B) . A separat e NOL

O distributio n functio n wa s fi tt o th e elicite d cumulativ e distributio n function s (CDFs ) fo rth e probabilit

y Judgment

s ove rrespons e rate R

, a teac h Pb B leve l Lj , wher

e j = 1 , ... , m (

m = 6) . This fittin g wa

s accomplishe d b

y derivin g least squares estimate s of

th e parameters v: an

d o- , denote d b

y y ; an d o; , fo rth e norma

l distributio n applied t o th e log-odd s transformed variabl e Y, a s describe d i n App . B . Thes e distributions , eac h wit h separate least-square s estimate s fo ry - an d a-, ar e referre d t o a s th e best-fittin g NOL O distributions . Th

e standar d regressio n rstatistic , whic h compare s actual judgment s t o thos e predicte d b

y th e fitte d function , assesse s ho w wel l th e derive d distributio n represents th e probabilit y judgment

s a tagive n Pb

B level . As show n i n App . B , th e NOL

O distributio n described th e encode d judgment s ver y well , wit h rvalue s generall y exceedin g 0.95 . (A n rvalue o

f 1. 0 indicate s aperfec t fit. ) Nevertheless , goodnes s of fi twa s compromised t o asmall degre e b y fittin g a

n expert' s probabilit

y judgment

s wit h afamil y of

equal-varianc e NOL

O distributions . Thi

s procedur e ensure s tha tth e derive d distribution s atdifferen tPb B level s neve rcros s on

e another , noteve n atth e extremes . Crossing woul d impl y thatexceedin g aspecifie d respons e rat e i s judge

d mor e probable a tPb

B leve l L j tha n a tL 2 

### , wher

e L 2 

### i s greate r tha n Lj . Equal-variance NOL

O distribution s were derive d b y (1 ) obtainin g aleast-square s estimat e of

th e standar

d deviatio n pooled ove rPb B levels , o' , (2) settin g all the o l equa l t o o , an

d (3 ) finding ne

w least-square s estimate s of th e means , y' . (se e App . B) . Th

e resul ti s ase tof

NOL O distributions , one fo reach Pb B leve l Lj , thatr

1 

### ha s a commo n varianc e an

d thatdiffer s only i

n th e mean . Goodness of fi tcan be assesse d b

y calculatin g rbetwee n observed an d fitte d judgments . Becaus e probabilit

y judgment

s wer e elicite d fo reac h Pb

B leve l L j ove rvirtually th e entir e close d [0% , 100% ] interval , an d becaus e thes e judgment s exhibite d n

o inconsistencie s (i.e. , crossings) , th e fi tof th e equal-varianc e NOL O distribution s wa

sP.2 9 1 7 generall y clos e t o tha t o f th e best-fittin g NOL O distributions
. Becaus e th e equal

varianc e distribution s canno t giv e ris e t o inconsistencies , thes e representation s of exper t judgment s ar e preferre dfo r estimatin g risk
. Indeed , eac h exper t accepte dthem , wit h a sligh t adjustmen t

require dfo r

Exper t D
. 3. 6 TH E EXPERT S Th e individual s liste di n Tabl e 5 wer e selecte di n th e fal l o f 198 4 b y OAQP S fo r participatio n a s expert s i n th e H b ris k assessment
. Al l o f

the magree dt o participate , wit h th e understandin g tha t thei r judgment s woul dremai n anonymous . Th e result s presente dar e fo r

Expert s A throug h E , bu t th e lette r

designation s ar e randoml y assigned
.
3. 7 RESULT S I n Sec
. 3.7 , th e function s fi t t o eac h expert' s probabilisti c judgment s ar e use dt o summariz e th e quantitativ e results
. Thes e function s accuratel y represen t th e underlyin g encode dvalues , bot h becaus e th e goodnes s o f fi t wa s excellen t

an dbecaus e eac h exper t endorse dth e outpu t

o f th e respectiv e function s a s representin g hi s judgments
. Appendi x B present s th e detaile dquantitativ e results , includin g encode djudgments , paramete r value s fo r

fitte dfunctions , an dgoodness-of-fi t measures . Sectio n B. 4 summarize s th e qualitativ e discussion s hel dwit h eac h exper t abou t th e effect s o f

lea dexposure . Recal l tha t

probabilisti c judgment s wer e encode dabou t dose-respons e function s fo r lead-induce dHb decrement s amon g U.S
. childre n age d0-6
. Hemoglobi n level s o f < 9. 5 g/d L an d< 1 1 g/d L wer e considered , an dmos t expert s divide dth e populatio n o f childre n int o tw o ag e group s (0- 3 an d4-6)
. Result s ar e presente dseparatel y fo r th e fou r combination s of

Hb leve l an dag e group . TABLE 5 Expert s Participatin g in th e H b Encoding s
Exper t Affiliatio n Julia n Chisol mJohn s Hopkin s Universit y Bernar dDavido w Ne w Yor k Cit y Boar do f

Healt h Pau l Hammon

dUniversit y o f

Cincinnat i Sergi o Piomell i Columbi aUniversity , Ne w Yor k Cit y Lea dPoisonin g Preventio n Progra m Joh n Rose n Montefior e Hospita l an dMedica l Cente rP.3 0 

### 1 8 Expert s A , D , an dE believ e tha t dose-respons e relationship s ar e differen t for th e tw o ag e groups . Expert C believe s tha t

asingl e dose-respons e functio n applie s t o childre n age d0- 6 an dtherefor e provide dasingl e se t o f probabilisti c judgment s fo r eac h H b level
. Expert

B wa s uncomfortabl e wit h th e notio n o

f judgmenta l probability encodin g an dtherefor e di dno t supply any judgments
. Hi s qualitativ e comment s ar e presente di

n Sec
. B.4. 2 o

f App
. B
. 3.7. 1 H b Leve l < 1 1 g/dL , Age s 0- 3 Th e forma t

o f th e figure s use dt o display th e judgment s of th e expert s i s explaine dusin g th e judgment s o f Expert A regardin g th e dose-respons e functio n for H b leve l < 1 1 g/dL i

n U.S
. childre n age d0- 3 (se e Fig
. 4)
. The curve s shown ar e analogou s t o dose-respons e function s foundi n th e literature , excep t tha t the y ar e base do

n probabilisti c judgment s rathe r than o n actua l data
. The soli dcurv e show s th e media n dose-respons e curv e —a t eac h PbB leve 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 probability tha t th e tru e respons e rat e i s belo w it
. Th e dotte dline s on eithe r sid e o f th e media

n curv e boundth e centra l 50 % CI
. Thus , a t

eac h PbB 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 lower

dotte dcurve , a0.5 0 probabilit y tha t i t i s betwee n th e tw o dotte dcurves , an da0.2 5 probabilit y tha t i t i s abov e th e upper

one . I n asimilar

manner , th e dashe dpai r o f curve s bound s th e 90 % CI
.

^ 7

. o".05/r<L e 

### i , 

### I
4 5 n r

5 5 i

6 5 7 5 

### Pb B Leve l (/zg/d Q FIGUR E 4 Dose-Respons e Functions , H b < 1 1 g/dL , Age s 0-3 , Exper tAP.3 1 1 9 Figur e 5 represent s th e probabilisti c judgment s of Expert s A , C , D , an dE rathe r cpmpletel y regardin g th e dose-respons e functio n fo r Hb leve l < 1 1 g/d L i n U.S
. childre n age d0-3
. (Wit

h Exper t

C s concurrence , hi s judgment s fo r childre n age d0- 6 ar e reproduce din th e figure s fo r eac h ag e group. ) Eac h expert' s judgment s ar e show n in a separat e panel
. Differen t scale s ar e use dt o maximiz e th e amoun t o f detai l show n fo r eac h expert
. Althoug h Fig
. 6 i s les s complete , i t provide s aconvenien t mean s o f

comparin g judgment s acros s experts
. Th e axe s ar e th e sam e a s thos e i n Fig
. 5 : th e vertica l bar s a t eac h Pb B leve l represen t eac h expert' s centra l 90 % C I fo r respons e rate , an dth e symbo l withi n eac h ba r

indicate s th e media n judgmen t a t tha t Pb B level
. Substantia l overla p i s eviden t i n th e judgment s of

Expert s C , D , an dE , eve n thoug h Exper t C s judgment s ar e fo r childre n age d0-6 , wherea s thos e o f th e othe r

expert s ar e fo r

childre n age d0-3
. Th e judgment s of

Exper t A ten dt o diffe r

fro mthos e of

Expert s C , D , an dE
. Non e of th e overlappin g judgment s o f Expert s C , D , an dE sugges t aPbB-leve l threshol dbelo w whic h ther e i s n o discernabl e lead-induce dH b decrement
. However , th e implication s o f th e chang e i n slop e betwee n 1 5 yg/d L an d2 5 ug/d L fo r Exper t D' s judgment s ma y prov e important
. Th e media n judgment s of Expert s C , D , an dE indicat e tha t th e bes t estimat e o f th e tru e respons e rat e fall s betwee n 4 % an d9 % a t Pb B = 5 yg/dL , an dtha t i t rise s t o betwee n 26 % an d33 % a t Pb B = 5 5 yg/dL
.

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Pb B Leve l (_ug/dL) — i 1 1 1 1 — 1 5 2 5 3 5 4 5 5 5 Pb B Leve l (Atg/dL ) FIGUR E 5 Dose-Respons e Functions , Hb < 1 1 g/dL , Age s 0-3 , Expert s A , C , D , and E (response-rat e an d PbB scale s wer e selecte d t o sho w th e detail s o f eac h expert' s judgments )P.3 2

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### Pb B Leve l (ug/dL ) FIGUR E 6 Compariso

n of Judgments , H

b < 1 1 g/dL , Age s 0-3 , Expert s A , C , D , an

d E Expert C expresse s th e leas t

uncertaint y i

n hi s judgment s abou t

dose-respons e relationships , an dExpert E expresse s th e most
. I n al l cases , th e varianc e in th e judgment s increase s with PbB leve l withi n th e rang e considered , a s indicate dby th e increasin g siz e o

f th e 90 % CI s represente dby th e vertica l bar s i n Fig
. 6
. Fo r

Expert s C , D , an dE , th e low end s o f th e 9>0 % CI s fo r respons e rat e rang e betwee n 9% and20 % a t PbB - 5 yg/dL , an dbetwee n 35 % an d62 % a t Pb B = 5 5 yg/dL
. Accordin g t o Expert

A' s judgments , PbB level s les s tha n abou t 4 5 yg/dL d o no t caus e H b level s belo w 1 1 g/d L in thi s ag e group . A t PbB = 4 5 yg/dL , th e mos t likel y respons e rat e i s 3% ; a t

PbB = 7 5 yg/dL , i t

rise s t o 17%
. Furthermore , wit h probabilit y 0.05 , th e actua l respons e rat e a t PbB = 4 5 yg/dL i s judge dt o b e greate r than 10% ; wit

h th e sam e probability , i t

i s judge dt o b e greate r than 39 % a t

PbB = 7 5 yg/dL
. Althoug h our primar y interes t

i s i n Pb B level s < 5 5 yg/dL , we inquire dabou t highe r level s her e t o provid e afulle r

pictur e o

f Expert A' s judgments
. 3.7. 2 H b Leve l < 1 1 g/dL , Age s 4- 6 Figure s 7 an d8 display th e experts ' judgment s regardin g dose-respons e function s fo r H b leve l sl l g/dL fo r

childre n age d4-6
. The y presen t th e dat ai

n exactl y th e sam e wa y a s Figs
. 5 an d6
. A s before , th e judgment s of Expert s C , D , an dE overlap2 1

© 3 0

20 - © OT § 10 - a OT © oc Exper t A ,-0.9 5

0.7 5

-//—i - 5 5 —J— 6 5 —r7 5 40- ,

30 - 20 - Exper t C

10- .

25- i Exper t D

Pb B Leve l {.ug/dL) 4 U - 30 - 70 - 10 -
0 - Exper t E

• x * . •

* y -* * •.- * ^ •,• * ^^**^

• •* * j^ - ""*" ^ •••* " "TTm-**** * _»——"*"* — O n i i i i i 5 1 5 2 5 3 5 4 5 5 5 Pb B Leve l (^g/dL ) FIGUR E 7 Dose-Respons e Functions , H b < 1 1 g/dL , Age s 4-6 , Expert s A , C , D , and E (response-rat e and PbB scale s wer e selecte d t o sho w th e detail s o f eac h expert' s judgments )
considerabl y and ar e differen tfro m thos e o f Exper tA . Accordin g t o Expert s C , D , and E , ther e i s no threshol d Pb B level . Th e mos tlikel y respons e rate s ar e betwee n 2 % and 7 % a tPbB = 5 yg/dL , wit h th e rate s risin g t o betwee n 14 % and 26 % a tPbB = 5 5 yg/dL . I n thi s case , Exper tD expresse s th e leas tuncertaint y amon g th e three , whil e Exper tE continue s t o expres s th e greates tuncertainty . Th e 0.0 5 fractile s fo rrespons e rat e fo r Expert s C , D , and E rang e betwee n 4 % an d 13 % a tPbB = 5 yg/dL , an d betwee n 17 % and 36 % a tPb

B = 5 5 yg/dL . A s before , Exper tA' s vie w i s tha tth e probabilitie s o f lead-induce d H

b effect s a t th e exposur e level s considere d ar e extremel y lo w in thi s ag e group . I n hi s judgment , Pb

B level s les s tha n abou t55 yg/d L d o no tcaus e H b level s below . 1 1 g/dL . Th e mos tlikel y respons e rat e a t5 5 yg/d L an d 7 5 yg/d L ar e 2 % and 11% , respectively . Wit h probabilit y 0.05 , th e actua l respons e rat e i s judge d t o excee d 6 % a t5 5 yg/dL ; with th e sam e probability , i ti s judge d t o excee d 25 % a t7 5 yg/dL . 3.7. 3 Hb Leve l < 9. 5 g/dL , Age s 0- 3 Figure s 9 and 1 0 displa y th e judgment s regardin g dose-rerpons e function s fo rH b leve l < 9. 5 g/d L fo rchildre n age d 0-3 . I n Exper tA' s judgment , PbB level s withi n th e40- i 2 2 P.3 4

30 - ^

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# T 

# M M •! 

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o-»-« - A | | T |#T|»|^IITI» I I IT^I I T I lll l C D E ACO E ACO E ACO E ACO E ACO E ACO E ACO E 5 1 5 -2 5 35 — —4 5 55 —

—6 5 7

5 — 

### Pb B Leve l (/xg/dL ) FIGUR E 8 Compariso

n of Judgments , H

b < 1 1 g/dL , Age s 4-6 , Expert s A , C , D , an

d E
rang e o f interes t(

< 5 5 yg/dL ) d

o notcaus e H

b level s t o dro

p as lo w as 9. 5 g/dL . Also , althoug h th e judgment

s fo rExpert

s C , D , an

d E tend t o overlap , they d o notdispla

y th e same degre e o

f similarity as atth e higherH b level . I n particular , Expert

s C an d E agre e thatatPb

B = 5 yg/dL , th e mostlikel y respons e rate i s 2% , whil e Exper tD i s certai n that th e respons e rate i s 0%. Further, Exper tC s median-response-rate judgment s increas e relativel y slowl y wit

h increasin g PbB , whil e thos e o f Exper tD increas e relativel y quickly . As aresult , a tPb B = 5 5 yg/dL , Expert

s D an d E agre e thatth e mostlikel y respons e rate i s 20% , whil e Exper tC judge s i tt o b e 7%

. Exper tE expresse s considerabl e uncertaint y i n hi s judgments , whil e Expert s C an d D expres s muc

h less . Th

e 0.05 fractile s forrespons e rate ar e 3 % an d 10 % a tPb B = 5 yg/dL , an

d 11 % an

d 54% a t5 5 yg/dL fo rExpert

s C an d E, respectively . Exper tD believe s th e respons e rate i s definitel y 0 % a tPb B = 5 yg/dL . 3.7. 4 H b Leve l < 9. 5 g/dL , Age s 4- 6 Figures 1 1 an

d 1 2 displa y th e judgment

s regarding dose-respons e function s forH b leve l < 9. 5 g/dL fo rchildren aged 4-6 . Th e pattern o

f judgment

s i s ver y simila rt o that fo rth e youngerage group , bu tth e respons e rate s ar

e lower .2 3 "«\

40- i

a , 30 - 

### " 5 O i O 20 - OT c o C L 10 H OT © c e 0 - 12- i



## £ 10 - © "5 8 " ac © 6 - OT § 4 - Q . © Z H c r flE x P 6rt C .-0.9 5 * ..0.7 5

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^ -•* ' a^^ ^ ••• ' • ' .-yy- ,--0.0 5

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1 5 5 Pb B Leve l Ug/dL ) Pb B Leve l Ug/dL ) FIGUR E 9 Dose-Respons e Functions , H b < 9. 5 g/dL , Age s 0-3 , Expert s C , D , an d E (response-rat e and PbB scale s wer e selecte d t o sho w th e detail s o f eac h expert' s judgments ) Exper t A judge s tha t

th e Pb B level s unde r consideratio n woul dno t reduc e Hb belo w 9. 5 g/dL , an dExper t D judge s tha t

th e Pb B leve l woul dhav e t o b e a t leas t 2 5 yg/d L t o d o so . Th e media n judgment s o f Expert s C an dE ar e consistentl y similar , whil e thos e o f

Exper t D ar e simila r

t o thos e o f

Expert s C an dE a t

Pb B = 3 5 yg/d L an d higher
. Fo r

Expert s C , D , an dE , th e range s o f media n judgment s ar e 0 % t o 2 % a t Pb B = 5 yg/dL , an d7 % t o 13 % a t Pb B = 5 5 yg/dL
. Exper t E agai n expresse s th e greates t degre e of

uncertainty
. Fo r

Expert s C an d E , a t Pb B = 5 yg/dL , th e 0.0 5 fractile s fo r respons e rat e ar e 3 % an d6% , respectively
. Fo r Expert s C , D , an dE , a t Pb B = 5 5 yg/dL , th e 0.9 5 fractile s fo r respons e rat e rang e fro m11 % t o 36% . 3. 8 DISCUSSION Th e lead-induce drespons e rate s reporte di n Sec
. 3. 7 ar e ove r an dabov e an y baselin e respons e rat e relate dt o iro n deficienc y o r othe r factors
. Thus , th e level s o f uncertainty , a s wel l a s an y difference s o r similaritie s of

opinion , ar e limite dsolel y t o th e effect s o f

lea do n H b level
.P.3 6

2 5 —3 5 

### Pb B Leve l (/xg/dL ) FIGUR E 1 0 Compariso

n of Judgments , H

b < 9. 5 g/dL , Age s 0-3 , Expert s A , C , D , an

d E Althoug h th e judgment

s of Expert s C , D , an

d E diffe ri

n detail , the y ar

e broadl y similar . I

ti s particularl y interestin g thatExper tC s judgment

s fo rchildren aged 0- 6 ten d t o b e jus tbelow thos e of Expert s D an d E fo rchildren age d 0- 3 an d jus tabove thos e fo rchildren aged 4-6 . Th e judgment

s o f Expert s C , D , an

d E diffe rfro

m thos e of

Exper t A , wh o believe s thatPb

B level s i

n th e rang

e considere d (

< 55 yg/dL ) have littl e o rn o effec to n H b levels . I n al l cases , uncertainty , a s indicate d b y th e length of

th e 90 % CI, increase s as th e Pb B leve l increases . Thi

s pattern i s expecte d becaus e statistica l uncertaint y abou ta binomia l paramete r(respons e rate , i n thi s case ) increase s as th e estimate d value move s towar d th e cente rof

th e range fo rtha tparameter . I n addition , les s information i s availabl e atlowe rH

b level s tha

n a thigherones , i

f fo rn o othe rreason tha

n th e lower one s occu rles s frequently . Since judgment s atlowe rlevel s requir

e greate rextrapolatio n fro m availabl e data , mor

e disagreemen tamon

g expert s i s t o b e expected . However , Expert s A , C , an

d D ar e mor e certai n a t< 9. 5 g/dL tha n a t< 1 1 g/dL , despit e th e greate r extrapolation . Indeed , Exper tA i s positiv e tha tther e i s n o effec ta t< 9. 5 g/dL . Apparently , Expert

s A , C , an

d D understan

d th e effect s of

lea d o n H b leve l suc

h that each i s mor

e confidentabou

trespons e rate s a tth e lowe rH b level . Th

e revers e i s true fo rExper tE .

### 2 5

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* 

## ' " '-""^y^

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i 1 5 2 5 3 5 4 5 5 5
30- i Exper t D 4 U - 30 - 20 - 10 - 0 - Exper t E /

/ / / / / /

**•— i 1 ~ " i 1 V 2 5 3 5 4 5 5 5 Pb B Leve l Ug/dL ) 5 1 5 2 5 3 5 4 5 5 5 Pb B Leve l Ug/dL ) 

### FIGUR E 1 1 Dose-Respons e Functions , H b < 9. 5 g/dL , Age s 4-6 , Expert s C , D , an

d E (response-rate an

d Pb B scale s were selecte d t o show th e detail s of eac h expert' s judgments ) Althoug h th e expert s wer e selecte dt o represen t th e rang e o

f respecte dopinion , th e pattern s o

f thei r judgment s ar e rathe r

similar
. Thi s resul t

illustrate s th e benefi t

o f encodin g judgmenta l probabilities
. The difference s o f opinio n eviden t

i n th e literatur e andi n debat e can reasonabl y b e attribute dt o problem s wit h definitions , t o difference s i n ho w t o interpre t

an dextrapolat e data , an dt o disagreement s abou t what constitute s prope r publi c healt h policy
. Whe n th e expert s ar e require dt o focu s o n th e scientifi c issue s an dt o conside r

carefull y thei r

level s o f uncertaint y abou t

thes e matters , the y disagre e much less
. Althoug h th e judgment s presente dher e ar e o f interes t i n thei r ow n right , the y ar e combine di

n Sec
. 5 with arang e o f PbB-leve l distribution s t o obtai n overal l ris k distributions
.35 - 2 6 P.3 8

3 0 -
25 - ^ Q > 

### " 5 2o ^ QC Q > OT 

### g « H Q

. w V QC 1 0 H 

# T T

0 -I—•—i—•— i 1—•—i—•— i 1—•— i 1 1 1—• - 

# T .



# i j . i ; 1 . . 

# i i 

# i. i i. i ! 

# i i ! 

# i i * T 

# 1 

# ii i

-i—i—i— r ACD E ACO E ACD E ACD E A C D E A

C D E 2. 5 7. 5 —12.5 — —17.5 —

—22.5 - 

### Geometri c Mea n PbB Leve l (^xg/dL ) •27.5 -


### FIGUR E 1 2 Compariso

n of Judgments , H

b < 9. 5 g/dL , Age s 4-6 , Expert s A , C , D , an

d Ewrmwji'w ty ^T! * ' 2 7 4 PROBABILISTI C DOSE-EFFEC T AM D BOSE-EESPOMS E FTOCTIQM S FO E LEAD-MDTCE D I Q DECEEE3ES3T 8
A s wa s tru e fo r

th e H b assessment , th e dat aregardin g th e effect s o f lea do n I Q i n th e populatio n o f

al l U.S
. childre n befor e thei r sevent h birthday s ar e incomplete
. Moreover , th e dat aar e ver y controversial , whic h make s i t doubl y necessar y t o encod e exper t judgmenta l probabilities
. T o paralle l th e H b situatio n exactl y woul dhav e entaile ddefinin g dose-respons e function s i n term s o f

th e percentag e o f

th e populatio n wit h lead-induce dI Q decrement s exceedin g tw o selecte damount s an dthe n encodin g judgmenta l probabilitie s abou t suc h functions
. Thi s approac h prove dinfeasibl e becaus e i t di dno t fram e th e issu e i n th e way tha t researcher s thin k

abou t i t o r i n term s of

event s tha t

wer e i n principl e observable
. Becaus e I Q depend s o n multiple , correlate dfactor s actin g ove r lon g period s o f

time , inference s abou t

th e effect s o f

lea do n I Q requir e comple x statistica l operation s usin g grou p data
. Thus , i t

i s impossibl e t o attribut e a n I Q decremen t in a n individua l t o a particula r

cause . T o pos e question s abou t outcome s tha t

expert s commonl y thin k abou t an dt o elici t probabilisti c judgment s suitabl e fo r aris k assessment , ahypothetica l (ideal ) experimen t

wa s created
. Ver y larg e number s of childre n wer e t o b e randoml y assigne da t birt h eithe r

t o acontro l grou p o r

t o on e o f

severa l lead-exposur e groups . Exposur e level s wer e t o remai n approximatel y fixe da t th e specifie dleve l unti l th e children' s sevent h birthdays , a t

whic h tim e th e WISC- RI Q tes t wa s t o b e administered
. Blood-lea dleve l wa s t o b e measure da t th e thir dbirthday
. Th e ver y larg e numbe r o f subject s pe r

grou p eliminate s th e nee dt o thin k abou t samplin g error , an dth e rando massignmen 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
. Th e group s diffe r

onl y i n thei r

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 probabilit y judgment s abou t expecte dmea n I Q difference s betwee n th e contro l grou p an deac h o f th e exposur e groups . Th e hypothetica l stud y canno t an dshoul dno t

b e done , bu t

i t i s i n principl e doable
. Furthermore , th e hypothetica l dat aar e identica l i n for mt o dat aactuall y collected , bu t

withou t certai n troublesom e features
. Indeed , th e poin t o f doin g th e comple x statistic s o n th e rea l dat ai s t o infe r wha t th e I Q differenc e woul db e betwee n a lead-expose dan dalead-unexpose dgrou p i n th e absenc e o f confoundin g variables
. Thus , researcher s hav e bee n thinkin g abou t thi s issue , whic h i s precisel y th e on e tha t th e expert s wer e aske dt o mak e probabilisti c judgment s about
. T o calculat e subjectiv e probabilitie s concernin g I Q dose-respons e function s base d o n judgment s abou t

mea n I Q differences , i t wa s necessar y t o obtai n judgment s abou t othe r matter s a s well
. Thus , probabilisti c judgment s wer e als o encode dconcernin g th e mea n I Q o f

th e unexpose dcontro l grou p an dth e standar ddeviatio n i n I Q withi n th e differen t exposur e groups . Th e I Q measur e wa s constructe ds o tha t i t wa s approximatel y normall y distribute dwithi n th e population
. Th e expert s wer e aske dwhethe r the y believe dtha t

anorma l distributio n coul dreasonabl y b e applie dt o I Q score s withi n eac h o f th e exposur e groups . Subsequently , judgmenta l probabilitie s abou t dose-respons e function s o f

interes t wer e calculate dusin g norma l distributio n theor y i n conjunctio n wit h

tiitik^u^MiikJdluiwIIMBMnllAiiMkJ i J I iii mi
. iP.4 0 2 8 probabilisti c judgment s abou tmean I Q decrement , control-grou p mean IQ , an d within group standar d deviation . Sectio n 4. 1 describe s th e developmen to f th e protocol , and Sec . 4. 2 outline s th e protoco l itself . Section s 4.3-4. 5 discus s th e conduc to f th e encodin g sessions , th e method s o f

probabilit y encoding , an d th e mathematica l representatio n o f 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 , and Sec . 4. 8 provide s som e summar y discussion . A s wil l b e discussed , th e encodin g session s too k plac e in th e sprin g o f 198 5 befor e th e availabilit y o f

severa l importan tneurologica l studie s on children . Thes e recen t studie s ar e discusse d in a n addendum (EPA , 1986c ) t o th e C D fo rlea d (EPA , 1986a) .
4. 1 PROTOCO L DEVELOPMEN T Tabl e 6 list s th e peopl e wh o serve d a s consultant s in developin g th e protocol . A s alread y indicated , ou rorigina l intentio n wa s t o develo p aprotoco l analogou s t o th e on e fo rH b decrement . I

n othe rwords , w e planne d t o encod e exper tprobabilisti c judgment s abou tdose-respons e function s fo rlead-induce d I Q decrements . I

n preparation , w e rea d relevan tportion s o f

th e C D and talke d wit h severa l o f ou rconsultants . Th e firs tdraf

to f th e protoco l wa s designe d t o elici tprobabilisti c judgment s abou tdose-respons e curve s fo rI Q decrement . Thi s draf twa s discusse d with mos to f th e peopl e liste d i n Tabl e 4 . Tw o factor s quickl y becam e apparent . First , althoug h th e concep to f

adose-respons e curv e i s wel l define d in thi s context , i ti s no tcommonl y used , fo rreason s mentione d earlier . Second , in respondin g t o th e questions , th e expert s wer e envisionin g hypothetica l experiments , considerin g wha tth e outcome s migh tbe , and the n extrapolatin g fro m thos e outcome s t o th e dose-respons e function s o f interest . W e conclude d tha ti twoul d b e fa rmore consisten twit h th e wa y th e expert s usuall y thought , and thu s easie rfo rthem t o respond , i f thei rprobabilisti c judgment s abou toutcome s o f

asuitabl e hypothetica l experimen twer e encode d directly . B y properl y designin g th e hypothetica l experiment , w e woul d no tnee d t o worry abou tsom e o f th e complexitie s tha taris e in actua l research . Also , th e extrapolation s tha tth e expert s wer e tryin g t o d o mentall y coul d b e don e mathematically . Accordingly , ane w versio n o f th e protoco l wa s develope d t o elici tprobabilisti c judgment s abou tth e outcome s o f th e hypothetica l experiment . Thi s protoco l als o indicate d how th e judgment s woul d b e use d and how th e assumption s mad e i n workin g with them woul d b e incorporated . Th e ne w draf twa s discusse d wit h mos to f th e consultants . The y al l foun d i tmuch easie rand more natura l t o respon d t o thi s versio n tha n t o th e previou s one . However , thei rcomment s le d t o athir d draft , whic h incorporate d a

n improve d desig n fo rth e hypothetica l experiment . Thi s draf twa s discusse d wit h mos to f th e peopl e wh o ha

d see n th e previou s one , and onl y ver y mino r change s wer e necessary .-X*t~-- "''TR"" " 2 9 

### TABL E 6 Consultant

s fo rth e I

Q Protoco l P.4 1

Consultant s Affiliation

Verno n Benignu s Rober t Bornshei n Jef f Cohen Anit a Curra

n

Cerr i Dawso

n
Kim Dietrich Clair e Ernhar t

Leste r Grant Lloy d Humphrey s Lyl e Jone s
Herber t Needlema

n Davi d Ott o Stephen Schroede r

Bernar d Weis s EPA , HERL a

University

o f Cincinnat i EPA , OAQP S Westcheste r County

Department o f Healt h University

o f Nort hCarolina , Chape l Hil l University

o f Cincinnat i Clevelan

d Metropolitan Genera l Hospita l EPA , ECAO b University

o f Illinois , Champaign-Urban

a University

o f Nort hCarolina , Chape l Hil l University

o f Pittsburg

h EPA , HER

L University

o f Nort hCarolina , Chape l Hil l University

o f Rocheste r

a Healt han

d Environmenta l ResearchLaboratory . Environmenta l Criteri a Assessment Office .. _ P.4 2


### Th e protoco l wa s then use dwit h tw o pilo t

subject s —on e a

n EP A environmenta l healt h scientis t

an dth e othe r

apsycholog y graduat e studen t doing arelate ddisserta

tion
. Althoug h th e judgmenta l probability encoding s wen t very well , minor

change s t o th e protoco l wer e mad e afte r analyzin g th e judgment s an ddiscussin g thes e analyse s wit h Lyle Jones
. Th e fina l versio n o f th e protoco l wa s discusse dwit h severa l peopl e wh

o ha d see n th e previou s drafts
. Everyon e agree dtha t i t wa s suitabl e fo r

it s intende duse . 4. 2 PROTOCO

L OUTLIN

E Th e complet e protoco l i s presente di n Sec
. C. l o

f App
. C ; only a

n outlin e i s provide dhere : Sec
. 1 introduce s th e ris k assessmen t

projec t andth e purpos e o

f th e probability encoding , an dSec
. 2 describe s th e hypothetica l experiment , i n which larg e number s o

f childre n ar e randoml y assigne da t birt h t o on e o

f si x exposure group s o r

t o a contro l group completel y sheltere dfromlead
. Environmenta l lea dexposur e i s assume d t o b e roughl y constan t

a t th e appropriat e leve l fo r eac h child
. Tha t

is , whe n th e Pb B leve l i s measure don hi s o r he r thir dbirthday , i t

i s a t th e designate dlevel
. The environmenta l exposure remain s th e sam e unti l th e sevent h birthday , whe n th e WISC-

R I Q tes t i s administered
. Thus , eac h exper t wa s aske dt o conside r

th e tim e cours e o

f lea d i n th e children' s system s accordin g t o hi s or he r ow n theoretica l understanding , subjec t t o th e constrain t

tha t PbB remaine da t

th e leve l designate dfo r

th e thir dbirthday
. Sectio n 2 als o explain s tha t probabilisti c judgment s wouldb e encode dregardin g (1 ) th e mea

n I Q decremen t

for eac h exposur e group relativ e t o th e unexpose dcontro l group , (2) th e mea

n I Q o f th e unexpose dcontro l group , an d(3 ) th e standar ddeviatio n i n I Q withi n th e individual groups . Further , th e shap e o f th e I Q distributio n withi n th e individual group s i s discussed
. However , i f a n exper t considere dth e effect s o f lea do n I Q t o b e differen t

for low socioeconomi c statu s (SES ) than fo r high SE S subpopulations , the n judgment s wouldb e encode dseparatel y fo r th e tw o groups . Fo r

thi s purpose , lo

w SE S childre n wer e define da s thos e livin g i n household s wit

h income s a t

o r belo w th e fifteent h percentile , wherea s high SE S childre n wer e define da s thos e livin g i n household s wit

h income s abov e th e fifteent h percentile
. Sectio n 3 define s th e populatio n a t ris k a s U.S
. childre n u

p t o thei r

sevent h birthday , whic h explain s wh y I Q i s measure da t

tha t time
. Section s 4 an d5 specif y th e exposure , physiological , an denvironmenta l condition s assume dfor th e hypothetica l experiment
. As wa s tru e fo r

th e H b protocol , Sec
. 6 elicit s discussio n prio r t o th e probability encodin g by focusin g on relevan t issue s i n th e literature
. Th e purpose s wer e t o ensur e tha t th e proble mwa s structure dproperl y for th e experts , t o mak

e sur e tha t

th e expert s consciousl y reviewe dthei r knowledg e befor e providin g probabilit y judgments , an dt o pro vid e abasi s fo r

understandin g an

y discrepan t

judgments
. Sectio n 7 discusse s factor s t o b e awar e o

f whe n encodin g probabilities , an dSec
. 8 document s th e encodin g procedure
. 4. 3 CONDUC

T O FTH E SESSION

S Th e session s too k

plac e i n th e sprin g o

f 1985 ; wit

h on e exception , the y were conducte di

n th e sam e wa

y a s thos e fo r

th e H b assessmen t

(se e Sec
. 3.3)
. The sol e3 1

exceptio n wa s tha tw e brough tinformatio n t o ai d th e experts , shoul d the y hav e wante d it , i n encodin g probabilitie s abou tth e mean I Q o f th e unexpose d contro l grou p an d abou t th e standar d deviatio n i n I Q withi n individual groups . Th e informatio n concerne d WISC-R I Q mean s an

d standar d deviation s fo rsubpopulation s stratifie d by variou s demographi c variables , a s compile d in Kaufman an d Doppel t(1976 ) an

d subsequentl y summarize d i n Sattle r(1982). *
4. 4 ENCODING TH

E JUDGMENT S Probabilit y encodin g bega n in th e firs tsessio n afte rth e relevan tliteratur e an d th e factor s affectin g th e effect s o f lea d on I

Q ha d bee n thoroughl y discusse d with th e expert . W

e encode d probabilit y judgment s fo rpossibl e mean I Q decrement s in si x lead exposur e group s relativ e t o th e unexpose d contro l group . Th e exposure s wer e suc h tha t a tthei rthir d birthdays , member s o f respectiv e group s ha

d Pb B level s o f

5 , 15 , 25 , 35 , 45 , and 5 5 yg/dL . However , highe rlevel s wer e encode d a tth e reques to f afe w o f

th e experts . T o determin e usefu l point s in th e spac e o f mean I Q decrement s fo rencodin g probabilities , eac h exper twa s firs taske d t o suppl y broad (98%-CI) range s fo rpossibl e mean I Q difference s betwee n th e contro l grou p and eac h o f th e exposur e groups . W e helpe d th e exper tdetermin e thes e range s b y posin g suitabl e questions . Fo rexample , afte rarang e wa s specified , w e aske d whethe rth e exper tcoul d construc taplausibl e explanatio n i f

someda y i twer e found tha tth e tru e mean differenc e wer e outsid e tha t range . I n asimila rmanner , 98 % CI s wer e obtaine d fo rth e mean I Q o f th e contro l group an d th e within-grou p standar d deviation . A tthi s point , al l o f th e expert s agree d tha t withi n aparticula rSES level , th e sam e standar d deviatio n judgment s applie d t o al l exposur e group s and tha ti twa s reasonabl e t o assum e normal (Gaussian ) I Q distribution s fo ra n individua l subgroup . Followin g th e firs tsession , function s wer e fi tt o th e judgments . Summarie s o f th e fitte d function s an d descriptiv e informatio n wer e sen tt o th e U.S . expert s fo rthei r revie w befor e th e secon d session . Becaus e o f tim e an

d financia l constraints , i twa s impossibl e fo rth e European expert s t o revie w thes e material s befor e th e secon d meeting . Durin g th e secon d visit , al l material s wer e reviewed , additiona l probability encodin g wa s carrie d ou ta s necessary , an d eac h exper tindicate d whethe rth e fitte d distributio n correctl y represente d hi s o rhe rjudgments . I n severa l instances , subsequen t function , fittin g wa s necessary , and furthe rdiscussio n wa s conducte d b y mai l an d telephone . Fortuitously , tw o o f th e European s wer e in th e Unite d State s shortl y afte r th e secon d session , and i twa s possibl e t o hav e ashor tthir d sessio n with eac h o f them .

•Thes e normativ e dat acoul d no tb e use d in plac e o f th e experts ' judgment s regardin g control-grou p mean I

Q and within-grou p I

Q standar d deviatio n becaus e the y wer e base d on childre n wit h varyin g amount s o f lea d in thei rsystems . Thus , th e expert s ha d t o adjus tthes e value s a s the y though tappropriat e give n thei rview s on th e effect s o f lea d o n IQ . Each perso n coul d choos e t o tak e th e tabulate d value s a s poin testimates .P.4 4 3 2 4. 5 REPRESENTIN G TH E JUDGMENT S A s i n th e H b ris k

assessment , calculatin g ris k require dtha t

distribution s b e fi t

to ' th e assesse dpoints
. Althoug h th e natur e o f th e variable s bein g judge dwa s differen t fro mtha t

o f th e H b variables , th e judgmen t curve s wer e agai n generall y S shaped
. Th e judge ddifferenc e i n mea n I Q wa s bounde dfro mbelo w b y zero . Theoretically , thi s nee d not.hav e bee n th e case , bu t non e o f th e expert s gav e an y credenc e t o th e possibilit y o f lea dexposur e enhancin g IQ
. Judgment s abou t th e mea n I Q o f

th e contro l grou p an dth e standar ddeviatio n i n I Q fo r individua l group s wer e s o fa r fro man y limit s tha t

fo r al l practica l purpose s the y coul db e treate da s unbounded
. Thus , th e require ddistribution s wer e differen t

fro mthos e use dfo r

th e H b assessment
. Fo r al l o f th e experts , judgment s abou t control-grou p mea n I Q an dwithin-grou p I Q standar ddeviatio n wer e fi t wel l b y eithe r

norma l o r

lognorma l distributions
. Th e goodness-of-fi t

measur e wa s agai n th e r statistic , whic h compare s actua l judgment s wit h thos e predicte db y th e fitte dfunction
. With regar dt o difference s i n mea n IQ , th e judgment s o f

som e expert s fo r

eac h Pb B leve l wer e roughl y symmetri c abou t aparticula r value , wherea s othe r

judgment s wer e positivel y skewe d(i.e. , smal l probabilitie s wer e attribute dt o ver y larg e differences)
. I n general , th e forme r

wer e bette r

fi t wit h norma l distribution s an dth e latte r wit h lognorma l distribution s (i.e. , distribution s ove r th e logarithm s o f

I Q differences)
. Mor e specifically , th e followin g fou r familie s o f

distribution s wer e fi t t o eac h expert' s judgment s abou t difference s i n mea n IQ : (1 ) normal , allowin g aseparat e mea n an dvarianc e fo r

eac h Pb B level ; (2 ) lognormal , allowin g aseparat e mea n an dvarianc e fo r eac h Pb B level ; (3 ) equal-varianc e normal ; an d(4 ) equal-varianc e lognormal
. I n th e tw o latte r

cases , th e distribution s wer e fi t usin g asingl e poole dvarianc e fo r each , bu t allowin g separat e mea n value s a t eac h Pb B level
. Generally , th e norma l function s fi t bette r tha n th e equal-varianc e norma l functions , an dth e lognorma l function s fi t bette r tha n th e equal-varianc e lognorma l functions
. However , eac h se t o f judgment s wa s distinctl y bette r fi t b y eithe r

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

distribution s wa s considere dfurthe r

fo r tha t set
. A s argue di n Sec
. 3.5 , 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 equal-varianc e fit s wer e s o poo r

fo r al l expert s bu t

on e tha t

ther e wa s n o poin t

i n pursuin g them
. Fo r th e equal-varianc e fit s t o b e acceptable , th e slope s o f th e transforme djudgment s mus t b e abou t th e same , whic h wa s no t th e cas e fo r

th e I Q decremen t

judgments
. Althoug h th e fitte dcurve s d o cross , th e distribution s ar e space ds o fa r apar t tha t th e crossing s occu r onl y towar dth e extrem e end s of th e curves . I t

i s fa r mor e importan t

tha t th e judgment s ar e represente daccuratel y withi n th e range s o f interest
.
4. 6 TH E EXPERT S Th e individual s liste di n Tabl e 7 wer e selecte di n Marc h o f 198 5 b y OAQP S fo r participatio n i n th e ris k assessment
. Al l o f

the magree dt o participate , wit h th e3 3 TABL E 7 Expert s Participatin g i n th e I Q Encoding s

Exper t Affiliatio n
Ki m Dietrich Clair e Ernhar t
Herber t Needlema

n Michae l Rutte r
Gerhar d Winneke
Willia m Yul e University o f Cincinnat i Clevelan

d Metropolita

n Genera l Hospita l University

o f Pittsburg

h Institut e o f Psychiatry , London , Unite

d Kingdo

m University

o f Dusseldorf , Dusseldorf , Wes t German y Institut e o f Psychiatry , London , Unite

d Kingdo

m

understandin g tha t

thei r judgment s woul dremai n anonymous . Th e result s presente dar e fo r Expert s Fthroug h K, bu t th e lette r

designation s ar e randoml y assigned
. 4. 7 RESULT S i n Sec
. 4.7 , th e function s fi t t o eac h expert' s probabilisti c judgment s ar e use dt o summariz e th e quantitativ e results
. Thes e function s accuratel y represen t th e underlyin g encode dvalues , bot h becaus e th e goodnes s of fi t wa s excellen t

an dbecaus e eac h exper t endorse dth e outpu t

of th e respectiv e function s a s representin g hi s o r he r judgments
. Appendi x C present s th e detaile dquantitativ e results , includin g encode djudgments , paramete r

value s fo r

fitte dfunctions , goodness-of-fi t measures , an dderive dprobabilitie s abou t dose-respons e functions
. Sectio n C. 4 summarize s th e qualitativ e discussion s hel d wit h th e expert s abou t

th e effect s of

lea do n I Q an dbehavior
. Recal l tha t

th e expert s wer e give n th e optio n o f makin g separat e judgment s fo r lo w an dhig h SE S children
. Th e lo w SE S grou p wa s define da s thos e childre n whos e famil y income s d o no t

excee dth e fifteent h percentile ; th e remainin g childre n wer e t o b e considere din th e hig h SE S group . Al l o f th e experts , wit h th e exceptio n of Exper t F , believ e tha t

a t th e dose s unde r

consideration , lea dinteract s wit h variable s tha t contribut e t o SE S level
. Therefore , separat e judgment s wer e provide dfo r th e tw o SE S level s b y al l expert s excep t Exper t F
. Judgment s abou t

th e mea n I Q value s o f

th e lo w an dhig h SE S level s o f th e contro l grou p ar e presente dsimultaneously , a s ar e th e judgment s abou t within-grou p standar d deviations
. However , judgment s abou t mea n I Q decrement s ar e mos t easil y understoo di

fP.4 6 3 4 

### the y ar e discusse dseparatel y for th e tw o SE

S levels
. Expert

F' s judgment s will b e repeate dfor

compariso n purposes . 4.7. 1 Control-Grou

p Mea n I Q Expert I wa s unabl e t o provid e judgment s abou t th e mea

n I Q o f agrou p o

f childre n sheltere dfromlea dexposure ; th e judgment s .o f th e othe r

expert s ar e shown i

n Fig
. 13
. Expert

Fprovide don e se t

o f judgments , reasonin g tha t SE S statu s wa s no t

a facto r influencin g thes e judgments
. The symbo l withi n eac h bar i s th e media

n judge d valu e fo r mea n IQ
. I n othe r words , ther e i s a0.5 0 probability tha t th e control-grou p mea n I Q woul db e abov e th e indicate dvalu e an da0.5 0 probability tha t i t wouldb e below
. The horizonta l bracket s a t th e end s o

f th e bar s boun

deac h expert' s 90 % CI , tha t is , th e interva l suc h tha t ther e i s a0.0 5 probabilit y of th e tru e mea

n I Q fallin g belo w it , a0.9 0 probabilit y o

f it s fallin g withi n it , an da0.0 5 probabilit y o f it s fallin g abov e it
. Expert s G , H , andJ show considerabl e agreemen t i n thei r judgment s regardin g th e mea n I Q o f th e low SE

S group . Thei r

median judgment s rang e fromabou t 9 5 t o 9 7 points
. The upper

end s o f th e 90%-C I bar s rang e betwee n 9 8 an d10 0 points
. Expert

K' s media n judgmen t

i s 8 5 points ; th e mea

n I Q i s judge dt o excee d9

0 points , wit

h probabilit y

o I O 11 5 n
110 -
105 -
100 - 

### 95

- 90

- 85 - 8 0 T
T

I • I 

### T 

## t i t 

## : l 

## i

— i 1 1 1 r F G H J K

—LowSE S — T I I 

### T

* A 

# 1 I i

— i 1 i F G H J K Hig h SE S — 

### FIGUR E 1 3 Media

n Values an

d 90 % CI s fo rFunc tion s Fi tt o Judgment

s aboutth e Mea

n I Q of th e Control Group , Expert s F , G , H , J , an

d K3 5



### 0.05
. The judgment s o f thes e four

expert s regardin g th e high SE S group overlap considerably
. Thei r

media n judgment s rang e from10 3 t o abou t 106 points
. Th e upper end s o f th e 90 % CI s rang e fro m10 7 t o 11 0 points
. Expert Fdisplay s th e leas t

uncertainty , wit

h judgment s abou t

th e entir e populatio n fallin g a s expecte dbetwee n thos e o f th e othe r

expert s fo r

bot h lo w an dhigh SE S levels
. Expert

F' s media

n judgmen t

i s 10 1 points ; th e tru e mea n I Q i s judge dt o excee d10

2 points , wit

h probability 0.05
. 4.7. 2 Within-Grou

p IQ Standar

d Deviatio n Expert I was . unabl e t o provid e judgment s abou t thi s variabl e a s well ; th e judgment s o

f th e remainin g expert s ar e shown i n Fig
. 14
. Expert

Fwa s certai n tha t

th e within-grou p I

Q standar ddeviatio n wouldb e 1 5 points
. Considerin g eac h SE S group t o b e somewhat mor e homogeneou s than th e overal l population , Expert G wa s certai n tha t

th e standar ddeviatio n woul

db e 1 4 point s i

n eac h case . The judgment s o

f Expert s H , J , an dK

ar e relativel y similar
. They estimate d lowe r standar ddeviation s fo r th e lo w SE

S group becaus e it s IQ s wouldb e more homogeneou s tha n thos e o f th e high SE

S group . The media

n standar ddeviatio n fo r

th e
16- ,
15 -

14 - 

# i^

12

-
11 -
1 0 

## T
t I I 1

i i r F G H J K 

### Low SE S — i i i

F G H —

i r J K 

### Hig h SE S — FIGUR E 1 4 Media

n Values an

d 90%-C I Judgment s abou t0|Q , Expert

s F , G , H, J , an d KP.4 8 3 6 lo w SE S leve l wa s judge dt o b e abou t 1 3 point s i n al l cases ; th e larges t uppe r limi t o f th e 90 % CI s i s abou t

1 4 points
. Exper t

J gav e th e sam e judgment s fo r bot h th e lo w an dhig h SE S levels
. Expert s H an dK estimate dmedia n value s of approximatel y 1 4 point s fo r th e hig h SE S level
. Th e uppe r limit s of

thei r 90 % CI s ar e abou t

1 5 points
. 4.7. 3 Mea

n I Q Decrement s fo rth e Low SE S Grou p Figur e 1 5 summarize s th e judgment s of th e expert s regardin g mea n I Q decrement s fo r

th e lo w SE S group . Th e soli dcurve s sho w th e media n judge dI Q decrement s fo r

eac h Pb B level
. I

n othe r words , ther e i s a0.5 0 probabilit y tha t th e actua l mea n I Q decremen t

woul db e greate r

tha n th e indicate dvalue , an da0.5 0 probabilit y tha t i t woul db e less
. Th e dotte dan ddashe dpair s o f curve s boun dth e 50 % an d90 % CIs , respectively
. Figur e 1 6 compare s th e judgment s o f th e si x experts
. Th e vertica l bar s represen t eac h expert' s 90 % CI ; th e symbol s ar e hi s o r he r media n judgments
. Th e effect s o f lea d o n I Q ar e consistentl y judge dt o b e les s b y Exper t Ftha n b y th e othe r

experts
. Exper t

F als o evidence s considerabl y les s uncertaint y abou t th e magnitud e o f

thos e effect s compare dwit h th e othe r experts
. Exper t

Fi s certai n tha t

ther e i s n o effec t

o f lea do n I Q up t o a t

leas t 1 5 yg/dL
. A t

2 5 yg/dL , hi s o r

he r media n judge dI Q decremen t i s abou t 0.2 5 points ; a t

6 5 yg/dL , i t

increase s t o 1. 7 points ; Accordin g t o Exper t F , a t 2 5 yg/dL , th e I Q decremen t

exceed s approximatel y 0. 5 points , wit h probabilit y 0.05 ; a t 6 5 yg/dL , i. exceed s 3. 7 points , wit h th e sam e probability
. Similaritie s ar e eviden t i n th e judgment s o f th e othe r

experts , bu t

small , consisten t

difference s occu r

a s well
. Onl y Expert s G , H , an dJ giv e an y credenc e t o I Q effect s a t

Pb B level s a s lo w a s 5 yg/dL ; Expert s I an dK believ e ther e ar e effect s a t level s a s lo w a s 1 5 yg/dL
. Th e judgment s of Expert s H an dJ ar e consistentl y ver y close , a s ar e thos e o f

Expert s G , I , an dK, whic h a s agrou p ar e somewha t lowe r tha n thos e of Expert s H an dJ
. Fo r th e fiv e set s o f

exper t judgment s (i.e. , excludin g Exper t F) , th e media n judge dI Q decremen t a t 5 yg/d L range s fro m0 t o 2. 3 points ; a t 5 5 yg/dL , i t range s fro mabou t

6. 7 t o 11. 1 points
. Accordin g t o th e judgment s of Expert s G , H , an dJ , th e 0.9 5 fractile s fo r

I Q decremen t

rang e fro m1. 8 t o 4. 5 point s a t 5 yg/dL ; accordin g t o th e fiv e experts , the y rang e fro m9. 9 t o 15. 1 point s a t 5 5 yg/dL
. 4.7. 4 Mea n I Q Decrement s fo r th e Hig h SE S Grou p Figure s 1 7 an d1 8 displa y th e judgment s abou t mea n I Q decremen t

fo r th e hig h SE S group . A s wa s tru e fo r th e lo w SE S population , th e effec t o f lea do n I Q i s judge dt o b e les s b y Exper t

Ftha n b y th e othe r

experts
. A t

Pb B level s o f

2 5 yg/d L an dabove , th e judgment s o f

th e other s overlap , wit h thos e o f Expert s H an dJ agai n bein g ver y simila r an dsomewha t

greate r tha n thos e o f

Expert s G , K , an dI , whic h ar e similar
. Onl y Exper t H give s an y credenc e t o th e existenc e o f a n effec t

o n I Q a t

5 yg/dL ; Expert s G , I , an dJ d o s o a t 1 5 yg/dL , an dExpert s Fan dK d o s o a t 2 5 yg/dL
. Th e media n I Q decremen t a s judge db y al l th e expert s range s fro m0 t o 2. 4 point s a t 1 5 yg/d L an dfro m1. 4 t o 7. 9 point s a t 5 5 yg/dL
. Accordin g t o Expert s G , H , I , an dJ ,

### 3 7 " "ffrTTT"" ' P.4 9

4- i Exper t F

-•0.7 5 Exper t G

16- , Exper t H l - 9 - 6 - 3 

## 1

j Expert I
• + • • / / .• • •. • ** •*' * y^^ * ** ^y •*' f • * _^y . * * / .* -/ ^ •

* * » ^ / y'yy.y'

^<** * Sy\-- ** f ">* •' ^ ^ TVC- ' * . " * >''" " 1 1 1 1 1 j 1 5 2 5 3 5 4 5 5 5

15- i Exper t J

Pb B Leve l Oug/dL ) 15- i 1 2 9 - 6 - 3 - Expert K

— i 1 1 ; i r 5 1 5 2 5 3 5 4 5 5 5 6 5 Pb B Leve l Oug/dL ) FIGUR E 1 5 Judgment s abou tLead-Induce d I Q Decrements , Lo w SE S Population , Expert s F , G , H , I , J , an d K(Ay x and Pb B scale s wer e selecte d t o sho w th e detail s o f eac h expert' s judgments )
th e 0.9 5 fractile s fo r

I Q decremen t

rang e fro m0. 9 t o 5. 1 point s a t 1 5 yg/dL ; accordin g t o al l th e experts , th e 0.9 5 fractile s rang e fro m3 t o 9. 5 point s a t 5 5 yg/dL , wit h probabilit y 0.05 . 4.7. 5 Chang e i n Percentag e o f Low SE S Group wit h I

Q < 8 5 Th e judgment s abou t

control-grou p mea n IQ , mea n I Q decremen t a t eac h exposur e level , an dwithin-grou p I Q standar ddeviatio n ca n b e used , alon g wit h th e45 -

4 0 -
3 5 - & ? 30 - O QC 2 5 - © V ) C 2 0 O Q . V) & 1 5
10 - 

# I T 11 1 i o u . •-i—I

- F 6 H 

# T

j t 

## T i t 

# iii r i :

r6 M J K P 4 

# ? 

# i i

15 - e H J -25 - 

### T

_I 

# u I T 

### I I 

## 1 * I T 

# I T 

# U I T 

# I: - t i i

T

. X 

## T 1 

# T 1
S H - 3 5 J K F C H

4 5 J K 6 H

- 5 5 J K F C H J K

6 5 — 

### PbB Leve l (.ug/dL) FIGUR E 1 6 Compariso n o f

Judgment s abou tLead-Induce d I Q Decrements , Lo w SE S Population , Expert s F , G , H , I , J , and K assumptio n of

within-grou p norma l I Q distributions , t o calculat e probabilitie s abou t th e lead-induce dchang e i n th e percentag e o f th e populatio n wit h IQ s belo w an y critica l level
. Thes e probabilities , whic h shoul dcorrespon dt o judgment s abou t I Q dose-respons e function s ar e respons e rate s an dar e th e result s neede dfo r furthe r ris k calculations
. Here , w e illustrat e th e result s fo r acritica l I Q o f

8 5 points
. Result s fo r critica l I Q value s o f 7 0 an d8 5 point s ar e tabulate di n App
. C , Tabl e C.8
. Greate r uncertaint y i s eviden t i n thes e dose-respons e function s tha n i n th e separat e judgment s show n above , becaus e th e uncertaintie s surroundin g thre e parameter s ar e bein g combined
. Calcula

tion s ar e no t

possibl e fo r

Exper t I , becaus e tha t

perso n decline dt o judg e control-grou p mea n I Q an dwithin-grou p I Q standar ddeviation
. Figure s 1 9 an d2 0 sho w th e calculate dprobabilitie s abou t th e dose-respons e functio n fo r

th e percentag e increas e i n IQ s < 8 5 point s i n th e lo w SE S population
. Th e curve s ar e analogou s t o thos e i n precedin g figures
. A s expected , Exper t F' s judgment s sugges t muc h lowe r

dose-respons e function s tha n thos e o f th e others
. Th e result s fro m Expert s G , H , J , an dK overla p considerably , wit h thos e fro mExpert s H an dJ bein g ver y simila r an dslightl y highe r

tha n thos e fro mExpert s G an dK , whic h ar e als o similar
. Accordin g t o Exper t

F , th e media n respons e rat e i s les s tha n 1 % a t 2 5 yg/dL , risin g t o 4 % a t

6 5 yg/dL
. With probabilit y 0.05 , i t exceed s 1 % a t

2 5 yg/dL ; wit h th e- 3 9 P.5 1

4 - i
3 - 

# J?> J

1 - Exper

t F •0.9 5

•0.7 5

0 -I—//— i 1 1 1 r — 5 2 5 3 5 4 5 5 5 6 5 1 0 8 - 6 - 4 - 2 - Expert G

— i 1 1 1 r ~ 5 1 5 2 5 3 5 4 5 5 5

9- i

6 - 1 2 < 3 - Expert J

— i 1 1 1 r — 1 5 2 5 3 5 4 5 5 5 Pb B Leve l (/zg/dL ) Expert K 8- i
6 - 4 - 2 - 0-\-//—\ 1 1 1 r 5 2 5 3 5 4 5 5 5 6 5 Pb B Leve l (/zg/dL ) 

### FIGUR E 1 7 Judgment

s abou tLead-Induce

d I Q Decrements , Hig

h SE S Population , Expert

s F , G , H , I, J , an d K(A

—an d Pb B scale s were selecte d t o sho

w th e detail s of

eac h expert' s judgments )-FTI . »» » 40 P.5 2

10- 1

8 -



### 1 2 < 4 -

2 -

0-+ - 

### T

•-O-r-O-A-V F •H I i

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F I N i I F • M I J KF S H I J I F •H I III I J « F t H I J K •15- 2 5 3 5 4 5



### PbB Leve l (/xg/dL ) 5 5 6 5



### FIGUR E 1 8 Compariso n o f

Judgment s abou t

Lead-Induce dIQ Decrements , Hig h SE S Population , Expert s F , G , H , I , J , an dK

sam e probability , i t

exceed s 7 % a t

6 5 yg/dL
. Fo r

Expert s G , H , an dJ , th e media n respons e rat e i s fro m2.5 % t o 6 % a t 5 yg/dL ; includin g K

, i t i s betwee n 21 % an d32 % a t 5 5 yg/dL
. Fo r

Expert s G , H , an dJ , th e 0.9 5 fractile s (0.9 5 cumulativ e probabilit y levels ) fo r respons e rat e rang e fromabou t 5-11 % a t 5 yg/dL , 17-26 % a t

25 yg/dL , an d32-45 % a t 5 5 yg/dL . 

### 4.7. 6 Chang e in Percentag e o f High SE S Group with I Q < 8 5 The patter n o

f 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 , high SE S childre n ar e les s a t ris k tha n lo w SE S children
. Th e result s fo r Expert Far e th e sam e a s thos e show n previously , becaus e the y ar e base do n th e sam e judgments
. Accordin g t o Expert s G , H , andJ , th e media

n respons e rat e i s fromabou t 1 % t o 3 % a t

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

, i t i s fromabou t

5 % t o 12 % a t

5 5 yg/dL
. Accordin g t o Expert s G, H , an dJ , th e 0.9 5 fractile s fo r respons e rat e rang e fro

mabou t 2% t o 8% a t

1 5 yg/dL , 4% t o 11 % a t 25 yg/dL , an d16% t o 18 % a t 5 5 yg/dL
.4 1
8- i 9 H 

### " 5 oc 9 4- | V ) c o S- 2 ~ l V ) © Expert F •0.9 5 Fractll e .-•0.7 5 Fractll e •0.5 0 Fraetil * ...-0.2 5 Fraetil *
0-\-//— p tjyy'l.-

0.0 5 Fraetil

. T 1 1 1 - 5 2 5 3 5 4 5 5 5 6 5
40- i Expert G Exper t H

© o ac 9 c o a tn 9 CC 4 0 - 30 - 20 - 10 -

I Expert J ,' * * • * • y y * y . ' / y •* y •* 

# y.y.-'' y..<y.- * y..yy.- ,' yy- * "Z-" .-- ' „»• " i i i i i j 1 5 2 5 3 5 4 5 5 5 40- i
30 - 20 - 10 - Exper

t K

Pb B Leve l (/zg/dL ) //- i 1 1 1 1 1 — 5 1 5 2 5 3 5 4 5 5 5 6 5 Pb B Leve l (jug/dL ) FIGUR E 1 9 Increase dProbabilit y o f Havin g I Q < 85 , Low SE S Population , Expert s F , G , H , J , an d K (A-T Q an dPb B scale s wer e selecte dt o sho w th e detail s o f eac h expert' s judgments )
4. 8 DISCUSSIO N I n vie w o f

th e extensiv e debat e concernin g th e effect s o f lea do n IQ , th e degre e o f consensu s reflecte di n th e study' s result s i s notable , especiall y sinc e th e expert s wer e selecte ds o a s t o spa n th e ful l rang e o f opinion
. A s occurre dwit h th e Hb results , 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 difference s ar e attributabl e t o differin g interpretation s of , an dextrapolation s from , evidence
.P.5 4

15 -

12 -

1 2 < 

### 9

-

6 -

3 - 

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F 8 H I j I F 8 H I J « f •H I J K i i

. i i i i i i i i i i i FOMITI K

F » H I J I F •M I J [ f 8 H I J K •1 5 2 5 35 - 45 - •55 - •65 -



### PbB Leve l (/xg/dL ) FIGUR E 20 Compariso n of

Increase dProbabilit y o f Having IQ < 85 , Lo

w SE S Population , Expert s F , G , H , J , an

d K Generally , Expert s H an dJ provide dsimilar judgments , a s di dExpert s G , I , an d K
. Thes e tw o set s o

f judgment s overlappe dt o agrea t extent
. Expert

Fconsistentl y estimate dsmalle r

effect s tha n di danyon e els e an dindicate dles s uncertaint y abou t them
. Uncertaint y (a s indicate dby variance ) generall y increase dwith increasin g Pb B level s withi n th e rang e o f interest , a s expected
. I n addition , individual subjectiv e probabilitie s cove r

broade r range s fo r

th e lo w SE S tha n fo r

th e high SE

S group . Thi s resul t ma y reflec t more dat abein g availabl e a t th e hig h SE

S leve l o r more uncertaint y abou t th e influenc e o

f covariate s a t

th e low SE

S level
. Th e judgment s regardin g both mea n I Q decrement s an ddose-respons e function s ar e o f interes t i n thei r ow n rigiht
. However , the y wil l b e combine din Sec
. 5 wit h Pb B distribution s (whic h represen t differen t level s o f exposure ) t o yiel dris k

distributions
.4 3 5 ESTIMATE

D RISK S OF ADVERSE HEALT H EFFECT S VERSUS GEOMETRI

C MEA N PbB LEVE

L
Ou r strateg y fo r

assessin g th e risk s o f

advers e healt h effect s associate dwit h an y particula r

NAAQ S scenari o i s t o combin e th e dose-respons e functio n fo r aspecifie d healt h effec t

wit h aPb B distributio n estimate dfo r th e scenari o (se e Sec
. 1.5)
. I n th e absenc e o f

an y uncertainty , th e calculatio n result s i n anumbe r tha t represent s th e fractio n o f

th e populatio n tha t

woul dsuffe r

th e healt h effec t

unde r th e particula r scenario
. I

n reality , however , th e uncertaint y presen t a t eac h ste p mus t

b e incorporate d int o th e analysis
. Thus , th e calculatio n produce s afamil y o f probabilit y distribution s fro mwhic h value s lik e thos e i n Tabl e 2 ca n b e estimated
. Th e estimate dPb B distributio n associate dwit h aparticula r NAAQ S wil l depen d o n numerou s factors , includin g lea duptak e fro mnonambien t ai r sources , definitio n o f

th e populatio n a t

risk , an dgeographi c distributio n o f th e populatio n wit h respec t t o poin t source s o f

lead
. However , investigatio n of suc h factor s i s beyon dth e scop e o f th e presen t work
. T o maximiz e th e work' s usefulness , ris k estimate s wer e derive dfo r variou s specifi c Pb B distributions
. Give n a n exposur e mode l tha t link s alternativ e NAAQ S t o populatio n Pb B distributions , i t wil l b e straightforwar dt o relat e alternativ e NAAQ S t o overal l ris k

measures . Appendi x D present s th e metho dan dth e necessar y assumption s fo r derivin g ris k estimate s give n aparticula r Pb B distributio n an dtabulate s th e results
. Sectio n 5. 1 explain s an djustifie s th e particula r Pb B distribution s used
. Section s 5.2-5.4 , respectively , presen t

estimate s of

th e risk s of

advers e healt h effect s involvin g EP , Hb , an dIQ
. O f

particula r

interes t ar e th e mos t

sever e hea't h effec t

level s an dth e mos t sensitiv e populations
. Thus , th e mai n focu s i s o n E P leve l > 5 3 yg/dL , Hb leve l < 9. 5 g/d L amon g childre n age d0-3 , I Q decremen t amon g lo w SE S children , an drespons e rat e fo r I Q leve l < 7 0 amon g lo w SE S children
. Sectio n 5. 5 present s th e result s o f th e sensitivit y analysis
.
5. 1 ESTIMATED Pb

B DISTRIBUTION S Th e 1 1 lognorma l Pb B distribution s use dassum e th e sam e geometri c standar d deviatio n (GSD ) o f

1.4 2 yg/dL , bu t

diffe r i n geometri c mea n (GM)
. Th e G M value s increas e i n step s o f

2. 5 yg/d L fro m2. 5 yg/d L t o 27. 5 yg/dL
. Th e lognorma l for man dth e GS D valu e correspon dfairl y wel l t o th e actua l Pb B distribution s amon g populations
. Th e rang e of G M value s use di s broa denoug h t o represen t th e effect s o f

an y air-lea dscenari o o f interes t t o EPA
. I f othe r Pb B distribution s ar e assumed , the n significantl y differen t ris k estimate s ma y result
. Complet e listing s of th e dose-respons e uncertaintie s ar e provide din Apps
. A-C ; thos e wh o believ e tha t adifferen t

Pb B distributio n i s appropriat e ca n us e th e metho ddescribe di n App
. D t o obtai n additiona l ris k estimates
.P.5 6 4 4 

### 5. 2 OVERVIE

W O F TH E RIS KRESULT

S FO RE P As discusse di

n Sec
. 2 an dApp
. A , E

P dose-respons e uncertaint y wa s calculate d fromdat apublishe di

n Piomell i e t

al
. (1982)
. Recal l tha t tw o level s o

f E P were considere dt o b e advers e t o health : > 3 3 yg/dL an d> 5 3 yg/dL
. Thes e level s ar e on e and tw o standar ddeviation s abov e tn e "reference " E P leve l (21. 7 yg/dL ) measure di n th e grou p o f childre n havin g th e lowes t Pb B levels
. Th e followin g discussio n "focuse s on th e more sever e o

f thes e tw o level s (

> 5 3 yg/dL)
. T o produc e ris k

result s fo r

EP , th e probabilisti c dose-respons e function s wer e combine daccordin g t o th e metho dpresente din App
. D with th e Pb B distribution s describe di

n Sec
. 5.1
. Result s fo r

E P leve l > 5 3 yg/dL a s afunctio n o f G M Pb B value s ar e summarize di

n Fig
. 21
. The ris k

estimat e fo r

eac h G M valu e i s actuall y aprobabilit y distributio n ove r

apercentag e o

f th e population , bu t

only th e median s an dth e 90 % CI s ar e shown
. Th e E P respons e rat e distributions ar e essentiall y th e sam e fo r G M value s < 1 0 yg/dL
. At

G M = 12. 5 yg/dL , th e media n increase s slightly
. A large r increas e i

n th e
35- i

30 -
25 - * ? © 

### " 5 20

- OC © tn Q

. tn © oc 1 0

5 - 

### T 1 

### T 

# i 

# T i T 

# i

5 1 0 1 5 2 0 2 5 Geometri c Mea n Pb B Leve l (/zg/dL ) - 1 3 0 

### FIGUR E 2 1 Ris k Results fo rth e Occurrence of E PLevel > 5

3 yg/d L (media n value s ar

e indicate d b

y circle s an

d 90 % CI s by bars extendin g abov

e an d below th e media

n values )P.5 7 4 5 "" •
respons e rat e occur s fo rG M value s from 1 5 yg/d L t o 17. 5 yg/dL , arang e tha tinclude s th e threshol d (PbB = 16. 5 yg/dL ) reporte d in Piomell i e tal . (1982). *

• A s apoin to f

reference , th e median Pb B i s 1 5 fo r237 2 childre n age d si x month s t o fiv e year s examine d durin g th e secon d NHANE S I I (Annes te tal. , 1982) . A tG M = 1 5 yg/dL , th e E

Prespons e rat e distributio n ha s amedia n valu e o f 5.5 % and a90 % C

I o f 4.1-6.8% . 5. 3 OVERVIE

W OF TH

E RIS KRESULT S FORH

b Recal l fro m Sec . 3 tha tth e probabilisti c judgment s o f fou rexpert s regardin g dose-respons e function s fo rlead-induce d H b decrement s wer e obtaine d fo rtw o H b level s ( < 9. 5 g/d L and < 1 1 g/dL) . Function s tha tth e expert s agree d represente d thei r judgment s wer e combine d with variou s Pb B distribution s t o produc e ris k distributions . Th e metho d use d wa s th e sam e a s tha tuse d fo rth e E Pris k distributions . Result s o f

th e calculation s fo rH b leve l < 9. 5 g/d L fo rchildre n age d 0- 3 ar e summarize d in Fig . 22 . Media n value s o f

th e ris k distribution s and th e 90 % CIs aroun d thos e value s ar e indicate d fo reac h G M Pb B value , base d on function s fi tt o th e judgment s o f

Expert s A , C , D , an

d E . Th e 90%-C I bars ar e o f variou s texture s t o hel p reader s distinguish th e result s o f individual experts . Result s fo rsi x G M value s tha t increas e in step s o f

5 yg/d L from 2. 5 yg/d L t o 27. 5 yg/d L ar e show n fo rth e fou r experts . Tabl e D. 2 give s th e result s fo r1 1 G M value s ove rth e sam e range , bu tin step s o f 2. 5 yg/dL . Figur e 2 2 show s tha tth e ExpertA ris k distribution s ar e zer o fo ral l G M value s becaus e ExpertA judge d tha tH b leve l < 9. 5 g/d L canno tb e attribute d t o lea d exposure . Th e ExpertD ris k distribution s ar e nonzer o a tG M = 7. 5 yg/dL , an

d th e 90 % CIs o f

th e ExpertD ris k distribution s overla p th e 90 % CIs fo rth e Expert s C an d E a tG M value s > 7. 5 yg/dL . Th e 90 % CI s fo rth e ExpertC and E ris k distribution s overla p fo ral l G M value s considered . Th e Exper tE ris k distribution s exhibi tth e larges tuncertainty , indicate d b y th e comparativel y lon g CIs , whic h increas e in lengt h a s G M increases .
5. 4 OVERVIE

W O F TH

E RIS KRESULT S FORI

Q Judgment s regardin g I Q effect s wer e obtaine d in amanne rtha tallowe d consideratio n fro m tw o perspectives . Th e firs to f thes e i s mea n I

Q decremen t
•Th e greate rsensitivit y o f hem e synthesi s t o lea d effect s in th e presenc e o f iro n deficienc y wa s accounte d fo rin thi s stud y b y excludin g th e ag e grou p in whic h iro n deficienc y i s mos tprevalent . Recen tanalyse s (EPA , 1986c ) indicat e tha tmor e direc t contro l fo riro n statu s result s in differen tdose-respons e relationship s fo rPb B and E Pa t differen tiro n levels . Th e phras e "ExpertA ris k distributions " mean s th e ris k distribution s base d on th e judgment s o f

Exper tA .P.5 8

6O- 1

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## " 5 ac © 30 - w c o Q

. OT © 20 -

10 - 

### T

T



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# f t T

i 

# 1 a. -•—p - A C D E 5 

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# i

I 

# i i 1

-i—•—i—i—i—i—•— r ACO E ACO E 1 5 -•—I—I— i i ACO E -•— i 1—i—i—•— i 1— r

A C D E ACD E

—2 5 3 5 — 

### Pb B Leve l (/xg/dL ) •4 5 5 5


### FIGUR E 22 Ris k Results fo rth e Occurrence of H b Level < 9. 5 g/d L amon g Childre n Aged 0- 3 (media

n value s ar

e indicate d b

y geometri c symbols an

d 90% CI s b y bar s extendin g above an

d below th e media

n values ) (A-rrr). Th

e secon d i s mor

e complicated , involvin g th e lead-induce d increas e i n th e percentag e of

childre n havin g IQ s belo w aspecifie d critica l leve l denote d b y IQ* . (Th

e detail s o f thes e calculation s ar

e provide d i n App . C.) Fo

rbot h perspectives , th e Pb

B leve l o f interes twa

s thatmeasure

d a tth e 36t

h mont h of life ; th e I

Q o f interes twa

s tha t measure d o n th e sevent

h birthday . Judgment s abou tdose-respons e function s wer e combined wit

h Pb B distribution s t o produc e ris k distributions foreach o f th e I Q effects . Results fo rmea n I Q decremen t amon g lo w SE S childre n (lowes t15

% of th e population , based o n famil y income ) ar

e presente d i

n Sec. 5.4.1 . Complet

e results fo rlo

w an d hig h SE S children are give n i

n Table D.3 . Sectio n 5.4. 2 present s results fo ra

n IQ* value o

f 7 0 fo rlow SE

S children . This valu e corresponds t o tw o standar d deviation s below 100 . Othervalue s o f IQ * coul d have bee n used . Result

s fo ral l fou

rcombination s of

IQ* (7 0 an d 85) an d SE S leve l (lo

w an d high ) ar e give n i n Tabl e D.4 .47



### 5.4. 1 Risk

Distribution s ove r

Mea n IQ Decremen t A ris k distributio n for

mea n I Q decremen t

i s calculate db

y combinin g aPb

B distributio n wit

h a n individual' s judgment s abou t mea n I Q decrement s (relativ e t o a contro l group o

f childre n sheltere dfromlead ) a t differen t Pb B levels
. Figur e 23 , which i s base di n par t o n function s fi t

t o th e judgment s o

f Expert s Fthroug h K

, give s media

n value s for

mea n I Q decremen t

and90 % CI s aroun dthos e value s fo r Pb B distribution s havin g G M value s o

f 2.5-27. 5 yg/d

L (i n step s o f 5 yg/dL ) an daGS

D o f 1.4 2 yg/dL
. Th e 90%-C I bar s ar e o

f variou s texture s t o help reader s distinguis h th e result s o f individual experts
. A t G M = 2. 5 yg/dL , amea

n I Q decremen t

o f zer o result s fo r

Expert s F , I , an d K
. The Exper

t Fris k estimate s ar e nonzer o for G M > 12. 5 yg/dL , bu t

ar e comparativel y small , eve n a t

G M = 27. 5 yg/dL
. Over

th e entir e rang e o

f G M values , th e Expert

I an dK ris k distribution s ar e quit e similar ; th e sam e i s tru e fo r thos e o f Expert s H an dJ
. Abov e G M = 7. 5 yg/dL , th e median s o f th e Expert

G ris k distribution s ar e clos e t o thos e o f eithe r Expert I or K
. The 90% CI s for

th e Exper

t G ris k distribution s ar e generall y large r (i.e. , displa

y mor e uncertainty ) than thos e for th e Expert

I an dK distributions
. Abov e



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### •7.5

- 12. 5 

### •17.5 22. 5 27. 5

Geometri c Mea n Pb B Leve l (/xg/dL ) FIGUR E 2 3 Risk

Result s fo r

Mea n IQ Decremen t

in Lo w SE S Childre n (median value s indicate dby geometri c symbol s an d90 % CI s by bar s extendin g abov e an dbelo w th e media n values ) ar e4 8 P.6 0



### G M = 7. 5 yg/dL , al l th e 90 % CI s overlap , excep t tha t fo r Expert F
. Th e 90 % CI s for

th e Expert H ris k distribution s ar e large r

than thos e fo r

th e othe r

expert s a t

al l G M values
. 5.4. 2 Increase d Probabilit y of Lead-Induce

d I Q Level s Being £IQ * Th e uncertaintie s i

n (1 ) mea n IQ o f childre n sheltere dfro mlead , (2 ) within-grou p I Q standar ddeviation , an d(3 ) mea n I Q decremen t

a t differen t PbB level s wer e combine d t o calculat e th e lead-induce dincreas e i n probability (expresse da s arespons e rate , i n percent ) o

f childre n havin g IQ s < IQ * fo r IQ * value s o

f 7 0 an d85
. Thes e result s wer e the n combine dwit

h th e Pb

B distribution s describe dearlier
. Th e resultin g ris k distribution s ar e analogou s t o dose-respons e functions
. Figur e 2 4 show s th e result s for

lo w SE S childre n an

d IQ * = 70
. A s wa s tru e for IQ decrement , th e Expert Fris k distribution s ar e differen t fro mthos e of

al l th e othe r experts , excep t

a t G M = 2. 5 yg/dL , wher e th e Expert K ris k distributio n i s als o zero . A t G M > 7. 5 yg/dL , th e 90 % CI s for Expert s G , H , J , an dK

overlap
. The Expert

K median s ar e large r tha n al l other s a t

G M > 12. 5 yg/dL becaus e Expert K judge dth e mea

n IQ level s

T J © w O © u 

### o c 12- i

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I

F G H J K 

### •7. 5 12.5

—

17. 5 — Geometri c Mea n Pb B Leve l (/xg/dL ) F G H J K



### —22.5

—

— 27. 5 —
FIGUR E 2 4 Response Rate s fo rI Q Level < 7

0 amon g Lo w SE S Childre n (media n value s ar e indicate d by geometri c symbol s an d 90 % CI s by ba n extendin g abov e an d belo w th e media n values )P.6 1 4 9

amon g lo w SE S childre n sheltere dfro mlea dt o b e quit e lo w (aroun d85)
. No estimate s ar e give n fo r

Exper t I becaus e tha t

individua l di dno t

provid e th e neede djudgment s abou t mea n I Q level s fo r

childre n sheltere dfro mlea dexposur e o r fo r I Q standar ddeviation
.
5. 5 SBHSnTvTTY ANALYSI S Tw o sensitivit y analyse s wer e conducte dt o stud y th e effect s o f (1 ) havin g dose

respons e distribution s o n interval s smalle r tha n 1 0 yg/d L an d(2 ) changin g th e GS D valu e assume dfo r

th e Pb B distributions
. W e considere dth e Hb ris k assessmen t

fo r th e firs t sensitivit y analysi s an dth e EP , Hb , an dI Q ris k assessment s fo r

th e secon dsensitivit y analysis
. W e chos e th e Hb judgment s fo r th e firs t sensitivit y analysi s becaus e th e log-odd s transformatio n resulte di n function s wit h approximatel y equa l slopes
. Thi s "commo n slope " allowe dinterpolatio n wit h ahig h degre e o f confidenc e betwee n th e probabilit y distribution s encode dfo r Expert s C , D , an dE
. Th e I Q judgment s wer e les s suitabl e fo r thi s typ e of

analysi s becaus e th e slope s of th e transforme ddistribution s wer e no t equal
. Furthermore , w e chos e t o conside r childre n age d0- 3 becaus e the y ar e th e mos t sensitiv e t o lea dexposur e an dthei r dose-respons e distribution s displa y th e larges t variations , whic h tend s t o accentuat e an y sensitivitie s tha t ma y b e present
. Twenty-on e dose-respons e distribution s wer e specifie dfo r Expert s C an dE (si x distribution s o n 10-yg/d L interval s wer e encoded ) b y plottin g th e media n value s o f th e transforme ddistribution s versu s th e si x Pb B level s an ddrawin g asmoot h curv e throug h th e points
. Th e smoot h curv e allowe destimatio n o f media n value s i n step s of 2. 5 yg/d L fro m5 yg/d L t o 5 5 yg/dL
. (Eightee n distribution s wer e specifie dfo r Exper t E becaus e onl y fiv e distributions , beginnin g a t Pb B = 1 5 yg/dL , wer e encode din hi s case. ) Thes e values , alon g wit h th e commo n slop e value , completel y specifie dth e dose-respons e distributions
. Thes e distribution s wer e the n combine dwit h Pb B distribution s i n afashio n identica l t o tha t

use dt o produc e th e result s describe di n Sees
. 5.2-5.4
. Fo r Expert s C , D , an dE , th e ris k distribution s base do n th e large r numbe r of Pb B level s ar e virtuall y identica l t o thos e base do n th e smalle r numbe r of Pb B levels
. Th e difference s betwee n th e tw o set s o f calculation s ar e ver y small , bu t systematic , fo r

eac h expert
. Fo r

Expert s C an dE , th e ris k distribution s base do n fewe r Pb B level s ar e abou t 0.1 % close r

t o th e origi n tha n ar e th e correspondin g ris k distribution s base do n mor e Pb B levels
. I

n othe r words , th e ris k

estimate s w e reporte dar e slightl y smalle r tha n thos e tha t woul dhav e bee n produce db y afiner-graine danalysis
. Th e opposit e i s th e cas e fo r Exper t D s th e ris k

distribution s base do n mor e Pb B level s ar e abou t 0.2 % close r

t o th e origin
. Thes e result s strongl y indicat e tha t encodin g a t

onl y fiv e o r

si x Pb B level s wa s adequate , a t

leas t fo r Hb effects
. Th e secon dsensitivit y analysi s wa s simple r tha n th e first
. W

e repeate dth e ris k calculation s fo r

EP , Hb , an dI Q effect s (performe dassumin g aGS D o f 1.4 2 yg/d L fo r

th e Pb B distribution ) fo r

tw o additiona l GS D values ; 1. 3 yg/d L an d1. 5 yg/dL
. Th e chose n value s boun dthos e reporte di n th e literatur e an dsummarize di n th e C D fo r lea d(EPA , 1986a)
. Geometri c standar ddeviatio n value s fo r Pb B distribution s i n population s of childre n ar e extensivel y discusse di n th e EP A staf f pape r tha t review s NAAQ S fo r

lea d (EPA , 1986b)
. Th e 1.42-g/d L valu e i s reporte di n NHANE S I I (Annes t e t al. , 1982)
.



## ma^__\__w^__\\\\\\\\\\^mmmMmmP.6 2



### Fo rE Pleve l 2 5

3 yg/dL , ris

k results ar

e virtuall y unchange

d atlow ( < 7. 5 yg/dL ) G M Pb B values . Difference s ar e greates tatG

M = 15 yg/dL : results a tGS D = 1. 3 yg/dL ar e abou t28% lower(i.e. , arespons e rate o f 4 % versus 5.5%) , an

d result s atGS

D , = 1. 5 yg/dL ar

e abou t22% highe

rtha n thos e assumin

g GS D = 1.4 2 yg/dL . AtG

M = 27. 5 yg/dL , results forGS D value s o

f 1. 3 yg/dL an

d 1. 5 yg/d L ar e withi n 11 % o

f thos e assuming aGS

D o f 1.4 2 yg/dL . Th

e threshold forlead-induced E Peffects , whic

h wa s calculate d b

y Piomelli e tal . (1982) t o be a taPb B leve l o f abou t16. 5 yg/dL , probabl

y explain s th e observatio n thatresults ar e mos tsensitiv e t o G

M Pb B value s aroun

d 15 yg/dL . Results fo rExpert

s C an d E ar e virtuall y unaffecte d b

y th e GS D valu e fo rH

b leve l < 9. 5 yg/d

L an d children age

d 0-3 . Fo

rExper tD , difference s i

n mea n value s o

f th e risk distribution s ar

e abou t10 % forG

M value s > 1

5 yg/d L (e.g. , media

n respons e rate s at G M = 27. 5 yg/dL are 4.6% , 5.3% , an d 5.7% fo rGS

D = 1.3 , 1.42 , an

d 1. 5 yg/dL , respectively) . Th

e differenc e beginning at1 5 yg/dL ca

n probabl y be attribute d to Exper t D' s judgmen

tthatathreshold exist s fo rlead-induced H b effect s i

n th e 15-2 5 yg/dL Pb

B range . Fo

rI Q decrementamon

g lo w SE S children , th e differentGS D value s have essentiall y n

o effec to

n th e ris k distributions fo ran

y of th e six I

Q expert s (Expert

s F throug h K) . Th e difference s ar

e generall y les s tha

n 0. 1 mea n I Q points . Th

e same i s true fo rth e I Q respons e rate atIQ* = 7 0 an d lo w SE S children . Difference s betwee n GS D = 1.4 2 yg/dL an

d th e othe rtw o GS

D level s ar

e les s tha n 0.2 % (i n term s o f respons e rate ) fo rExpert

s H , J , an d K , an d les s tha n 0.1 % forExper

tG . Ris k distribution s fo rExper tF ar e unaffected .--•- —5T" ~ " *
6 CONCLUDIN G REMARK S
Forma l ris k

assessment s wer e conducte dt o ai dth e EPA Administrato r in determinin g an adequat e margi n o f safet y fo r

th e curren t

revie w o f

th e NAAQ S fo r lead
. Th e ris k

assessment s focu s o n thre e potentiall y advers e effect s o f exposur e t o lea d in childre n fro mbirt h throug h th e sevent h birthday : EP elevation , H b decrement , an dI Q effect
. Th e sam e genera l strateg y was followe din al l thre e cases : fo r tw o level s o f eac h effect , probabilit y distribution s ove r populatio n respons e rat e wer e estimate da t a serie s o f Pb B levels
. Thes e distribution s wer e estimate dfro mdat afo r th e EP assessmen t

an dfro mexper t

judgment s fo r

th e H b an dI Q assessments
. Thes e estimate s ar e of interes t

i n thei r

ow n right ; however , the y wer e als o combine dwit h Pb B distribution s t o yiel dprobabilit y distribution s ove r th e estimate dpercentage s of childre n experiencin g th e particula r healt h effect
. Fo r eac h o f

tw o level s o f

E P elevation , th e dose-respons e probabilit y distribution s wer e calculate ddirectl y fro mth e dat aof alarg e study
. Becaus e appropriat e dat awer e unavailabl e fo r th e H b an dI Q assessments , i t wa s necessar y t o obtai n probabilit y judgment s fro mexperts
. Fo r eac h effect , aprotoco l wa s develope dt o standardiz e an ddocumen t th e procedure s use dt o encod e th e judgmenta l probabilities
. Dose-respons e probabilit y judgment s wer e obtaine dfro mfou r H b experts
. Fiv e I Q expert s provide dprobabilit y judgment s regardin g expecte dI Q decrement s cause db y lea d exposure , expecte dIQ i n th e absenc e o f lea dexposure , an dwithin-grou p I Q variability ; a sixt h provide djudgment s wit h respec t t o th e firs t

variabl e only
. Dose-respons e probabilit y distribution s ove r th e occurrenc e of

I Q level s belo w 7 0 an d8 5 point s wer e calculate dfro mth e judgment s of th e firs t

fiv e I Q experts
. Fo r bot h H b an dIQ , th e judgment s of

eac h perso n wer e treate dan dpresente dseparatel y fo r al l analyses
. Additiona l analyse s indicate dth e exten t o f agreemen t

amon g experts
. Probabilit y distribution s ar e presente din graphica l an dtabula r for mfo r

expecte d lead-induce dIQ decremen t an dfo r dose-respons e function s fo r tw o level s o f

eac h o f th e thre e effects
. Fo r

Hb , judgment s wer e obtaine dseparatel y fo r childre n age d0- 3 an d 4-6
. Judgment s o f

thre e of

th e fou r

expert s displa y substantia l agreement
. Fo r IQ , judgment s wer e obtaine dseparatel y fo r childre n of

lo w an dhig h SE S groups . Th e judgment s o f

on e exper t

differe dconsiderabl y fro mthos e of th e othe r

five , whic h ar e relativel y simila r

bu t fal l int o tw o distinguishabl e groups . Blood-lea ddistribution s ar e expresse da s lognorma l distribution s wit h geometri c mean s ove r

awid e rang e an dageometri c standar ddeviatio n of 1.42
. Fina l ris k estimates , therefore , ar e presente di n term s o f probabilit y distribution s ove r th e percentag e of

childre n experiencin g particula r effect s a s afunctio n o f geometri c mea n Pb B level
.-wzr 

### REFERENCE

S
Annest , J.L. , e t

al. , Blood-Lead

Levels for

Persons 6

Months - 74 Years of

Age: United States, 1976-80, U.S
. Departmen t o f Health an dHuma

n Services , Advanc e Dat afrom Vital an dHealt h Statistic s o f th e Nationa l Cente r

fo r Health Statistics , No
. 7 9 (Ma y 12 , 1982)
. EPA , Ai r Quality Criteria for

Lead, draf

t (1986a)
. Fo r

copies , contac t

Cente r for Environmenta l Researc h Information , USEPA/OR D Publications , 2 6 W
. St
. Clair , Cincinnati , Ohi o 45268 , (513 ) 569-7562
. EPA , Review of

the National

Ambient Air Quality Standards for

Lead: Assessment

of Scientific and

Technical

Information, Offic e o

f Ai r Qualit y Plannin g an dStandards , draf t staf f pape r (1986b)
. Fo r

copies , contac t

Jef f Cohen , USEPA/OAQPS , MD-12 , Researc h Triangl e Park , N.C
. 27711 , (919 ) 541-5655
. EPA , Lea dEffects on Cardiovascular Function, Early Development, and Stature: An Addendum to US. EPA Air Quality Criteria for

Lead (1986c)
. Fo r

copies , contac t

Cente r fo r Environmenta l Researc h Information , USEPA/OR D Publications , 2 6 W

. St
. Clair , Cincinnati , Ohi o 45268 , (513 ) 569-7562
. Hammond , P. , R
. Bornschein , an dP
. Succop , Dose-Effect and Dose-Response Relationships of

Blood Lead to Erythrocyte Protoporphyrin in Young Children, Environmenta l Research , 33:187-19 6 (1985)
. Kaufman , A.S. , an dJ.E
. Doppelt , Analyst' s of WISC-R Standardization Data in Terms of the Stratification Variables, Chil dDevelopment , 47(1):165-17 1 (1976)
. Piomelli , S. , e t

al. , Threshold

for Lead Damage to Heme Synthesis in Urban Children, Proc
. Nationa l Academy o f Science s (Medica

l Sciences) , 79:3335-333 9 (1982)
. Ruckleshaus , W.D. , Risk

in a Free Society, Risk

Analysis , 4:157-16 2 (1984)
. Sattler , J.M. , Assessment of Children's Intelligence and Special Abilities, 2ndEd. , Allyn andBacon , Bosto n (1982)
. Schwartz , J. , persona l communication , U.S
. Environmenta l Protectio n Agency , Washington , D.C
. (1986)
. Seaman , C , persona l communication , Ne w Yor k University Medica

l Center , Ne

w Yor k (1985)
. Wallsten , T.S. , andD.V
. Budescu , Encoding Subjective Probabilities: A Psychological and Psychometric Review, Management Science , 29:151-17 3 (1983)
. Wallsten , T.S. , B.H
. Forsyth , an dD.V
. Budescu , Stability and Coherence of

Health Experts? Upper

and Lower Subjective Probabilities about Dose-Response Functions, Organizationa l Behavio r

andHuma

n Performance , 31:277-30 2 (1983)
.53



### Whitfield , R.G. , an

d T.S . Wallsten , Estimating Risks of Lead-Induced

Hemoglobin Decrements underConditions of Uncertainty: Methodology, Pilot Judgments, and Illustrative Calculations, Argonn e Nationa l Laborator

y Repor tANL/EES-TM-27

6 (Sept . 1984) . Winkler , R.L. , A n Introduction to Bayesian Inference and Decision, Holt, . Rinehar tan d Winston , Ne w Yor k (1972) . ^mP.6 6 55

APPENDIX A FITTIN G FUNCTION S TO DAT A ON LEAD-INDUCE D ELEVATE

D E PLEVEL ST T APPENDIX A FITTIN G FUNCTION S TO DAT A O N LEAD-INDUCED ELEVATE

D E PLEVEL S
Sectio n 2 discusse s dose-respons e relationship s betwee n Pb B an d elevate d E

P levels . Becaus e th e dat apublishe d i n Piomell i e tal . (1982) * ar e complet e an d reliable , probability encodin g o f exper tjudgment s wa s unnecessary . Thes e dat a(se e Fig . 1) , when combine d with sample-siz e dat afo rtha tstud y (se e Tabl e 3) , ar e sufficien tt o develo p th e followin g expression s fo rth e mean dose-respons e curve s fo rth e tw o E Plevel s (

> 3 3 ug/d L and > 5 3 yg/dL ) o f

interest . i10.7 , fo rL < 16. 4 yg/d L F P = \ -

1 (100 * [0.103 U - 16.4 ) - 1.24] , fo rL > 16. 4 yg/d L fo rE P> 3 3 yg/dL , an

d (2.4 , fo rL < 16. 6 yg/d L R E P = ) 100*" 1 [0.103( L - 16.6 ) - 1.98] , fo rL > 16. 6 yg/d L fo rE P> 5 3 yg/dL , where :

R= populatio n respons e rat e (percentage ) o f childre n havin g E Plevel s greate rthan orequal t o th e specifie d value , L = Pb B leve l (yg/dL) , an

d 100« ~ [• ] = invers e o f

th e cumulativ e distributio n functio n (CDF ) o f a standardize d normal random variable . Th e Piomell i e tal . (1982 ) dat aindicat e athreshol d fo rE Peffect s a taPbB leve l o f abou t 16. 5 yg/dL . (A s discusse d in Sec . 5.2 , new analyse s indicat e asomewha tdifferen tdose respons e relationshi p when direc tadjustment s ar e made fo riro n status. ) Further , respons e rate s o f

2.4 % and 10.7 % wer e foun d t o b e "natura l frequencies " (respons e rate s a tPb B level s < 15. 5 yg/dL ) fo rth e occurrenc e of E Plevel s > 5 3 yg/d L and > 3 3 yg/dL , respectively . Probabilit y distribution s ove rth e populatio n respons e rat e determine d fo r10 PbB-E Pcombination s ar e summarize d in Tabl e A.l . Thes e distribution s ar e eithe rbet a Bt R; - ( x. !),( „ - X - 1) 1 C RJ U R'
•Piomelli , S. , e tal. , Threshold forLead

Damage to Heme Synthesis in Urban Children, Proc . Nationa l Academ y o f Scienc e (Medica l Sciences) , 79:3335-333 9 (Ma y 1982) .TABL E A. 1 Probabilit y Distribution s and Parameter s fo rE PLevel s amon g Ne w Yor k Cit y Childre n

Pb B Leve l (yg/dL )
2-1 7 17-2 1 21-3 1 31-4 1 41-9 8 Functiona l

For m

Norma l Norma l Norma l Norma l Beta EP > 3 3 yg/d L

Paramete r
E[R] a = 10. 7 E[R ] = 14. 9 E[R ] = 37. 5 E[R ] = 76. 1 X= 4 2 Value s

SD[R] b= 1. 1 SD[R ] = 1. 6 SD[R ] = 2. 1 SD[R ] = 4. 1 N = 4 3 Func t iona l

For m

Norma l Norma l Norma l Norma l Bet a EP > 5 3 yg/d L

Paramete r
E(R ] = 2. 4 E[R J = 3. 8 EfR ] = 14. 6 E[R ] = 49. 0 X= 4 0 Value s

SD(R ] = 0. 5 SD[R ] = 0. 9 SD[R ] = 1. 5 SD[R ) = 4. 8 N = 4 3 o

a E(R ) denote s the expecte d valu e o f R , i n percent . . SD(R ) denote s the standar d deviatio n o f R , i n percent . Source : Dat a ar e fro m Piomell i e t al . (1982) .59

o rnormal a teac h Pb

B level , where : N = numbe ro f

childre n a taspecifi c Pb B level , X = numbe rof

childre n havin g E

Plevel s > 3 3 yg/d L o r> 5 3 yg/dL , and R' = 0.01R . Th e CD F B(R' ) fo rth e bet adistributio n i s

R ' B(R' ) = J B(R')dR '

R= 0 ° ° o 

# •XC>" '
The mean E[R] an

d standar d deviatio n SD[R] o f th e bet adistributio n and , wher e appropriate , it s normal approximatio n ar e 

# „,„.!§!
. [SJ-^i ]
Fo rmos tPbB-EPcombinations , th e quantit y NR'( 1 - R' ) wa s larg e enoug h ( > 5) t o justif

y usin g th e normal approximation .6 1

APPENDIX B FITTIN G FUNCTION S TO ENCODED JUDGMENT S RELATIN

G T O LEAD-INDUCE D H b DECREMENT 

## " 1P.7 1 6 3
APPENDIX B FITTIN G FUNCTION S TO ENCODED JUDGMENT S RELATIN

G TO LEAD-INDUCED H b DECREMENT Appendi x B i s organize da s follows : Sec
. B. l reproduce s th e protoco l use dfo r th e Hb encodin g sessions ; Sec
. B. 2 detail s th e mathematica l formulation s fo r th e dose

respons e models ; Sec
. B. 3 tabulate s encode djudgments , specification s fo r function s fi t

t o thos e judgments , an dCI s fo r encode djudgment s an dfitte dfunctions ; an dSec
. B. 4 summarize s th e discussion s hel dwit h eac h o f th e experts
. Becaus e H b expert s ar e generall y knowledgeabl e abou t EP , significan t

portion s o f

thes e discussion s focu s o n th e significanc e of

elevate dE P levels , a n additiona l topi c o f interes t t o EPA
.
B. 1 H b PROTOCOL
B.l. l Introductio n Th e U.S
. Environmenta l Protectio n Agenc y i s charge db y th e Clea n Ai r Ac t wit h settin g an drevisin g NAAQ S fo r selecte dpollutant s a t level s sufficien t

t o protec t

th e publi c healt h wit h a n adequat e margi n o f safety
. A s yo u know , th e scientifi c base s fo r NAAQ S ar e presente dan dreviewe di n CDs
. I n suppor t o f 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 mwhic h th e mos t susceptibl e population s ca n b e determine dan d fro mwhic h variou s advers e healt h effect s ca n b e identified
. Th e C D summarize s an d evaluate s th e availabl e clinical , epidemiological , an danima l o r toxicologica l laborator y evidenc e wit h regar dt o th e physiologica l an dadvers e healt h effect s of lead , an d therefor e represent s ou r mos t up t o dat e knowledg e o n lea deffects
. A s on e aspec t

of th e revie w process , EPA assesse s healt h risk s b y identifyin g th e mos t sensitiv e population s fo r eac h pollutan t

an destimatin g probabilisticall y th e number s o f

peopl e i n th e population s wh o ma y suffe r eac h o f

variou s well-define d advers e healt h effect s attributabl e t o th e pollutant
. I t i s believe dtha t

informatio n abou t th e healt h risk s associate dwit h variou s potentia l standard s wil l ai dth e EP A Administrato r

in selectin g tha t

standar dwhich , in hi s o r he r judgment , protect s th e publi c healt h wit h a n adequat e margi n of safety
. Becaus e th e ris k

estimate s tha t

EPA seek s ar e ofte n base di n par t o n dose

respons e relationship s an duncertai n lead-exposur e estimates , 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 evidenc e an dt o probabilisticall y estimat e lea dexposur e unde r alternativ e NAAQS
. Obtainin g th e healt h ris k estimate s the n involve s combinin g probabilit y estimate s fo r dos e respons e an dexposure . Th e proble mof

estimatin g dose-respons e relationship s i s simila r t o tha t whic h exist s in clinica 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 eP.7 2 6 4 

### fro m th e dat

at o mak e th e bes tdecisio n forthe patient . Here , too , i tis necessar y t o us e scientifi c judgmen

tt o extrapolate fro

m th e availabl e data . Th e extrapolatio n i s no

t certai n and, therefore , w e will ai d yo u to representyou

ropinio n probabilistically . Furthermore , sinc e th e extrapolatio n depend s o n one' s interpretatio n o

f th e literature , differen tpeopl e will have differen tjudgments . Fo reach healt

h effect , w

e inten d t o obtai n th e probabilisti c judgment s o f abou tfiv e experts t o sample th e rang e o f respecte d opinions . Th

e mode l fo restimatin g risk

s wil l no tmerg e thes e judgment

s int o asingl e averag e judgment, bu

tratherwill estimat e th e rang e o f risk s base d o n the rang

e o f judgments . I

f w e as ris k analysts d

o ou rjo b properly , the

n notonly will w

e b e abl e t o sho w th e EP A Administrato rth e rang e o f estimate s base

d o n th e rang

e o f judgments , bu

t w e will als o b e abl e t o sho w som e o f th e source s of

th e disagreements . Indeed, asid e benefi to f thi s exercis e i

n whic h w e probe you

rknowledg

e i n astructure d manne

rma y b e t o help identif

y source s o

f greates tdisagreement . Base d o n th e evidenc e i

n th e lead CD , two populations hav e been identifie d a

s being mos

tsusceptibl e t o the effect s o f lea d intoxication . On

e is children fro

m birt h throug h the sevent

h birthday , an

d th e otheri s pregnan

twomen, o

rmor e precisely , the fetuse s carried b

y pregnan

twomen. * A numbe

ro f advers e healt

h effect s hav

e bee n identifie d forwhic

h w e woul d like to estimat e dose-respons e functions includin g the on e discusse d below . B.1. 2 Lead-Induce

d H b Decrements W e woul d lik e to representi

n probabilisti c for

m you ropinio n abou tthe locatio n an d shap e o f dose-respons e function s fo rcertai n well-define d level s o f lead-induce d H

b reductio n i

n th e population o

f U.S . children fro

m birt h throug h th e sevent

h birthday . W

e realiz e thatavailabl e dat ad o notfull y define thes e functions ; i f they did , the

n i twoul d be unnecessar

y t o obtai n you

ran d othe rexperts ' opinion

s abou tthem . Nevertheless , i

f th e population , th e exposur e conditions , an

d th e healt

h effect s ar

e all precisel y defined , the n suc h function s i

n fac texist , an

d w e woul d like you

rbes tjudgmen

tabou twha tthey woul d loo k lik e i f th e dat acould b e collected . Ther e ar e difference s o

f opinion , o

f course , as to wha

tdegre e o

f reduction i

n H b leve l constitute s ahealt

h risk . Th

e Clea n Ai rActmake

s i tclea rthatEP

A shoul d se tit s standards to protec tagains tadvers e healt h effects . However , th e reduction i n H b leve l considere d t o b e advers e ma y b e differen tfo rregulator y purpose

s tha n forclinica l action . Sinc

e i ti s generall y agreed fo rchildre n thataH

b leve l o f abou t1 2 g/dL is norma l an d abou t9 g/dL i s anemic , w

e will specif

y tw o H b level s i n thatinterval , namely 9. 5 g/dL an

d 1 1 g/dL , an

d trea teach a

s the physiological effec tfo rpurpose s o f specifyin g adose-respons e function . W e will elici tfro

m yo u probabilit

y judgment

s abou t th e shape an

d locatio n o

f th e dose-respons e curve foreach o f th e two level s o

f effect s i n th e sensitiv e population .

•I n thi s report, w

e focu s onl

y o n children age

d 0-6 .P.7 3 6 5 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 birth ' throug h thei r

sevent h birthdays
. However , yo u ma y believ e o n variou s ground s tha t younge r an dolde r

childre n i n thi s grou p hav e differen t dose-respons e function s fo r lead

induce dH

b reduction
. I

f so , the n w e wil l elici t

you r judgment s separatel y fo r ag e group s 0- 3 an d4-6 . B.l. 4 Exposur e Condition s W e wil l b e askin g you r

judgmen t

abou t populatio n respons e rate s a t variou s Pb B levels
. Assum e tha t

th e Pb B leve l unde r consideratio n fo r

agive n judgmen t

i s i n equilibriu ma s aresul t

o f asufficientl y lon g ter mconstan t lea dexposur e withou t gros s excursion s abov e o r

belo w th e state dlevel
. B.1. 5 Physiologica l Condition s Becaus e th e effec t

of lea do n Hb leve l depend s o n man y parameter s o f aperson' s system , i t

i s necessar y t o specif

y assumption s abou t

thos e parameter s i n th e population
. Th e effec t

of lea di n th e syste mdepend s o n th e person' s nutritiona l an dmetaboli c status
. Th e incidenc e o f iro n deficienc y i s greate r in childre n tha n i n adults , an dgreate r ye t i n childre n age d0- 3 tha n age d4-6 , wit h awid e rang e of iro n level s i n childre n up t o thei r sevent h birthday
. Assum e tha t th e distributio n o f

iro n level s i s tha t

whic h yo u believ e i t

actuall y t o b e i n th 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 ; phosphorous ; an d magnesium
. Assum e i n al l case s tha t thes e nutrient s ar e distribute din th 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 o f

diet s an d nutritiona l level s of

U.S
. children
. I t i s als o wel l establishe dtha t E P leve l i s positivel y correlate dwit h Pb B level
. However , th e correlatio n i s no t perfect , an dther e i s arang e o f E P value s a t

an y give n Pb B level
. You may believ e tha t th e effec t

o f lea dvarie s wit h E P level
. I f so , assum e tha t E P i s distribute da t

eac h Pb B leve l a s yo u believ e i t i n fac t is
. B.1. 6 Factor s t o Conside r I n orde r t b 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 i n 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
. Firs t o f all , coul dyo u tel l u s somethin g abou t how , i n you r

judgment , lea dan diro n interac t t o reduc e Hb level s an dsomethin g abou t th e relatio n betwee n iro n an dlea d level s i n th e body ? Similarly , w e woul db e intereste di n you r opinion s abou t

th e sam e question s wit h regar dt o zin c an dlea dan dt o calciu man dlead
. I t appear s tha t

lea d affect s Hb level s throug h thre e somewha t separat e routes : interferenc e wit h hem e synthesis , interferenc e wit h globi n synthesis , an ddecrease dlif e expectanc y o f erythrocytes
. Briefly , wha t i s you r interpretatio n o f

th e literatur e o n thes e variou sP.7 4



### effect s o f lead ? E Pleve l increase s wit

h iro n deficiency , bu

ti tals o increase s wit

h Pb B an d i s considered t o b e aprox y measur e fo rth e amoun

to f lead recentl y cumulated i n bod y tissue . Considerin

g onl y tha tportion o

f E Pelevatio n du

e t o lead , i

n you rjudgment, i s the relationship betwee n Pb B an d H b differen tatdifferen tE Plevels ? Finally , w

e kno w thatsome groups o

f children ar

e atgreate rrisk o

f exposur e to lea d du e t o thei rlivin g i

n deterioratin g pre-195 0 housin g o ri n urba n area s wit

h large amount s o f vehiculartraffic . These children woul d tend to hav

e hig h lea d levels , bu

td o yo u believ e thatthere ar

e als o independen

treasons to thin

k thatthei rdose-effec tcurve s will b e differen tfro

m childre n wh o liv e i n othe rcircumstances ? Fo rexample , thes e ma

y be th e same children wh o tend to hav

e poore rdiet s an

d les s acces s t o medica l care . Wha ti s you ropinio n regarding the possibilit y o f acorrelatio n betwee n increase d exposur e an d increase d susceptibility ? Ar e there othe rfactor s to conside ri n thinking abou tth e dose-respons e functions forlead-induced H b decrements thatwe shoul d discus s now ?
B.1. 7 Factors t o Kee

p i n Min d Whe n Makin g Probabilit

y Judgment

s Ther e i s usuall

y uncertaint

y associate d wit

h conclusion s thatw

e dra w fro m research an

d mor e generall y i

n ou reveryda y thinking . However , noteveryon e i s awar e o f all th e source s thatcontribut e t o thei runcertainty , no

rar e mostpeopl e familia rwit h th e proces s of

actuall y expressin g thei runcertaint y i n probabilisti c terms . Whe n a n exper ti s aske d t o mak

e probabilit

y judgment

s o n sociall y importantmatters , i tis particularly importan

tthath e o rsh e conside rth e relevan tevidenc e i n asystemati c an

d effectiv e manne

ran d provide judgment

s thatrepresenthis o

rhe ropinions well . Experimenta

l psychologists an

d decisio n analysts hav

e amassed aconsiderabl e amoun to f dat aconcerning th e wa

y peopl e for

m an d expres s probabilisti c judgments . Th e evidenc e suggests thatwhe n considerin g large amount s o f complex information , most peopl e emplo

y simplifyin g heuristic s an d demonstrat

e certai n systemati c distortion s of thought, i.e. , cognitiv e biases , whic h adversely affec tthei rjudgments . Th e purpose o

f thi s sectio n i s t o mak

e yo u awar e of thes e biase s an

d heuristic s s o that , a s muc h a s possible , yo

u ca n avoid the

m i n makin g probabilit

y judgments . W

e wil l firs trevie w th e mostwidesprea

d biase s an

d heuristics , an

d the n offe rsom e suggestion s t o hel p yo u mitigate thei reffects . B . 1.7. 1 Sequentia

l Consideration of

Information Generally , th e orderi

n whic h evidenc e i s considere d influence s th e fina l judgment, althoug

h logicall y thatshoul

d notb e th e case . O f necessity , piece s o

f information ar

e considere d one b

y one i n asequential fashion . However , thos e considered firs tan

d las ttend t o dominat

e judgment. I

n part , initial informatio n ha s it s undu e influence becaus e i tprovides th e framewor k whic h subsequentinformatio n i s then tailore d t o fit . Fo

rexample , peopl e usually search fo revidenc e t o confirm thei rinitial hypotheses ; the y rarely look fo revidenc e thatweighs against them . The late revidenc e ha s its undu e effec tsimply becaus e i ti s freshe ri n memory .

### 6 7 Relate dt o thes e sequentia l effect s i s th e phenomeno n o f anchorin g an

d adjustment
. Basedo

n earl y partia l information , one form s a n initia l probability estimat e regardin g th e even t

i n question. Thi s ancho r judgmen t

i s the n adjuste da s subsequen t informatio n i s considered
. Unfortunately , suc h adjustment s ten dt o b e to o conservative
. I

n othe r words , to o littl e weight i s attache dt o informatio n considere d subsequen t

t o th e formatio n o

f th e initia l judgment
. B.l.7. 2 Effect s of

Memor y o n Judgmen

t It i s difficul t

for mos t peopl e t o conceptualiz e andmak e judgment s abou t

large , abstrac t universe s or

populations
. A natura l tendenc y i s t o recal l specifi c member s and then t o conside r

the mrepresentativ e o

f th e populatio n a s awhole
. However , th e specifi c instance s ofte n ar e recalle dprecisel y becaus e the y stan dou t i n some way , suc h a s bein g familiar , unusual , especiall y concrete , o r personall y significant
. Unfortunately , th e specifi c characteristic s o f thes e singula

r example s ar e the n attributed , ofte n incorrectly , t o al l th e member s o

f th e populatio n o

f interest
. Moreover , thes e memor y effect s ar e ofte n combine dwit

h th e sequentia l phenomen adiscusse dearlier
. For example , i

n considerin g th e evidenc e regardin g th e dose-respons e curv e o f aparticula r

pollutant , yo

u might naturall y firs t

think o f astudy yo

u or apersonal frien drecentl y completed
. O r yo u might think o f astud y yo

u recentl y read , or

one tha t wa s unusua

l an dtherefor e stand s out
. Th e tendenc y might the n b e t o trea t

th e recalle dstudie s a s typica l o f th e populatio n o

f relevan t

research , ignorin g importan t difference s amon g studies
. Subsequent

attempt s t o recal l informatio n coul dresul t i n thinkin g primaril y o

f evidenc e consisten t wit h th e initia l item s yo

u though t of
. B.l.7. 3 Estimatin g Reliability o f Informatio

n Peopl e ten dt o overestimat e th e reliabilit y o f information , ignorin g factor s suc h a s samplin g erro r

an dimprecisio n o

f measurement
. Rathe r

the y summariz e evidenc e i n term s o f simpl e anddefinit e conclusions , causin g the mt o b e overconfiden t i n thei r judgments
. Thi s tendenc y i s stronge r whe n one ha s aconsiderabl e amount o f intellectua l and/o r persona l involvemen t

i n aparticula r

field
. I n suc h cases , informatio n i s ofte n interprete di

n awa y tha t i s consisten t

wit h one' s belief

s andexpectations , result s ar e overgeneralized , andcontradictor y evidenc e i s ignore dor underestimated
. B . 1.7. 4 Relatio n betwee n Even tImportanc

e an d Probabilit

y Sometime s th e importanc e o f events , or

thei r possibl e cost s o r

benefits , influence s judgment s abou t th e certaint y o

f th e event s when , rationally , importanc e shoul dno t

affec t probability
. I

n othe r words , one' s attitude s towar dris k ten dt o affec t one' s abilit y t o mak

e accurat e probability judgments
. Fo r example , man

y physician s ten d t o overestimat e th e probabilit y o f very sever e diseases , becaus e the y fee l i t i s importan t t o detec t andtrea t

them ; similarly , man

y smoker s underestimat e th e probability o f advers e consequence s o f smoking , becaus e the y fee l tha t th e odd s d

o no t apply t o themselve s personally
.

### B.l.7. 5 Estimatio n of Probabilitie s Anothe r limitatio n i s relate dt o one' s abilit y t o discriminat e betwee n level s o f uncertaint y andt o us e appropriat e criteri ao f discriminatio n for

differen t range s o

f probability
. Peopl e ten dt o estimat e bot h extrem e andmid-rang e probabilitie s in'th e sam e fashion , usuall y doin g apoor jo b i n th e extremes
. It

help s her e t o think

i n term s o f odd s a s wel l a s probabilities
. Thus , fo r example , changin g aprobability-estimat e from 0.51 0 t o 0.50 1 i s equivalen t t o achang e i

n odd s fro

m1.041: 1 t o 1.004:1,

- bu t achang e froma n estimat e o

f 0.99 9 t o 0.99 0 change s th e odd s by afacto r o f abou t 1 0 from999: 1 t o 99: 1 The close r

t o th e extreme s (eithe r 0 or 1 ) tha t one i s estimatin g probabilities , th e greate r

th e impac t

o f smal l changes
. . B . 1.7. 6 Recommendations Althoug h extensiv e an dcarefu l trainin g woul db e necessar y t o eliminat e al l th e problem s mentione dabove , some relativel y simpl e suggestion s can help minimiz e them
. Mos t importan t

i s t o b e awar e o

f one' s natura l cognitiv e biase s andt o tr y consciousl y t o avoi dthem
. T o avoi dsequential

effects, keep i

n min dtha t th e orde r

i n which yo

u think o f informatio n shoul dno t

influenc e your

final judgment
. I t

ma y b e helpfu l t o actuall y not e o n pape r th e importan t

fact s yo u ar e considerin g andthe n t o reconside r the mi n tw o or more sequences , checkin g th e consistenc y o f you r judgments
. Tr

y t o kee p a

n open min

d unti l yo u hav e gon e throug h al l th e evidence , anddon' t le t th e earl y informatio n yo u conside r swa y yo u more than i s appropriate
. T o avoi dadvers e memory effects, defin e variou s classe s o f informatio n tha t

yo u dee mrelevan t

andthe n searc h your

memor y for example s o

f each
. D o no t restric t your thinkin g onl

y t o item s tha t

stan dou t

for specifi c reasons . Mak

e aspecia l attemp t

t o conside r conflictin g evidenc e an dt o think o f dat atha t

ma y b e inconsisten t

wit h a particula r theory
. Also , b e carefu l t o concentrat e o n th e give n probability judgmen t an d d o no t le t your ow n value s (ho

w yo u wouldmak

e th e decisio n yourself

) affec t thos e judgments
. T o accuratel y estimate the reliability of information, pa

y attentio n t o suc h matter s a s sampl e siz e an dpower o f th e statistica l tests
. Kee p i n min dtha t dat aar e probabilisti c i

n nature , subjec t

t o element s o

f rando merror , imprecis e measurement , an d subjectiv e evaluatio n an dinterpretation
. I n addition , th e farthe r

one mus t

extrapolate , o r generalize , fromaparticula r stud y t o asituatio n o

f interest , th e les s reliabl e i s th e conclusio n andth e les s certaint y shoul db e attribute dt o it
. Rely mor e heavil y o

n informatio n tha t

yo u conside r

more reliable , bu t

do no t trea t i t a s "absolut e truth. " Kee p i n 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 an outcom e influenc e th e poin t

a t which actio n i s take n wit h respec t t o it , bu t no t th e judgmen t

tha t i s made abou t

th e outcome' s likelihood
.—•P.7 7 6 9 Finally , i n makin g probabilit y judgments , thin k primaril y in term s of

th e measur e (probabilit y o r

odds ) wit h whic h yo u fee l mor e comfortable , bu t sometime s translat e t o a n 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 i n term s o f

odds , whic h ar e unbounded , instea do f probabilities , whic h ar e bounded
. Fo r

example , on e ca n mor e easil y conceptualiz e odd s of 1:20 0 tha n a probabilit y o f

0.005
. B.l. 8 Possibl e Advers e Healt h Effe.ct s o f Elevate d E

PLevel s I t seem s wel l establishe dtha t ther e i s apositiv e dose-respons e relationshi p betwee n Pb B an dEP
. Althoug h thi s elevate dE P ca n b e trace dt o hem e synthesi s interference , ther e i s disagreemen t a s t o what , i f

any , advers e healt h effect s ar e associate dwit h lead-induce delevate dEP
. W e woul dlik e t o discus s you r view s o n thi s issu e i n ou r

secon dvisi t

afte r w e hav e complete dencodin g you r probabilisti c judgment s concernin g th e Hb/Pb B dose-respons e function
. I n you r judgment , i s lead-induce delevate dE P associate dwit h alteration s i n an y of th e following , an di

f so , a t wha t leve l o r rang e of level s o f

E P woul 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 centra l nervou s syste m(CNS ) functions , 2
. Live r

detoxificatio n capabilities , o r 3
. Rena l o r

endocrin e functio n (in particular , reduce dbiosynthesi s of 1,25-dihydroxyvitami n D)
. I s ther e arelatio n betwee n lead-induce delevate dE P an danemi aof an y sor t beyon dtha t

whic h ca n b e indexe db y Pb B leve l alone ? Doe s elevate dE P sugges 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 h effect s tha t yo u believ e may b e associate dwit h elevate dEP ?
B.1. 9 Fina l Preparatio n fo rElicitatio n o f Probability Judgment s Th e shap e an dlocatio n o f th e dose-respons e curv e a s w e define di t abov e ar e 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 , i n amathematica l sens e suc h arelationshi p doe s exist
. Ou r goa l i s t o hav e yo u represen t probabilisticall y you r ow n uncertaint y abou t th e locatio n an 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 n respondin 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 n reviewe d i n th e C D an dconsul t

it , th e literature , 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 n of larg e amount s o

fP.7 8 70 comple x evidence . You ma y fin d i thelpfu l t o revie w th e sectio n o rrais e question s abou t th e point s mad e in i tbefor e w e begin . Uncertaint y abou tadose-respons e relationshi p ca n b e represente d probabil isticall y i

n tw o differen tways . 1 . Uncertaint y abou tth e percentag e o f th e define d populatio n tha t woul d b e affecte d b y give n Pb B concentration s ca n b e represente d probabilistically , and 2 . Uncertaint y abou tth e PbB concentration s tha twoul d b e require d t o affec tagive n percentag e o f th e define d populatio n ca n b e represente d probabilistically . W e wil l concentrat e on on e way a tatime , focusin g primaril y o n th e firs tone . Fo rthes e purpose s i ti s helpfu l t o imagin e tha teveryon e in th e populatio n ha s a specifie d Pb

B leve l tha tha s becom e stabilize d i n th e manne rdescribe d abov e under Exposure Conditions. Then , a s aresult , som e percentag e o f th e populatio n wil l suffe rth e H b response . Now , in orde rfo ru s t o determin e you runcertaint y abou tth e percentage s o f th e populatio n tha twoul d b e affecte d by give n Pb B levels , w e mus tintroduc e adefinition . Le tC b e th e Pb

B concentratio n i

n question . Definition : R(C ) i s th e percentag e o f th e populatio n fo rwhic h aPbB leve l o f C woul d caus e th e define d H b healt h effect . Thus , R(C ) i s precisel y th e percen to f th e populatio n tha twoul d sho w arespons e i f th e entir e populatio n had Pb B level s o f

C unde rth e condition s define d above . R(C ) i s usuall y calle d th e populatio n respons e rate . Th e valu e o f

R(C ) fo ragive n C i s uncertain , and w e woul d lik e t o obtai n probabilit y judgment s fro m yo u abou tit s possibl e values . W e wil l elici tyou rjudgment s abou tth e possibl e value s o f R(C ) b y specifyin g aparticula rpercentag e and havin g you conside rhow likel y i ti s tha tR(C ) i s les s tha n tha tvalue . T o hel p yo u mak e you r probabilit y judgments , w e wil l make us e o f adevic e calle d aprobabilit y wheel , whic h ha s adjustabl e sector s o f

blu e and orange . W e ca n rea d on th e back o f th e whee l th e percentag e o f

th e whee l tha ti s eac h color . I n makin g you rjudgment s yo u ar e t o imagin e tha tth e whee l i s aperfectl y fai rrandom device , an d tha ttherefor e th e probabilit y o f it s stoppin g with th e pointe ro n blu e i s exactl y represente d b y th e relativ e are atha ti s blue . W e wil l the n procee d a s follows . Fo reac h Pb B concentratio n C , w e wil l specif y aparticula rpercen tr , and als o se tth e probabilit y whee l t o hav e aspecifi c relativ e are a o f blue . Then yo u ar e t o conside rcarefull y th e question : D o yo u conside ri tmor e probabl e tha tth e tru e populatio n respons e rat e R(C ) i s les s tha n ro rtha tth e whee l woul d sto p with th e pointe ron blu e (on arandom spin) ?P.7 9 7 1
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 n r , 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

o n blue , o r 3
. Yo u canno t

judg e eithe r

even t a s mor e probabl e tha n th e other
. Fo r aparticula r

concentratio n C an dpercen t r , som e whee l setting s wil l hav e a smal l enoug h relativ e are ao f blu e tha t

yo u wil l fee l confiden t makin g th e firs t

response . Othe r whee l setting s wil l hav e alarg e enoug h relativ e are aof blu e tha t

yo u wil l fee l confiden t makin g th e secon dresponse . 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 h yo u fee l mos t

comfortabl e makin g th e thir dresponse . Onc e w e hav e determine dth e poin t a t whic h yo u ar e mos t

comfortabl e wit h th e thir dresponse , an dstil l focusin g o n th e give n Pb B concentratio n C , 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 n C unti l w e hav e specifie dvariou 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 n th e nex t

probabilisti c representatio n b y specifyin g ane w C an dcontinuin g a s before
. W

e wil l d o thi s fo r

anumbe r

of value s of

C
. I t frequentl y happen s tha t an expert' s judgment s alte r somewha t

ove r th e cours e o f asessio n suc h a 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 h you r response s and , a t appropriat e times , sho w the mt o yo u fo r you r consideratio n an dcomparison
. A t thes e time s yo u ma y wis h t o chang e som e o f th e judgment s yo u gav e earlier
. 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

o f cours e ar e ther e know n correc t answers . Rather , w e wan t you r bes t an dmos t

considere djudgmen t i n ligh t

o f 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 C D o r othe r source s a s yo u wis h a 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 h instructions. ) Recal l tha t

uncertaint y abou t

th e dose-respons e functio n ca n als o b e expresse din term s o f th e Pb B concentratio n necessar y t o produc e th e effec t i n agive n percentag e o f th e populatio n r , if

th e entir e populatio n ha dth e sam e Pb B concentration , stabilize da s th e resul t

o f exposur e i n th e manne r discusse dearlier
. Mor e specifically , proceedin g a s before , le t

u s introduc e adefinition : Definition : C(R ) i s th e Pb B leve l tha t woul dcaus e th e define dH b healt h effec t i n Rpercen t

o f th e population
.P.8 0

_, p j 

### The valu e o

f C(R ) i s uncertai n for

agiven R, an dw

e want t o obtai n you

r judgment s abou t it s possibl e values
. Analogously t o wha t w e hav e alread y done , for agive n Rwe wil

l specif y concentration s c an das k yo u t o conside r

ho w likel y i t

i s tha t th e tru e C(R

) i s les s than th e specifie dc . Mor e specifically , utilizin g th e wheel a s before , we will as k yo u th e question : D o yo u conside r

i t more likel y tha t

th e tru e concentratio n C(R ) is-les s tha n c , or tha t th e whee l wouldsto p wit h th e pointe r

o n blu e (o n arando mspin) ? Yo u can giv e on e o

f thre e responses : 1
. Yo u judg e i t more probabl e tha t

C(R ) i s les s than c , 2
. Yo u judg e i t

more probabl e tha t

th e whee l wouldsto p wit h th e pointe r i n blue , o r 3
. Yo u canno t judg e eithe r

even t a s mor e probabl e tha n th e other
. Afte r determinin g th e whee l settin g a t which yo

u fee l mos t

comfortabl e wit

h th e thir d response , w

e will specif

y ane w c andrepea t

th e process . A s before , fo r eac h Rw e will elici t your comparativ e judgment s for variou s value s o

f c . B. 2 DETAILE

D MATHEMATICA

L FORMULATION

S Thi s sectio n discusse s i

n detai l th e mathematica l technique s use dt o represen t probability judgment s abou t dose-respons e relationships
. Afte r basi c definition s an dth e notatio n ar e introduced , th e NOL O functio n i s discusse da s adistributio n tha t can b e fitte dt o probability judgment s andtha t meet s certai n criteria
. Method s ar e presente d for obtainin g least-square s estimate s o f th e parameter s o

f aNOL O distributio n an dfor assessin g th e goodnes s o f fit
. The famil y o

f equal-varianc e NOL

O distribution s i s presente dnext , alon g wit h method s for

obtainin g least-square s estimate s o f it s parameter s andassessin g it s goodnes s o f fit
. Althoug h thi s famil y ma y sacrific e some goodnes s o

f fi t t o th e judgments , i t

meet s al l th e specifie dcriteria
. B.2. 1 Definition s an

d Notatio n Reader s ar e assume dt o b e familiar wit h th e basi c concept s o

f probabilit y theory (e.g. , definition s o

f rando mvariables , probability density functions , an dexpectatio n an d highe r moments)
. Fo r uncertai n quantit y X , le t fx( x 

### ) = 

### judgmenta l probability densit y functio n (PDF) fo r X , an dF x 

### (x ) = judgmenta l CDFfor X
. B y definitio n
x F Y 

### (x ) = J fv 

### ( x )dxP.8 1

Thus , F x ( x ) i s th e judgmenta l probability * tha tX i s les s tha n o requa l t o x . Furthermore , le ty = E[X] , o rth e expecte d valu e o f X . The n x

K = J " x « f Y ( x « )dx
- o X o o

— TM And , le to 2 = V[X] , th e varianc e o f X . The n

C D o 2 = J ( x - E[X]) 2 f Y ( x )d x x J *

• o ' X o o —° > Th e uncertai n quantitie s o f interes ti n thi s ris k assessmen tar e populatio n respons e rates , denote d R , a teac h o f severa l Pb B levels , denote d L . Durin g encodin g session s wit h th e experts , judgment s representin g aCD F fo rarespons e rat e Rgive n a populatio n Pb B leve l L (i.e. , judgment s representin g F n n [R] ) wil l b e elicite d fo ra numbe ro f

Pb B levels . Take n together , thes e judgment s wil l provid e afamil y o f probabilisti c relationship s tha trepresent s th e judgmenta l probabilit y tha tth e populatio n respons e rat e ( afractio n betwee n 0 an d 1 ) wil l b e les s tha n o requa l t o aparticula rvalu e R , give n aPb B leve l o f L , fo raspecifi c advers e healt h effect , population , an d exposur e conditions .

A s alread y discussed , calculatin g ris k generall y require s interpolatio n betwee n assesse d points . Suc h interpolatio n i s bes taccomplishe d b y fittin g afunctio n t o th e judge d probabilities .
B.2. 2 NOL O Functio n

Becaus e probabilisti c judgment s abou tdose-respons e relationship s generall y for m a n S-shape d curv e ove rth e close d [0% , 100% ] interval , the y ca n b e difficul tt o represen t wit h closed-for m mathematica l functions . On e functio n tha ti s relativel y eas y t o wor k wit h i s th e NOL O distribution , whic h i s obtaine d b y fittin g anorma l distributio n t o th e natura l lo g o f

th e odd s implie d b y th e populatio n respons e rate s R . Thu s 

### x = 

# Torn * ° K



# - x K



# - - Y • ln(X) , —< Y < « wher e X i s th e odd s variabl e an d Y i s th e log-odd s variable . The variabl e Y i s assume d t o b e normall y distribute d with mean y an d varianc e a . Th e degre e t o whic h this assumptio n i s appropriat e ca n b e teste d with eac h se to f judgments . I

f Y i s normall y distributed , X i s lognormall y distributed . Althoug h no closed-for m expressio n i s readil y

•Al l probabilitie s hereafte rreferre d t o ar e judgmenta l probabilities , eve n if the y ar e no t s o specified .P.8 2



### availabl e fo rth e distribution o n R , all probabilisti c an

d statistica l results of

interes to

n Rca n b e obtaine d throug

h th e distribution o

n Y sinc e i 

### F R 

### (r ) = pr[

R< r ]

an d 

# - p

r[ l * Cr^) ]

f v 

### (y ) - rHi * y l

" P ' 

# zs(

y 

# -^

= • 

### y - u.

wher e pr[>] denote s probability , an d Z i s th e uni

tnorma l rando m deviate fo rwhic

h *(Z ) i s extensivel y tabulate d an

d availabl e i

n compute rlibraries . Thu s
F 

### R (r ) 

### " F 

### X 

# [TH

• F , 

# [«rH)]

• F „ 

## l 

# »(rH) " \

m {^ri\ - ,
Tabl e B. l summarizes th e quantitie s of interes tforthes e variables . Th e parameters y an

d a ca n b e estimate d i

n aleast-square s sens e fro m a n assesse d distribution . Letth e n assesse d point s fo raCD

F be denoted (Rj , Fj ) fo ri = 1 ,

... , n, wher

e R j i s th e population respons e rate an d F j i s th e associate d cumulativ e judgmenta

l probability . Least-square s estimate s y an d o fo ry an

d o can b e obtaine d b

y linearl y re gressing th e z

j o n th e yj . Th

e reciprocal o

f th e slop e o

f th e regressio n equatio n i s o , an dT T

TABL E B. 1 Variable s Pertainin g t o th e NOLO Functio n

Variabl e Quantit y o f Interes t
Definin g Y= ln(X ) X= e Y= * DR = 100 X equation s 10 0 - R 1 • X 2 2 Distribution * N( y , o ) A( y

, o ) y y y

y y +o 2 / 2 Mea ny „ y = e y

y y x
2 2 2 2

2 y * o a 

# A

2 y - o e y y 100 e y

2 y - o lOO e y y 2 y - o i • e y y Varianc e o o = e y y f e y - l ) y x Median y

Mod e y

a N( y , o ) denote s th e norma l PD Fan dh[u , o ) denote s th e lognorma l PDF
. Th e PD Ffo r Rcanno t

b e expresse di n close d form
. ^lea n an dvarianc e expression s fo r Rar e obtaine dusin g numerica l methods
. y i s th e y-intercep t

(i.e. , valu e o f

y correspondin g t o z = 0 i n th e regressio n equation)
. Sinc e mjudgmenta l distribution s ar e assessed , on e fo r eac h Pb B leve l j fo r

j = 1 , ... , m , ther e ar e mmean s (ui, •.. , y m ) an dstandar ddeviation s (oj , ... , o m ),on e pai r fo r eac h o f th e judge ddistributions
. Th e goodnes s o f

fi t o f eac h distributio n fi t

t o th e judgment s fo r

eac h Pb B leve l i s give n b y th e standar dregressio n r statisti c obtaine db y regressin g th e F^ o n F i f wher e

r• 1 - •z.2 

# n- i - z )

### an

d F - denote s the estimate d F value s (i.e. , F ^ = *((y £ - y)/o}) , an d b y obtainin g the rvalu e o

f thi s regression . I

f th e rvalu e i s sufficientl y high , th e NOL O distributio n wit h parameters y : an

d o ; describe s th e judgment s wel l forlead leve l j . Thi s distribution ca

n the n be use d forinterpolation . T o summarize , formulas were presente d fo rcalculatin g th e parameter s o f a NOL O distribution , whic

h ca n b e use d t o representajudge

d probabilit

y distributio n over apopulation respons e rate fo ragive n Pb B level . Goodness o

f fi ti s give n b

y aregressio n rstatistic . Th

e NOL O variabl e an

d it s PD F ca n b e used t o estimat e judgmenta l probabilitie s fo rth e respons e rate variabl e Ran d t o estimat e risk . B.2. 3 Representin g aProbabilisti c Dose-Respons e Surface wit h aFamily of Equal-Varianc

e NOL O Distribution s I f th e o j ar e approximately equal , i ti s desirabl e t o se tthe m equa l t o asingl e pooled value before proceeding further(i.e. , se to ; = o p 

### = o fo rall j) . This ste p ensures thatth e fitte d distributions fortw o differen tPb B level s nevercros s one another . (Crosse d distributions woul

d impl y thatexceedin g aspecifie d respons e rate i s mor e probabl e a tPb B leve l L , tha

n atL, » wher e L « i s greate rtha

n Lj. ) A poole d estimat e o f o , denote d o p 

### , ca

n b e obtained b

y firs tsubtractin g th e mea n y • fo reach se to

f assesse d point s

y 

### j» i = y 

### j» i " U



### 3' £ori 

### * l 

### ''"' n 

### j an d 

### J • I t••• » • wher e n : i s th e numbe

ro f assesse d point

s fo rFR/L . an d v 

### i i * s a n assesse d 

### poin to n Fp/T, . Th

e y' . . ca n then be used to calculat e amea n (whic h shoul d b e ver y clos e t o zeroran d avariance (whic h will be th e pooled , least-square s estimat e o ' ) b y regressin g P zi ; o n y ! . . Th

e individua

l least-square s estimate s o f th e mean

s ca n be recalculate d ateac h Pb

B leve l b y finding th e best-fittin g lin e (i n th e least-square s sense ) wit h aslop e of l/o' . Unde

rthes e conditions , th e resul ti s simply n . J J n . . . J j i= l 

### I y ; ;
= 1 J' 1 

### Th e results of

thes e las tstep s ar

e denote d a s y! , ... , y' . Goodness of fit^again can b e obtained b

y regressing th e recalculate d estimate s (whic h ca n be denote d a s F ! . ) o

n th e origina l F • j . J 

### ' l 

### I f afunctiona

l relationshi p ca

n b e establishe d betwee n Pb B level s an

d th e y'. , a judgmenta

l PD F overRca

n be calculate d fo ran

y Pb B level , shoul

d thatb e necessary for interpolatin g betwee n Pb B levels . Thi

s continuu

m o f densit y function s i

n essenc e is a probabilit y surfac e ove rth e dose-respons e plane . A Pb B distribution ca

n b e combined wit

h th e dose-respons e curve s t o yiel d a n estimat e of

th e overal l fractio n of

th e population Rsufferin g th e advers e health effect . Suc h calculation s resul ti

n th e ris k estimate s summarized i n Sec. 5 an

d describe d i

n detai l i n App . D .P.8 5 7 7
B. 3 RESULT S Result s ar e presente d in thre e tables : Tabl e B. 2 present s th e encode d judgments , Tabl e B. 3 summarize s th e function s fi tt o th e judgments , an d Tabl e B. 4 compare s th e encode d judgment s wit h th e fitte d functions . Th e table s ar e organize d s o tha teac h expert/Hb-level/age-categor y combinatio n i s listed , beginnin g wit h ExpertA an d continuin g alphabeticall y throug h ExpertE . Th e table s ar e explaine d usin g .th e judgment s o f Exper tA a s a

n example . Exper tA chos e t o separat e th e populatio n o f U.S . childre n age d 0- 6 int o tw o subpopulation s —childre n age d 0- 3 an d 4-6 . Thi s individual provide d judgment s onl y a t th e < 1 1 g/d L H

b level . Becaus e hi s judgment s indicate d tha tth e lead-induce d H b effec t a tPbB level s belo w 4 5 yg/d L i s ver y small , i twa s unnecessar y t o obtai n probabilisti c judgment s a tth e < 9.5-g/d L H b level . Tabl e B. 2 give s th e probabilisti c judgment s o f ExpertA regardin g th e occurrenc e o f H b leve l < 1 1 g/d L amon g U.S . childre n age d 0- 3 an d 4- 6 a taserie s o f

Pb B levels . Th e probabilit y judgment s ar e CDF s o f judgmenta l probability ; tha tis , fo reac h Pb B leve l L , th e correspondin g entrie s in th e F colum n represen tth e judge d probability tha tth e tru e respons e rat e R-

p i s les s tha n o requa l t o th e rat e Rshown in th e Rcolumn . ExpertA did no tfee l tha tther e wa s ameasurable , lead-induce d H b effec ta tPb

B level s belo w 4 5 yg/dL . Th e curve s displa y awide rrang e o f plausibl e populatio n respons e rate s a t successivel y highe rPb B levels , suggestin g tha tExpertA i s les s certai n abou tth e actua l respons e rate s a thighe rPb B levels . The dat ad o no tindicat e athreshol d fo ra n H b effec tin th e rang e o f

45-7 5 yg/dL . Fo rth e reason s presente d in Sec . 1 , mathematica l function s wer e fi tt o th e judgment s o f

ExpertA . Th e correspondin g curve s fo rth e variou s Pb B level s ar e guarantee d neve rt o cross . The y wer e obtaine d by fittin g regressio n line s t o th e NOL O transformatio n o f

th e judgments . Ithappen s tha tthi s transformatio n lead s t o norma l distributions , wit h ahigh degre e o f accuracy . Thes e distribution s ar e als o convenien tfo r subsequen tanalysis . Th e NOL O distribution s ar e uniquel y define d by th e mean and varianc e o f

th e underlyin g normal distribution s an d th e transformatio n function s (se e Sec . B.2) . Tabl e B. 3 summarize s th e relevan tparameter s fo reac h of th e conditiona l CDF s fi tt o th e judgment s o f ExpertA . Include d in th e tabl e fo reac h Pb B leve l a twhic h a CD F wa s assesse d ar e th e mean an d standar d deviatio n of th e underlyin g normal distribution , th e mean an d standar d deviatio n o f

th e NOL

O distribution , an

d th e r 2 value s o f regression s o f

th e fitte d function s on encode d judgments . I n general , th e rvalue s ar e reassuringl y high . Tabl e B. 4 summarize s an d compare s th e probabilisti c judgment s an d th e fitte d functions . Th e median i s tha tpopulatio n respons e rat e tha ti s exceede d with probability 0.5 . Th e 90 % C

I i s a . se to f

populatio n respons e rat e value s suc h tha tther e i s a0. 9 probabilit y o f

th e tru e valu e fallin g withi n it . Fo rexample , fo rchildre n age d 0- 3 havin g Pb B level s o f

55 yg/dL , th e media n encode d respons e rat e i s 9% , an d th e 90 % C

I i s 1-15% . I n othe rwords , with probabilit y 0.05 , th e tru e respons e rat e i s les s than o requal t o 1 % an

d wit h probabilit y 0.05 , i ti s greate rtha n o requa l t o 15% . Paralle l statement stOOtO^UON H OOOOOOO O

....... . VOVOVOOOUI.*«M« — totou i m VO U l

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- N N t r o * ro o o r1 e

o

I U l 

# 5

r w C O

. tt » 

### o 9 1

J N I O t ^ : 1

o I U l 1

J N I O t 

### M ' 1 X o * I A t O

. U l IQ a .

P l X T J ro 1 P l
X c r I A

O Q C LP.9 0 8 2

TABL E B. 2 (Cont'd )

Pb B Leve l (yg/dL )
5 5 0

- R
5 8 2 2 3 6 A O A 7 H b< 9

- 3 y r F

0.0 1 0. 1 0. 5 0.7 5 0. 9 0.9 9 Exp

e

. 5 g/d L AR
6 1 1 1 5 2 2 2 6 3 0 - 6 y r F

0.0 5 0. A 0. 5 0.7 5 0. 9 0.9 8 r t E

0 - R
1 0 2 0 3 0 A O 5 0 5 5 H b<

• 3 y r F

0.0 1 0.3 5 0. 5 0.6 2 0.9 A 0.9 9 1 1 g/d

L - AR
5 1 0 1 5 2 0 2 5 3 0 3 5 • 6 y r F

0.0 1 0.0 5 0. A 0. 5 0.7 5 0. 9 0.9 8

a R denote s populatio n respons e rat e (percentag e havin g Hb level s < 9. 5 g/d L o r < 1 1 g/dL) . b F denote s cumulativ e probability
. coul db e mad e fo r

th e fitte dfunctions
. Th e encode dmedia n value s ar e fairl y clos e t o thos e o f th e fitte dfunctions , differin g b y onl y 2-4%
. However , th e fitte dfunction s exhibi t mor e uncertaint y tha n d o th e judgments
. Thes e feature s an ddifference s wer e pointe dou t

t o Exper t

A , wh o finall y conclude dtha t th e fitte dfunction s bette r capture d hi s bes t judgment s abou t

th e effect s o f

Pb B o n Hb level s amon g th e tw o group s o f U.S
. children
.
B. 4 DISCUSSION SUMMARIES CONCERNIN G ELEVATE D E PAN D H

b DECREMENT S Th e followin g summarie s ar e base do n note s take n durin g th e interview s wit h th e experts
. A t

times , th e point s mad e ar e fragmentar y an dhighl y specialized
. Eac h exper t ha s ha da t

leas t on e opportunit y t o revie w hi s section
. B.4. 1 Exper tA

• Ther e i s absolutel y n o evidenc e tha t zin c protoporphyri n (ZPP ) i s toxi c pe r se .

• Th e biosynthesi s o f hem e i s regulate db y anegativ e feedbac k proces s whos e rate-limitin g factor s ar e heme , hem e oxygenase , an d 6-aminolevulini c aci dsynthas e (ALAS)
. Th e enzyme s i n th e-gy

TABLE B. 3 Function s Fi tt o Judgment s abou tPopulatio n Respons e Rate s fo r Lead-Induce d H

b Decrement s P.9 1

• - Pb B Leve l (yg/dL ) Expert A, A 5 5 5 6 5 7 5 Expert A, 5 5 6 5 7 5 Expert C, 5

. 1 5 2 5 3 5 A 5 5 5 Expert C, 5 1 5 2 5 3 5 A 5 5 5 Functiona l

H i

Hb

Hb

Hb For m

< i i
NOL O NOL O NOL O NOL O

< 11 NOL O NOL O NOL O
< 9. 5 NOL O NOL O NOL O NOL O NOL O NOL O
< i i
NOL O NOL O NOL O NOL O NOL O NOL O g/dL,

9/dL, Defin i

Parame t

u y Ages 0-3 -3.35A 6 -2.933 8 -2.072 A -1.575 A Ages 4-6 -3.682 6 -2.271 3 -2.061 7

• g/dL, Ages 0-

9/dL, -3.999 5 -3.AA8 1 -3.129 8 -2.918 7 -2.7A2 A -2.578 1 Ages 0-6 -3.682 6 -2.271 3 -2.061 7 -1.696 5 -1.319 0 -1.0A9 8 n

g ers a



### ° y

0.682 0 0.682 0 0.682 0 0.682 0

0.59A 5 0.594 5 0.59A 5 6 0.276 4 0.276 A 0.276 A 0.276 A 0.276 4 0.276 4

0.272 0 0.272 0 0.272 0 0.272 0 0.272 0 0.272 0 Measure s o f

Distri b ove r E[R Hb ]



### A. l 6. 0 12. 8 19. 0

2. 8 10. 5 12. 5

1. 8 3. 2 4. 3 5. 2 6. 2 7. 2

2. 5 9. 5 11. 5 15. 7 21. 3 26. 1 utio n

R b SD(R Hb ]

2. 5 3. 7 7. 1 9. 6

1. 6 5. 3 6. 1

0. 5 0. 9 1. 2 1. 4 1. 7 1. 9

0. 7 2. 4 2. 9 3. 8 4. 8 5. 6 t^ 2 fo r Regressio n o f F on F

0.8 9 0.8 4 0.9 3 0.9 4

0.9 7 0.9 0 0.9 5

0.9 8 0.9 9 0.9 9 0.9 9 0.9 9 0.9 7

0.9 7 0.9 0 0.9 5 0.9 9 0.9 7 0.9 8m J N m m

5 S S S o o r * r * o o

i i t-. M

. . o o o u i t o N | v o U l U l
o o

. . I- T I- * N l N l N l N l N l N l u > m

5 S O r o

i M

. M J N J N O t
o

. t -
. N l N | N | M U l

s s o r * o

i M

. U l o J N V O
o

. I - T N | N l N l I - T U l

s s o f o

1 U l • J N 0 0 O v O v
o • J N o o V O J N U l

9S o r * o

i U l

. 0 0 N l U l v o
o • J > o o v O J N 

# s r

T JertD,Hb

I A

K T K I v q 

### ft
4 . < o ro i n

T U 1 C h U l

U l

S B O t - o

1 o N l M U l J N
o • J N V O 1 — V O J N U l

z O r « o

i I - T M J * 0 0 U l
o • J N v O • — V O u > U l

s s o c o

1 I - T J N a t U l U l
o • J N V O t- - V O M U l

a s o f o

1 I— T N l J N J > I s )
o • J N V O H- r V O I - T m

S S o f o

i M
N l o v O N l
o • J N v O t—a V O U l

5 o r * o

i U l

I — I N l J N N l
o • J N v o 1— I v O 

## s ?
• oertD,Hb

I A
1- 4 fr~ V Q 

### ft
• * i > V Q ro C O o i U l U l

U l

S S o f o

1 M

. M J N U l U l
o

. M K - T N | N | J N U l

X o f o

1 M

. U l 1— I M U l
O

. M l - T N | N l U l U l

X O t - o

1 U l

. o J N J N U l
o • M

• - T N | N l M U l

X o r * o

i O v • J N O v O J N

1 —

. O J N o V O 

# s
• oertD,Hb

I A V O U l
• Q \ 

### ft N * » V Q 0 1 in aU 1 O t W*«UN H m m u i u i m

U l O v O N I U l M
..... . U i t O O t O t U > M

K > M I- T I- T I- T H- T

..... . J N o o o J N m o U l M I- * t— U l U l V O U l O t J N M U l 0 0 0 0 0 0 J N

O 0 0 N I o v U l M O v J N U l U > O O v O N I J N O

... . N I O v O t U l

M H - I- TO

... . t— N l O U l X X X X X

oooo o f f f f

f oooo o

I I I I I I - T!- •M U l J N J N N l J N 0 0 U l O N l V O N l Cr r t o O v v o u i v. - v l V D H I O M

OOOO O

.... . U l U l U J U l U l u i m m m m m m U l U l U l

O J N N l M H - HtOtOH H

U i J N M O O N I m O t N I J N 

### 8 ? t J ro H r t 

## 5

I A V O O l V Q \ Q
. t- l

n> ( n o i U i

ooooo o V O v o v O N I J N N | t O t O t o

O v V O J N ooooo o
v O v O v O v o v O v O N I t o N I N I O t U l o o o o
v o v O v o 0 0 0 0 J N U l J N oooo o t o V O t O 0 0 t O t O N I 0 0 J N t O • c f O Q I D

~ N < Q . to f *- *— ' •* ! C 3
" J O O r t 1 • — a o a Co • O ar xa H

ta O o 3

• o t o O i to
» »-» i 3 f . m a n fto 3 1 O Q ( 0 J : *

n P O E C o r

C A o P O B C O *

O PO •-•> to OQ ' -*J> 1 n > O u > 3 u > (-• • T J O 3 o a

e H Tn > ( 0 0 1 O r t w < 1 c i c r n c 1 0 p o r t • - •O O " t 3

C OP.9 3 85 '

TABL E B. 3 (Cont'd )

• Pb B ••Level (yg/dL )
Expert E, 5 1 5 2 5 3 5 4 5 5 5 Function !

Hb For m

< 9.5 NOL O NOL O NOL O NOL O NOL O NOL O Definin g

Parameter s i l

u y g/dL, Ages 0- -3.782 0 -2.799 2 -2.472 5 -1.960 2 -1.564 3 -1.400 2 

### °

y

•3 0.960 0 0.960 0 0.960 0 0.960 0 0.960 0 0.960 0 Measure s o f

Distributio n ove r E[R Hb ]

3. 3 8. 1 10. 6 15. 8 21. 0 23. 4 • R

SD[R Hb ]

3. 3 7. 2 8. 9 12. 0 14. 5 15. 5 r 2 fo r

Regressio n o f F on F

0.9 8 0.9 6 0.9 6 0.9 6 0.9 9 0.9 9 Expert E, Hb < 9.5 g/dL, Ages 4-6 5 1 5 2 5 3 5 4 5 5 5 Expert E, 5 1 5 2 5 3 5 4 5 5 5 NOL O

NOL O NOL O NOL O NOL O NOL O Hb < 11 g/dL NOL O NOL O NOL O NOL O NOL O NOL O -4.162 3

-3.685 6 -3.337 6 -3.021 8 -2.114 1 -1.912 1

, Ages 0-3 -2.346 3 -2.113 0 -1.931 1 -1.655 2 -1.301 4 -0.919 9 0.822 4

0.822 4 0.822 4 0.822 4 0.822 4 0.822 4

0.599 1 0.599 1 0.599 1 0.599 1 0.599 1 0.599 1 2. 1

3. 3 4. 6 6. 1 13. 2 15. 5

9. 9 12. 1 14. 1 17. 6 23. 0 29. 9 1. 8

2. 8 3. 7 4. 8 9. 2 10. 3

5. 3 6. 3 7. 1 8. 4 10. 1 11. 8 0.9 8

0.9 9 0.9 8 0.9 5 0.9 8 0.9 3

0.9 8 0.9 9 0.9 8 0.9 5 0.9 8 0.9 3 Expert E, Hb < 11 g/dL, Ages 4-6 5 NOL O 1 5 NOL O 2 5 NOL O 3 5 NOL O 4 5 NOL O 5 5 NOL O

a Y = ln[R/( l - R) ] deviatio n o„ . -2.854 5 -2.638 1 -2.215 1 -1.978 4 -1.709 6 -1.528 6 i s normall y 0.591 2

0.591 2 0.591 2 0.591 2 0.591 2 0.591 2 distribute d 6. 3

7. 6 11. 1 13. 5 16. 8 19. 4 wit h 3. 5

4. 2 5. 8 6. 8 8. 1 8. 9

mea n yan

d 0.9 0 0.9 5 0.9 7 0.9 4 0.9 7 0.9 8
standard
Using y 

### y . an

d numerica l methods , value s can be calculate d fo r the mea n E[R ] an

d th e standar d deviatio n SD[R ] o f th e response rat e distributio n (whic h i s NOLO ) ove r R . R i s expresse d a s a percentage .P.9 4 8 6 TABLE B. 4 Compariso n o f Judgment s and Fitte d Function s Concernin g Populatio n Respons e Rate s fo rLead-Induce d Hb Decrement s

Respons e Rate 8 a t Pb B Leve l j
_ Inde x4 5 yg/d

L 5 5 yg/d

L 6 5 yg/d

L 7 5 yg/d

L Expert A, Hb < 11 g/dL, Ages 0-3 Encoded Judgments Media n 50 2 CI b 90 2 C I 5

2 , 7 1 , 9 tted Functions Media n 50 2 C I 90 2 C I 98 2 C I 3

2 , 5 1 , 1 0 1 , 1 5 9

A , 1 3 1 , 1 5

5 3 , 8 2 , 1 4 1 , 2 1 1 4

9 , 1 8 A , 2 1

1 1 7 , 1 7 A , 2 8 3 , 3 8 2 0

11 , 3 1 5 , 3 5

1 7 12 , 2 5 6 , 3 9 A , 5 0 Expert A, Hb < 11 g/dL, Ages 4-6 Encoded Judgments Media n 50 2 C I 90 2 C I Fitte d Functions Media n 50 2 C I 90 2 C I 98 2 C I 3 2 , A 1 , 6

2 2, 4 1 , 6 1 , 9 11

6 , 1 6 3 , 1 8

9 6 , 1 3 A , 2 2 3 , 2 9 1 5

8 , 1 9 A , 2 A

11 8 , 1 6 5 , 2 5 3 , 3 A

## "W

TABL E B. 4 (Cont'd )

Respons e Rat e a t Pb B Leve l Inde x 5 yg/d L 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L A 5 yg/d L 5 5 yg/d L Expert C, Hb < 9.5 g/dL, Ages 0-6 Encoded Judgments Media n 50 2 C I 90 2 C I 2

1 , 3 1 , A 3

2 , A 2 , 5 A

A , 5 3 , 6 5

A , 6 A , 7 6

5 , 7 5 , 8 7

6 , 8 6 , 9 Fitted Functions Media n 50 2 C I 90 2 C I 98 2 C I 2

1 , 2 1 , 3 1 , A 3

3 , A 2 , 5 2 , 6 A

A , 5 3 , 6 2 , 8 5

A , 6 3 , 8 3 , 9 6

5 , 7 A , 9 3 , 1 1 7

6 , 8 5 , 1 1 A , 1 3 Expert C, Hb < 11 g/dL, Ages 0-6 Encoded Judgments Media n 50 2 C I 90 2 C I 8

6 , 1 0 3 , 1 0 9

8 , 1 2 5 , 1 3 1 2

10 , I A 7 , 1 5 1 6

IA , 1 9 11 , 2 0 2 0

17 , 2 6 15 , 2 7 2 7

2A , 2 9 18 , 3 1 Fitted Functions Med ] 50 2 90 2 98 2 La n C I C I C I 6 , 5 , A , 1 9 1 1 1 3 1 0

8 , 6 , 5 , 1 1 I A 1 7 1 2

10 , 8 , 6 , I A 1 7 2 0 1 5

13 , 10 , 9 , 1 8 2 2 2 6 2 1

18 , 15 , 12 , 2 A 2 9 3 3 2 6 23 , 18 , 16 , 3 0 3 5 4 0TABL E B. 4 (Cont'd )
Respons e Rat e a tPb B Leve l P.9 6

Inde x5 yg/dL 1 5 yg7d L 2 5 yg/d

L 3 5 yg/dL A

5 yg/d L 5 5 yg/d

L Expert D, Hb < 9.5 g/dL, Ages 0-3 Encoded Judgments Media n 50 2 C I 90 2 C I Fitted Functions Media n 50 2 C I 90 2 C I 98 2 C I Expert D, Hb < 9.5, Ages 4-6 Encoded Judgments Media n 50 2 C I 90 2 C I Fitted Functions Media n 50 2 C I 90 2 C I 98 2 C I 1 c , 2 c , 3

1 1 , 1 1 , 2 0 , 2 3

2 , 5 1 , 7

2 2 , 3 1 , A 1 , A 8

6 , 1 1 A , I A

8 6 , 9 A , 1 3 3 , 1 6 1 6

11 , 1 9 8 , 2 A

I A 12 , 1 8 9 , 2 3 7 , 2 8 2 0

16 , 2 5 11 , 3 1

2 0 16 , 2 4 12 , 3 0 12 , 3 6

0. 5 0 , 1 0 , 1

0. 2 0 , 0 0 , 1 0 , 2 5

3 , 6 2 , 8

5 A , 5 3 , 6 3 , 7 8

6 , 1 0 A , 1 2

7 7 , 9 5 , 1 0 5 , 1 2 1 0

8' , 1 1 6 , 1 4

1 0 8 , 1 1 7 , 1 3 6 , 1 5TABL E B. 4 (Cont'd )

Respons e Rat e a t Pb B Leve l Inde x 5 yg/d L 1 5 yg/d L 2 5 yg/d L 3 5 yg/d L A 5 yg/d L 5 5 yg/d L

• L •••IH-1-MI I •! •I •— ^ HI ! • •1 1 I • ! I I I II I ! •I I II I •I •• •'• ••' "

_••••••••--lll l Expert D, Hb < 11 g/dL, Ages 0-3 Encoded Judgments Media n 50 2 C I 90 2 C I A

2 , 1 0 1 , 3 6

A , 1 2 2 , 1 5 1

5 11 , 1 8 11 , 2 1 1 8

16 , 2 2 IA , 2 6 2 2

19 , 2 6 17 , 2 9 3 0

26 , 4 0 21 , 5 2 Fitte d Functions Media n 50 2 C I 90 2 C I 98 2 C I 4

3 , 6 2 , 9 1 , 1 2 6

5 , 8 3 , 1 3 2 , 1 7 1

5 11 , 2 0 7 , 2 8 5 , 3 5 19

14 , 2 4 9 , 3 4 7 , 4 2 2 2

17 , 2 9 11 , 3 9 8 , 4 7 3 3

26 , 4 0 18 , 5 2 13 , 6 0 Expert D, Hb < 11 g/dL, Ages 4-6 Encoded Judgments Media n 50 2 C I 90 2 C I 2

1 , A 1 , 6 3

2 , 6 1 , 9 7

6 , 9 5 , 1 1 9

8 , 1 1 7 , 1 3 1 0

9 , 1 3 8 , 1 6 1 4

12 , 1 6 10 , 1 7 Fitted Functions Media n 50 2 C I 90 2 C I 98 2 C I 2

1 , 3 1 , A 1 , 6 3

2 , A 1 , 6 1 . 9 8

7 , 8 6 , 1 0 5 , 1 1 1 0

9 , 1 1 7 , 1 2 7 , I A 1

1 10 , 1 2 8 , 1 4 7 , 1 6 14

12 , 1 5 10 , 1 7 9 , 1 9^__

_P.9 8

TABL E B. 4 Cont'd )

Respons e Rat e a t Pb B Leve l Inde x 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 Expert E, Hb < 9.5 g/dL, Ages 0-3 Encoded Judgments Media n 50 2 C I 90 2 C I 3

2 , 7 1 , 1 2 tted Functions Media n 50 2 C I 90 2 C I 98 2 C I 2

1 , 4 0 , 1 0 0 , 1 8 7

5 , 1 3 3 , 2 1

6 3 , 1 0 1 , 2 3 1 , 3 6 9

6 , 1 5 3 , 2 3

8 4 , 1 4 2 , 2 9 1 , 4 4 1 4

9 , 1 9 4 , 2 4

1 2 7 , 2 1 3 , 4 1 1 , 5 7 1 9

11 , 3 1 5 , 3 9

1 7 10 , 2 9 4 , 5 0 2 , 6 6 2 2

13 , 3 6 6 , 4 4

2 0 11 , 3 2 5 , 5 4 3 , 7 0 Expert E, Hb < 9.5 g/dL, Ages 4-6 Encoded Judgments Median 50 2 C I 90 2 C I 1

1 , 5 0 , 9 tted Functions Media n 50 2 C I 90 2 C I 98 2 C I 1. 5

1 , 3 0 , 6 0 , 1 0 2

1 , 6 0 , 1 0

2. 4 1 , 4 1 , 9 0 , 1 5 4

1 , 7 0 , 1 1

3. 4 2 , 6 1 , 1 2 1 , 1 9 6

3 , 9 1 , 1 3

5 3 , 8 1 , 1 6 1 . 2 5 1 3

8 , 2 0 3 , 2 5

11 7 , 1 7 3 , 3 2 2 , 4 5 1

5 9 , 2 2 6 , 2 9

1 3 8 , 2 1 4 , 3 6 2 , 5 0TABL E B. 4 (Cont'd )

Respons e Rat e a t Pb B Leve l Inde x5 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 Expert E, Hb < 11 g/dL, Ages 0-3 Encoded Judgments Media n 50 2 C I 90 2 C I 8

5 , 1 4 3 , 2 2 1 0

7 , 1 6 4 , 2 4 1

5 9 , 1 9 5 , 2 6 Fitted Functions Media n 50 2 C I 90 2 C I 98 2 C I 9

6 , 1 3 3 , 2 0 2 , 2 8 1

1 7 , 1 5 4 , 2 4 3 , 3 3 1 3

9 , 1 8 5 , 2 8 3 , 3 7 1 9

14 , 2 4 6 , 2 8

1 6 11 , 2 2 7 , 3 4 5 , 4 4 Expert E, Hb < 11 g/dL, Ages 4-6 Encoded Judgments

Fitted Functions 2 2 16 , 3 5 9 , 4 3 3 0

17 , 4 4 11 , 5 1

2 1 15 , 2 9 9 , 4 2 6 , 5 2 2 8

21 , 3 7 13 , 5 2 9 , 6 2

Media n 50 2 C I 90 2 C I 6

3 , 1 0 1 , 1 4 8

5 , 1 2 2 , 1 6 11

9 , 1 5 4 , 1 9 1 3

10 , 1 6 4 , 2 0 1 6

12 , 2 4 6 , 2 9 2 0

13 , 2 5 10 , 3 3

Media n 50 2 90 2 98 2 C I C I C I < 4 , 2 , 1 , 8 13 1 9 5 ,

3 , 2 , 7 1 0 1 6 2 2 1 0

7 , 4 , 3 , 1 4 2 2 3 0 1 2

8 , 5 , 3 , 1 7 2 7 3 5 1

5 11 , 6 , 4 , 2 1 3 2 4 2 1 8 13 , 8 , 5 , 2 4 3 6 4 6

a Th e respons e rat e i s expresse d a s a percentage . C I denote s credibl e interval .

c Lowe r C I limit s coul d no t b e calculate

d becaus e Exper t D did no t make probability

judgment s o

n respons e rat e value s les s tha n th e median a

t thi s Pb B level .P.100

. 

### 9 2 pathwa y fro m 6-aminolevulini c aci d dehydras e (ALAD ) t o ferrochelatas e ar

e presenti

n substantial excess . Ther e i s normally asubstantial exces s of

thes e intermediar

y enzymes . Fo

rexample , ther e i s 1

6 time s a s muc h ALA D a s i s necessary t o metaboliz e th e amoun to f AL A produce

d b y ALAS . Overall , fo revery 10,00 0 molecule s of

heme produced , th e equivalentof one molecul e i s los t as ALA , coproporphyrin, an d protoporphyrin. Lea d cause s partial inhibition o f AL A dehydratas e an

d ferrochela tase . E Pi s amarke

ro f th e partia

l inhibition thatoccurs a tth e ferrochelatas e step . I

n the presence o

f lead , increase d fre e E P (FEP ) level s are observed t o correlate wit h decrease d ALA

D levels . Som

e geneti c studie s sugges tthathig h FE Plevel s ar

e associate d wit

h decrease d ALA

D activities , eve n i

n th e absenc e o

f lead . ZP Pi s boun d t o th e re

d cel l an d therefore remains throughou tth e lif e o f th e re d cell , whic

h is abou t12 0 days . Insofa

ras i s known, al l cell s synthesiz e th e hem e necessary fo rcel l function , an d lea d inhibit s hem e synthesi s i

n mos tcell s o f th e body , including thos e i n th e liver , kidney , an

d brain . Th

e hem e enzyme s i

n thes e cell s ma

y hav e ver y shor thalf-lives . Thes e enzyme s ar e probabl

y quite importan ti n studying the effect s o

f lead . On

e of thes e i s th e P-45 0 famil y o f enzymes . I

n th e liver , they ar

e essentia l i

n th e metabolism of

drugs . Als o o

f concern i s th e activatio n rate of a n enzym e i n th e kidney , whic

h ma y b e inhibited t o aharmfu

l leve l b y lead . Ther e i s adose-dependentdecreas e i n th e leve l o

f 1,2 5 dihydroxy vitami n D i

n serum . Thi

s relationship i s nonlinear , an d th e leve l decrease s a tamuc

h highe rrate as th e Pb

B rise s above 35-4 0 yg/dL . Althoug

h th e mechanis

m fo rth e reductio n of

1,2 5 dihydroxyvitamin D i

n seru m i s no tfully understood , i ti s possibl e thati tma

y b e relate d t o a

n effec to

f lea d o n th e production o

f P-45 0 enzyme s i

n th e kidney . P-45 0 i s on e o f th e factor s necessary fo rth e hydroxylizatio n o f 1,2 5 dihydroxyvitamin D a tth e 1 position , whic h occurs i

n th e kidney . Furthe

rresearch will b e required t o evaluate th e biological significanc e of reduced seru

m level s o f

1,2 5 dihydroxyvitamin D . A ne w diseas e relate d t o th e virtua l absenc e o

f ALA D ha s been described . A geneti c disorder , i ti s transmitte d as arecessiv e trait . Th

e peopl e affecte d hav e symptoms simila rt o thos e associate d wit

h acut e intermitten tporphyria, anothergeneti c disordero

f porphyri n metabolism . I

ti s extremel y doubtfu

l tha tthi s diseas e ha

s anything t o d

o wit h low-leve l lea d exposure , althoug h at hig h Pb B level s (70-8 0 yg/dL an d higher) , i ti s possibl e tha tlea d inhibit s ALA D t o th e same exten ta

s foun d i n thi s ne w disease . I

np. 1 9 3 thi s ne w disease , ALAD activitie s ar e abou t 1 % of normal
. Furthermore , peopl e wit h ALAD level s a t abou t 20 % of norma l hav e bee n identified , an dthes e peopl e ar e health y an dwithou t an y symptom s whatsoever
. Clinicall y speaking , childre n wit h Pb B level s abou t 4 0 pg/dL , elevate dE P levels , an dothe r evidenc e of

iro n deficienc y ca n b e treate dwit h iron , an dthi s anemi ao r iro n deficienc y ca n b e corrected , eve n thoug h n o specifi c treatmen t fo r lea di s given
. Th e symptom s associate dwit h anemi awoul db e th e same , regardles s of whethe r th e caus e was lea dexposur e o r iro n deficiency
. However , iro n deficienc y increase s th e absorptio n of lea dfro mth e gut
. Anothe r possibl e effec t

involve s tryptopha n pyrrolase , whic h i s a heme-dependen t

enzym e i n th e liver
. I t ha s bee n postulate dtha t th e reduce dleve l of

hem e in porphyri amay b e responsibl e fo r som e o f th e symptom s see n in acut e intermitten t porphyri a(Litma n an d Correia , 1983)
. Regardin g th e possibl e effect s o f AL A 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 n barrier
. Bul l e t al
. (1983 ) hav e foun ddela y o f myelinizatio n of

th e nerv e sheath s i n th e brai n i n conjunctio n wit h Pb B level s i n th e 30-40-yg/d L rang e i n neonata l rats
. I t i s know n tha t

lea dinterfere s wit h oxidativ e phosphorylatio n an dhenc e energ y production
. Thi s lead-relate ddisruptio n o f energ y productio n ma y b e responsibl e fo r th e dela y i n mylenization
. Patient s wit h sickle-cel l anemi aappea r t o b e mor e susceptibl e t o th e toxi c effect s of

lead , althoug h th e mechanism s responsibl e ar e no t understood
. I n general , evidenc e seem s t o b e goo dtha t a n elevate dE P leve l indicate s a n increase dris k o f advers e healt h effects
. I t seem s t o b e agoo dindicato r

o f bot h iro n deficienc y an dlea dexposure . Th e E P leve l i s usefu l fo r

monitorin g long-ter mexposure . Epidemiologica l studie s shoul db e base do n dat aacquire db y extractio n technique s rathe r tha n b y th e hematofluorometer
. Extractio n technique s ar e use dt o calibrat e hematofluorometers
. Dat asho w tha t

hematofluorometer s giv e reading s tha t ar e systematicall y low ; therefore , i t woul dappea r

tha t the y shoul db e recalibrate da t

th e factor y ever y thre e month s o r so . Th e technica l difficultie s wit h th e hematofluoromete r hav e no t

ye t bee n resolved
._..
___P.2

_ 9 4 B.4. 2 Exper tB

• A chil dwit h ahig h Pb B leve l an dn o reductio n in Hb leve l ca n di e of neurologica l toxicity
. Thus , Hb leve l i s no t aver y usefu l inde x fo r th e advers e healt h effect s of lead , a t leas t fro maclinica l poin t

of view
.

• Neurologica l an dbehaviora l effect s (e.g. , aggressio n an d hyperactivity ) occu r

muc h mor e quickl y i n childre n tha n hematolog

ica l effects , an da t

muc h lowe r

Pb B level s (abou t

4 0 ug/dL)
.

• Th e bod y ca n compensat e fo r reduce dHb
. Oxyge n begin s t o b e transporte dothe r

ways , offsettin g t o som e degre e th e possibl e advers e effect s o f

reduce dHb
.

• Anemi aonl y become s aproble mwhe n th e body' s abilit y t o compensat e i s lost
.

• Damag e t o th e hem e syntheti c pathwa y i s crucial , bu t thi s damag e canno t b e attribute dt o reduce dHb
. Th e inhibitio n of hem e synthesi s ha s broa dimplication s fo r avariet y o f

organ s an dsystems , especiall y i n th e developin g child
. Besid e it s rol e in th e erythropoeti c syste mi n formin g Hb , hem e i s activ e i n live r function , vitami n D metabolism , an dth e CNS , al l o f whic h ar e affecte db y low-leve l exposur e t o lead
.

• A roug h dose-effec t relationshi p betwee n Pb B an dHb level s wa s expresse d—on e fo r

iron-deficien t

childre n an don e fo r noniron

deficien t children
. Exper t

B estimate dthat , o n th e average , noniron-deficien t

childre n wit h Pb B level s o f abou t 1 0 ug/d L an d 5 0 ug/d L woul dhav e H b level s o f abou t 1 2 g/d L an d10. 5 g/dL , respectively
. Fo r

iron-deficien t

children , h e estimate dHb level s of 1 0 g/d L an d6.5-7. 0 g/d L fo r Pb B level s of

1 0 ug/d L an d5 0 ug/dL , respectively
. However , Exper t B believe dtha t

i t wa s quit e possibl e tha t H b level s coul db e eve n lowe r fo r th e iron-deficien t

childre n a t Pb B level s o f

5 0 yg/L , bu t

jus t coul dno t

b e sure . H e coul dno t expres s thes e feeling s quantitatively , despit e effort s t o assis t hi m usin g judgmenta l probabilit y encodin g techniques
. B.4. 3 Exper tC

Ver y hig h E P level s ca n caus e porphyri adu e t o error s i n metabolism , wit h clinicall y recognizabl e ski n an dCN S effects
. However , ther e i s n o evidenc e o f alea dworke r

eve r developin g porphyri aa s aresul t

o f 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
.-JJ^~r - Ther e i s no evidenc e tha talead-induce d elevate d E Pleve l itsel f cause s healt h problems ; i ti s simpl y amarker , orindicator , of advers e healt h effect s du e possibl y t o lea d exposure . E Plevel s large rthan on e standar d deviatio n abov e th e mean shoul d b e followe d by aloo k a tPb B levels . Sinc e change s in E

Plevel s ten d t o la g change s i n Pb B levels , j ti s importan tt o b e lookin g a tboth ove rtim e t o ge tagoo d ide ao f what i s goin g on . Th e rat e o f ris e in E

Pversu s a

n increas e in Pb

B i s greate rtha n linear , bu tlagge d in time . A plo to f th e natura l lo g of E Pvalue s versu s Pb

B woul d b e roughl y linea runde rchronic , relativel y constan tlead-exposur e conditions . A lead-induce d elevate d E Pleve l i s a

n indicato ro f

interferenc e wit h hem e synthesis , whic h ma y b e compensate d fo rby derepressio n o f ALAS , th e rate-limitin g enzym e involve d in hem e systhesis , dependin g on th e degre e o f lea d exposure . I ti s possibl e tha ta n elevate d E

Pleve l i s a

n indicato ro f interferenc e b y lea d in th e body' s abilit y t o produc e 1,2 5 dihydroxyvitami n D . Th e cytochrom e P-45 0 enzymes , o f whic h ther e ar e more tha n 5 0 differen tisozymes , ar e relate d t o th e synthesi s o f

1,2 5 dihydroxyvitami n D . Ther e ar e stron g indication s tha tlea d reduce s synthesi s o f th e P-45 0 enzymes , whic h ma y in turn reduc e th e metabolis m o f 25-(OH)D , anecessar y ingredien tin th e biosynthesi s o f

1,25 dihydroxyvitami n D (Fraser , 1980) . Ther e i s als o suggestiv e evidence , butno tproof , tha televate d E

P level s indicat e reduce d abilit y of th e live rt o detoxify . Thi s effec t ha s bee n show n in anumbe ro f studie s involvin g high lea d exposur e in worker s an

d children . Furthermore , elevate d E Plevel s ma

y indicat e sufficien texposur e t o lea d o rothe rmetal s t o accelerat e th e destructio n (i.e. , reduc e thei r half-lives ) o f

th e hemoprotein s (Maines , 1976) . Regardin g th e CNS , i ti s no tclea rwhethe relevate d E Plevel s pe rs e caus e any effects . Som e animal studie s hav e bee n conducte d concernin g CN S effect s when ver y larg e dose s o f th e E Pprecurso r AL A ar e administered . Som e repor tCN S effect s an d other s no t (Moore an

d Meredith , 1976 ; Edwards e tal. , 1984) . I n astud y o f

lea d workers , Hammond e tal . (1980 ) determine d tha t AL A in plasm aan

d urin e wa s a s goo d amarke ro f th e degre e o f toxicit y o f

lea d a s PbB ; tha tAL A wa s a s goo d amarke ra s E Pfo r hematopoieti c syste m damage ; an d tha tAL

A an d Pb B wer e bette r indicator s o f

damag e tha n E

Pfo rothe reffect s (e.g. , neurologica l and renal) . Anothe rstud y (Lilli s e tal. , 1977 ) showe d tha tE Pwa s a P. 3P. 4 T6 ~ 

### bette r indicato r

o f hematopoieti c effect s than AL A an dPbB
. The difference s betwee n th e tw o studie s can probabl y b e attribute dt o th e differentia l measuremen t reliabilitie s o

f th e tw o laboratories
.

• Ther e i s no evidenc e o f a n E P versu s H

b relationshi p i

n childre n a t PbB level s < 5 0 ug/dL
. Also , ther e ar e factor s othe r than lea dtha t affec t E P level
.

• Th e possibility o

f lea dexposure causin g hypertensio n i s ane w issue
.

• T o summarize , evidenc e i s lackin g tha t elevate dE

P level s pe r

s e relate dt o lea dexposur e caus e advers e healt h effects
. B.4. 4 Exper

tD FEP Elevate dE

P level s cause db

y lea dexposure indicat e th e direc t toxi c effec t o f lea don heme , abasi c physiological syste mtha t i s commo n t o man y organ s an dcel l types
. Piomell i e t

al
. (1982; ) an dSilbergel dan dLamon (1980) hav e bot h suggeste dtha t

some o f th e effect s o

f lea do n th e CN

S ma y b e attributabl e t o altere dmetabolis mo f porphyri n compounds
. Other s hav e propose dtha t

perturbation s ma

y occu r i n CN S intracellula r calciu mmetabolism
. Liver A t Pb B level s o

f 30-4 0 ug/dL , evidenc e ha s shown tha t live r metabolis mo

f model compound s (e.g. , Cortisol ) i s altered , thereb y implyin g areduce dabilit y t o detoxif y th e bloo dstream
. Sinc e man y drug s hav e metaboli c pathway s tha t ar e similar

t o tha t o f Cortisol , thei r metabolis mma

y als o b e affecte dby Pb

B levels
. Calciu m

• Ther e i s evidenc e tha t th e calcium-mediate dbasi c enzymati c system s i n al l mammalian cell s ar e affecte da t Pb B level s abov e abou t 5 micromolar
. An

y disruptio n o

f thes e system s ma

y hav e pervasiv e effects
. Fo r

example , calciu mfromcalmoduli n can b e displace dby lead , calmoduli n bein g acentra l componen t o f th e norma l chemistr y o

f cells
. 1,25 Dihydroxyvitamin D

• A comple x enzym e syste mi s responsibl e fo r productio n o

f 1,2 5 dihydroxyvitami n D hormone
. Lea di s know

n t o impai r

severa lP. 5 9 7 

### aspects o

f thi s enzym e system , including electro n transport, mitochondria

l function , an

d the cytochrom e P-450 family o f enzymes . Impairmen

ti n th e productio

n of 1,2 5 dihydroxyvitamin D hormon e i n lead-toxi c childre

n ha s bee n confirme

d i n experimenta

l studie s i n vivo an d i n vitro . AtPb B level s o

f 33-5 5 ug/dL , there i s evidenc e o f a n approximately 66% decreas e i

n th e kidney' s abilit

y t o produc

e 1,2 5 dihydroxy vitamin D hormone . AtPb B level s abov

e 6 2 ug/dL , there i s evidenc e o f adecreas e i

n 1,2 5 dihydroxyvitamin D level s to adegree comparable to tha t reported i n childre n wit h inbor n error s i n metabolism . AtPb B level s o

f 12-120 ug/dL , there i s astatisticall y significan t negativ e correlatio n betwee n 1,2 5 hihydroxyvitami

n D an d Pb B levels . AtPb B level s abov

e 5 5 ug/dL , chelatio n therapy is immediately used . At25-5 5 ug/dL , th e results o f th e ethylenediamine tetraacetat e (EDTA

) provocative tes tar

e use d to determine whic

h children woul

d benefi tfro

m chelatio n therapy . 1,2 5 dihydroxyvitamin D affect s th e maturatio n o f cell s an

d enhance s th e differentiatio n o f cells . Rat

s an d mice havin

g leukemi awer

e treate d wit

h picomolarconcentration s o f 1,2 5 dihydroxyvitamin D , whic h resulte d i

n thei rlifespan s being extended . I

n vitro experiment

s usin g avariet y o f huma n cell s (e.g. , lymphoma, myeloid leukemiacells , an d monocytes ) hav

e replicate d thes e findings . Recentresearch show

s tha t1,2 5 dihydroxyvitamin D evidence s some immuno-regulator

y functions like othe rsteroi d hormones . Ther e i s early , evolvin g evidenc e that1,2 5 dihydroxyvitamin D ha

s a rol e i n controllin g insuli

n secretio n fro

m th e pancreas . Th e action s o

f 1,2 5 dihydroxyvitami

n D hormon

e involve notonl

y minera l absorption , bon

e remodeling , an

d calciu m homeostasi s i

n virtuall y all mammalia

n cells , bu

trecentl y reported information indicate s thati tha

s even mor

e pervasive effect s i

n humans . Som

e o f thes e effects , whic

h ar e no w recognized , include enhancemento f cel l differentiatio n (maturation) an d immuno-regulator

y capacity . Thi s evidence , togethe rwit h tha tdiscussed i

n th e sixt

h throug h eight h point s above , suggests thatadecreas e of 1,2 5 dihydroxyvitamin D hormon e i s likel y t o hav

e pervasive effect s o

n th e functio n o

f othe rorgans .P3_ 9 8 B.4. 5 Exper tE

Ther e doe s no t

see mt o b e an y evidenc e tha t a n elevate dE P leve l i s itsel f a n advers e healt h effect
. However , i t coul db e becaus e ther e i s aris k o f damag e t o othe r

organ s o r

function s anytim e th e balanc e o f a n essentia l metabolit e i s upset
. Fo r example , althoug h an essentia l amin o acid , phenylalanin e i s toxi c a t hig h levels
. Thi s toxicit y i s see n i n th e diseas e phenylketonuria , i n whic h exces s phenylalanin e canno t

b e metabolized
. Thus , i n th e absenc e o f a specia l diet , th e phenylalanin e build s u p an daffect s th e developin g CNS , causin g menta l retardation
. Also , exces s level s o f fluorid e caus e teet h t o becom e brittle , eve n thoug h prope r level s increas e th e hardnes s o f

teeth
. Thus , futur e researc h ma y sho w tha t elevate dE P i s a n advers e healt h effect
. Elevate dE P i s avaluabl e inde x o f advers e effect s o f

lea din system s an dorgan s (e.g. , CNS , liver , an dkidney)
. Th e bod y ca n compensat e fo r lea dinsul t

up t o apoint
. Fo r example , a t

lo w Pb B levels , th e inhibitio n of E P i s compensate dfor , bu t no t a t slightl y highe r

levels
. Piomell i e t

al
. (1982 ) repor t

a threshol di n th e rang e o f 16-1 7 ug/dL
. ALA D show s n o threshold
. Regardin g measuremen t o f EP , car e mus t

b e take n if

th e hematofluromete r

i s use dbecaus e th e amoun t o f E P tha t

i s ZP P decrease s proportionatel y a s tota l E P rises
. Becaus e th e hematofluromete r

measure s ZPP , i t

ma y b e underestimatin g tota l EP
. Belo w 3 5 ug/dL , ther e i s goo dagreemen t betwee n E P (extraction ) an dZP P (hematofluorometer)
. Abov e 3 5 ug/dL , ther e appear s t o b e a30 % differenc e betwee n ZP P (lower ) an dFE P (higher)
. I n assessin g th e nee dfo r treatment , bot h E P an dPb B level s shoul d b e considered , a s th e Center s fo r Diseas e Contro l do
. Critica l Pb B level s fo r

regulator y purpose s ma y nee dt o b e les s tha n thos e considere dfo r

clinica l purpose s i n orde r t o provid e a n adequat e margi n o f

safet y fo r

th e populatio n a t

large
. B. 5 APPENDI X B REFERENCE S Bull , R.J. , e t

al. , The Effects of

Lead on the Developing Central Nervous System of

the Rat, Neurotoxicology , 4:1-1 8 (1983)
. Edwards , S. , e t

al. , Neuropharmacology of Delta-Aminolaevulinic Acid, H. Effect of Chronic Administration in Mice, Neuroscienc e Letters , 50:169-17 3 (1984)
.Fraser , D.R. , Regulation of the Metabolism of

Vitamin D , Physiologica l Reviews , 60:551-61 3 (1980)
. Hammond , P.B. , e t

al. , The Relationship of Biological

Indices of

Lead Exposure to the Health Status of

Workers in a Secondary Lead Smelter, J
. Occupationa l Medicine , 22:475

- 48 4 (1980)
. Lilis , R. , e t

al. , Prevalence of

Lead Disease among Secondary Lead Smelter Workers and Biological

Indicators of

Lead Exposure, Environmenta l Research , 14:255-28 5 (1977)
. Litman , D.A. , an dM.A
. Correia , L-tryptophcm : A Common Denominator of Biochemical and Neurological

Events of

Acute Hepatic Porphyrias?, Science , 222:1031-103 3 (1983)
. Maines , M.D. , an dA
. Kappas , The Induction of Heme Oxidation in Various Tissues byTrace Metals: Evidence for the Catabolism of

Endogenous Heme by Hepatic Heme Oxygenase, Annal s of

Clinica l Research , 8(Suppl
. 17):39-4 6 (1976)
. Moore , M.R. , an dP.A
. Meredith , The Association of Delta-Aminolevulinic Acid with the Neurological

and Behavioral

Effects of

Lead Exposure, in Trac e Substance s i n Environmenta l Healt h - X , Universit y of Missouri-Columbia , pp . 363-37 1 (1976)
. Piomelli , S. , e t

al. , Threshold

for Lead Damage to Heme Synthesis in Urban Children, Proc
. Nationa l Academ y o f Scienc e (Medica l Sciences) , 79:3335-333 9 (Ma y 1982)
. Silbergeld , E.K. , an dJ.M
. Lamon , Rol e of Altered Heme Synthesis in Lead Neurotoxicity, J
. Occupationa l Medicine , 22:680-68 4 (1980)
. P. 7P. 8

APPENDI

X C FITTIN G FUNCTION S T

O ENCODE

D JUDGMENT S RELATIN

G TO LEAD-INDUCED I Q EFFECT SP. 9 APPENDIX C FITTIN G FUNCTION S TO ENCODED JUDGMENT S RELATIN

G TO LEAD-INDUCE D I Q EFFECT S
Th e organizatio n of

thi s appendi x i s simila r t o tha t o f App
. B.
. Sectio n C. l reproduce s th e I Q protocol , an dSec
. C. 2 summarize s th e mathematica l formulations
. Sectio n C. 3 tabulate s encode djudgments , specification s fo r function s fi t

t o thos e judgments , dat aconcernin g CIs , an dcomparison s o f encode djudgment s an dfitte d functions
. Finally , Sec
. C. 4 summarize s th e discussion s hel dwit h eac h o f th e experts
. C I I Q PROTOCOL
C.l. l Introductio n Th e U.S
. Environmenta l Protectio n Agenc y i s charge db y th e Clea n Ai r Ac t wit h settin g an drevisin g NAAQ S fo r selecte dpollutant s a t level s sufficien t

t o protec t

th e publi c healt h wit h an adequat e margi n o f safety
. A s yo u know , th e scientifi c base s fo r NAAQ S ar e presente dan dreviewe di n CDs
. 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 mwhic h th e mos t susceptibl e population s ca n b e determine dan d fro mwhic h variou s advers e healt h effect s ca n b e identified
. Th e C D summarize s an d evaluate s th e availabl e clinical , epidemiological , an danima l o r toxicologica l laborator y evidenc e wit h regar dt o th e physiologica l an dadvers e healt h effect s o f lead , an d therefor e represent s ou r mos t up t o dat e knowledg e o n lea deffects
. A s on e aspec t

of th e revie w process , EPA assesse s healt h risk s b y identifyin g th e mos t sensitiv e population s fo r eac h pollutan t

an destimatin g probabilisticall y th e number s o f

peopl e i n th e population s wh o may suffe r eac h o f

variou s well-define d advers e healt h effect s attributabl e t o th e pollutant
. I t i s believe dtha t

informatio n abou t th e healt h risk s associate dwit h variou s potentia l standard s wil l ai dth e EP A Administrato r

i n selectin g tha t

standar dwhich , i n hi s o r he r judgment , protect s th e publi c healt h wit h an adequat e margi n o f safety
. Becaus e th e ris k

estimate s tha t

EPA seek s ar e ofte n base di n par t o n dose

respons e relationship s an duncertai n lead-exposur e estimates , 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 evidenc e an dt o probabilisticall y estimat e lea dexposur e unde r alternativ e NAAQS
. Obtainin g th e healt h ris k estimate s the n involve s combinin g probabilit y estimate s fo r dos e respons e an dexposure . Th e proble mo f

estimatin g dose-respons e relationship s i s simila r t o tha t whic h exist s i n clinica 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 th e bes t decisio n fo 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 n i s no tP.1 0



### certai n and , therefore , w e will ai dyo

u t o represen t

your opinio n probabilistically
. Furthermore , sinc e th e extrapolatio n depend s o n one' s interpretatio n o

f th e literature , differen t peopl e will hav e differen t judgments
. Fo r

eac h healt h effect , we inten dt o obtai n th e probabilisti c judgment s o f abou t fiv e expert s t o sampl e th e rang e o f 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 will estimat e th e rang e o f risk s base don th e rang e o f judgments
. I

f we a s ris k

analyst s d

o ou r jo b properly , the n no t

only will , w e b e abl e t o show th e EP

A Administrato r

th e rang e o

f estimate s base do

n th e rang e o

f judgments , bu t we wil l als o b e abl e t o sho w some o f th e source s o

f th e disagreements
. Indeed , asid e benefi t o f thi s exercis e i

n which we prob e your

knowledg e i

n astructure dmanne r

ma y b e t o help identif

y source s o

f greates t disagreement
. Basedo n th e evidenc e i

n th e lea dCD , tw o population s hav e bee n identifie da s bein g mos t

susceptibl e t o th e effect s o f lea dintoxication
. One i s childre n fro mbirth throug h th e seventh birthday , andth e othe r i s th e fetuse s carrie dby th e pregnan t women. * A number

o f advers e healt h effect s hav e bee n identifie dfo r whic h we would like t o estimat e dose-respons e function s includin g th e one discusse dbelow
. C.1. 2 Lead-Induce

d I Q Decrements C.l.2. 1 Centra

l Nervous System an

d Behaviora

l Effect s of

Lea d A larg e number

o f studie s reviewe di

n th e C D sugges t tha t ther e ar e numerou s CNS an dbehaviora l effect s o f lea dexposure . Considerabl e uncertaint y surround s al l o f thes e effects , however , becaus e o f th e enormou s difficulty i n definin g an dmeasurin g them , andi

n isolatin g the mfromth e effect s o f covariates
. Sinc e our

goal i s t o obtai n probabilisti c estimate s abou t th e shap e o

f adose-respons e curv e for aparticula r

well

define deffec t

i f asufficien t

amoun t o f pertinen t

dat acoul db e collected , ou r firs t tas k i s t o selec t

on e CN S or behaviora l effec t

tha t i s o f acknowledge dimportanc e an dtha t can b e wel l specified
. The searc h fo r

lead-induce deffect s ha s include dstudie s o f electroencephalogra m (EEG ) effects ; sensory-motor , perceptual , an dattentiona l deficits ; cognitiv e decrement s o f variou s sorts ; hyperactivity ; negativ e classroo mbehaviors ; an dothe r effect s tha t

s o far hav e bee n studie donl

y i n animal models
. Fro mthi s larg e assortmen t o f effects , w

e hav e selecte dI

Q decremen t

a s th e advers e effec t

upo n which t o focus
. W

e ar e no t considerin g I

Q t o b e th e only no r

necessaril y th e bes t

measure o

f cognitiv e abilities
. No

r i s i t bein g considere da s asurrogat e for th e othe r

system s i

n which effect s hav e bee n explored
. (Becaus e o

f it s multifacete dnatur e i t probabl y involve s many o f them. ) Rather , we hav e selecte dI Q decremen t

becaus e ther e ar e more dat ao n thi s effec t

than on any other , an dbecaus e it s functiona l o r "clinical " significanc e i s clear
. It i s quit e conceivabl e tha t

a s researc h continue s i n futur e years , othe r

more "pure " CNS or behavioral effect s will emerg e tha t ar e obviously advers e andfor whic h asubstantia l

•I n thi s report , we focu s only on childre n aged 0-6 .P.1 1

body of dat aha s developed
. Unti l suc h a n even t occurs , i t

appear s tha t

lead-induce dI Q 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 o f

lea dma y b e cumulative , i t i s necessar y t o specif

y th e children' s age s a t whic h th e I Q decrement s ar e estimated
. I n al l cases , assum e tha t

I Q test s ar e give n o n th e children' s sevent h birthdays
. 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 n child , 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 n as 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

ahypothetica l idea l experiment
. I f yo u agre e wit h th e assumption s o n whic h th e hypothetica l experimen t i s based , the n you 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

I Q decrements
. Ther e ar e difference s of opinion , o f

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 h effects , bu t th e leve l define da s advers e ma y 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 n particula r magnitude s of

I Q 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 Pb B levels
. The n w 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 n a t

eac h Pb B leve l whos e I Q score s ar e belo w an y valu e of

interest , suc h as , fo r

example , belo w IQ s o f

70 , 80 , 90 , o r

100
. C.1.2. 3 Hypothetica l Idea l Experimen t Assum e tha t

a t birth , subject s ar e randoml y assigne dt o group s differentiate db y Pb B leve l targete dfo r

th e thir dbirthday
. Member s of eac h treatmen t

grou p ar e expose d t o lea dfro mbirt h unti l thei r sevent h birthdays , whil e member s o f acontro l grou p ar e sheltere dfro mlea dfro mbirt h unti l thei r sevent h birthdays
. Th e leve l o f environmenta l lea dassigne dt o achil di s roughl y constan t fo r th e seve n years ; however , eac h child' 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 d behavior
. Nevertheless , th e experimenta l condition s ar e suc h tha t a t thei r third birthdays , al l th e childre n i n eac h grou p hav e essentiall y th e sam e measure dPb B level
. Thus , group s diffe r

i n term s of

mea n Pb B o n th e thir dbirthday
. Environmenta l lea d level s necessar y t o yiel dagive n Pb B leve l a t ag e thre e i n aparticula r chil dremai n constan t throug h th e sevent h birthday
. Th e experimenta l manipulatio n affect s onl y lea dexposur e an dn o othe r aspec t o f th e children' s lives
. The n th e WISC- RI Q tes t i s administere dt o al l childre n o n thei r seventh birthdays
. Th e childre n i n eac h grou p hav e adistributio n o f I Q score s wit h som e mea n an dstandar ddeviation
. W e ar e intereste di n you r probabilisti c judgment s abou t th e I Q distribution s fo r group s of

childre n o n thei r

sevent h birthdays , al l of who mha d specifi c Pb B level s o n thei r thir dbirthdays
.P.1 2



### Not e thre e feature s abou t thi s hypothetica l experiment
. First , i t i s similar

t o a longitudina l study ; childre n ar e i n agroup fromconceptio n unti l thei r sevent h birthdays
. Second , i t

involve s rando massignmen t o f childre n t o groups , makin g i t unnecessar y t o worr y abou t covariates
. Third , PbB i s measure da t ag e three, an dI

Q a t ag e seven . I f you believ e I

Q effect s o

f lea dt o b e differen t

fo r lowe r SE S tha n for

middl e andupper SE S subpopulation s o

f childre n under

thes e experimenta l condftions , then w e will conside r

separat e hypothetica l experiment s for th e tw o subpopulations
. Otherwise , w e wil l conside r

only asingl e suc h experiment
. SE S i s acomple x variable
. Fo r simplicity , i

f we divid e th e populatio n int o lo w SE S an dhigh SE

S categories , le t

u s defin e lo

w SE S a s thos e childre n comin g fro m household s wit

h income s i

n th e lowes t

15%
. Unles s yo u disagree , we wil l als o assum e tha t th e distributio n of

IQ score s i s normal withi n eac h group . (Th e WISC- Rwa s develope dt o yiel dnormall y distribute dI Q score s for th e genera l population , wit h mea n I Q equal t o 10

0 an dastandar ddeviatio n o f 15. ) Furthermore , i

f w e conside r

onl y asingl e hypothetica l experiment , samplin g fro mth e full populatio n o

f children , then , unles s yo u disagree , we wil l assum e tha t th e I Q standar ddeviatio n i s 1 5 a t eac h Pb B level , an dwe wil l only hav e t o encod e you r probabil

isti c judgmen t

abou t th e mea n I Q a t ag e seve n for

eac h o f severa l PbB level s a t

ag e three
. I f we conside r

tw o hypothetica l experiments , eac h samplin g fromadifferen t SE S subpopulation , the n th e I Q standar ddeviatio n will possibly b e les s than 15
. Assumin g tha t I Q standar ddeviatio n i s th e sam e a t al l Pb B level s withi n SE

S subpopulations , we wil l hav e t o encod e your probabilisti c judgmen t

abou t th e standar ddeviatio n fo r eac h SE S group . Then , separatel y for

eac h SE

S group o r

for th e populatio n a s awhole , a s appropriate , we will encod e your probabilisti c judgmen t

abou t th e mea n IQ a t ag e seve n o f th e contro l group . Finally , we will encod e your probabilisti c judgment s abou t th e difference s i

n mea n I Q a t ag e seve n betwee n childre n wit h negligibl e Pb B (th e contro l group ) an dchildre n a t

eac h o f severa l elevate dPbB s a t ag e thre e (th e treatmen t groups)
. The followin g section s specif y furthe r th e condition s t o b e assume di n thi s hypothetica l experiment
. C.1. 3 Population a tRis

k Base do n th e CD , we can specif y th e mos t

susceptibl e populatio n a s al l U.S
. childre n frombirt h throug h thei r seventh birthdays
. W

e hav e alread y define dth e effec t a s bein g measure do

n th e seventh birthday
. However , a s alread y discussed , yo u ma y conside r I Q effect s o

f lea dt o b e differen t

fo r low SE S tha n fo r hig h SES subpopulation s o f children , resultin g i

n differen t

experimenta l outcome s fo r th e tw o groups . I

f so , then we will elici t

your judgment s separatel y fo r low SE S childre n an dfo r

hig h SE S children
.P.1 3

C.1. 4 Exposure Condition s W e wil l b e askin g you r

judgmen t

abou t mea n I Q value s o n th e sevent h birthday s a t variou s Pb B levels
. Assum e tha t th e Pb B level s unde r consideratio n fo r

agive n judgmen t hav e bee n measure do n th 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 n mor e o r les s con stan t sinc e birth , an dtha t

i n interactin g wit h th e environment , th e childre n exhibite dth e usua l rang e of

behavior s a t

eac h age . Thus , Pb B level s wer e no t necessaril y constan t fro mbirt h t o ag e seven , bu t exposur e an dbehaviora l factor s wer e suc h tha t a t ag e three , Pb B wa s a t

aspecifi c level
. Finally , assum e tha t th e change s i n Pb B level s fro mbirt h unti l th e sevent h birthda y ar e distribute da s yo u believ e the y actuall y are .
C.1. 5 Physiologica l an d Environmenta l Condition s Becaus e th e .effect s of lea ddepen do n man y parameters , i t i s necessar y t o specif y assumption s abou t

thos e parameter s i n th e population(s)
. C.l.5. 1 Physiologica l Condition s Th e effec t

o f lea di n th e syste mdepend s o n th e person' s nutritiona l an dmeta
boli c status
. Assum e tha t th e level s o f

iron ; zinc ; copper ; vitamin s A , C , D , an dE ; calcium ; phosphorus ; an dmagnesiu mar e distribute dwithi n th e populatio n o r withi n eac h o f th e tw o SE S 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 dnutritiona l level s of childre n withi n th e populatio n o r withi n eac h of

th e tw o SE S groups .
C.1.5. 2 Environmenta l Condition s Th e effec t

o f lea do n I Q als o ma y depen do n numerou s environmenta l an dcare givin g factor s tha t

var y withi n SE S level , suc h a s thos e assesse di n th e HOME (hom e observatio n fo r

measuremen t

of th e environment ) scale , parenta l IQ , an ds o forth
. Assum e tha t

thes e factor s ar e distribute dwithi n th e populatio n o r withi n eac h of

th e tw o SE S group s a s yo u believ e the y i n fac t are . C.l. 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 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 o f

variou s aspect s o f

th e literature
. How d o yo u evaluat e th e researc h concernin 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 h ca n b e explaine db y othe r factor s frequentl y associate dwit h lea dexposure ? I f so , d o yo u believ e tha t th e effect s o f

lea d simpl y ad dt o th e effect s o f othe r factors , o r

tha t th e effect s o f

lea ddepen do n th e level s o f othe r factors ? I

n th e latte r

case , wha t

ar e th e variable s tha t lea dexposur e___ ^ P.1 4 10 8 interact s with ? A relate d questio n concern s you ropinio n abou tth e relationshi p betwee n exposur e an

d susceptibility . Thatis , do yo u think tha tthos e childre n wh o ar e a tgreates t ris k o f exposur e du e t o thei rlivin g in deterioratin g pre-195 0 housin g o rin urba n area s with larg e amount s o f

vehicula rtraffi c o rdu e t o othe rreasons , ar e als o mos tsusceptibl e t o th e effect s o f

lead ? Fo rexample , thes e ma y b e th e sam e childre n wh o als o hav e poore rdiets , les s acces s t o medica l care , poore rcare-givin g environments , an d fewe r intellectua l resource s t o fal l back on . Wha ti s you ropinio n abou tth e tim e cours e o f lea d exposur e and o f

lea d effect s on CNS , cognitive , an d behaviora l development ? Wha tar e th e relativ e effect s o f cumulativ e versu s curren texposure ? Ar e th e effect s reversible ? I s ther e athreshol d fo r th e effects ? Wha

tar e th e implication s o f th e anima l mode l research , bot h th e behaviora l an

d th e morphological , fo rhuma n CNS , cognitive , an

d behaviora l effect s of lead ? Ar e ther e othe rfactor s t o conside rin thinkin g abou tth e dose-respons e function s fo rleadrinduce d I

Q effect s tha tw e shoul d discus s now ?
C.l. 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 d with conclusion s tha tw e dra w fro m researc h an

d more generall y i

n oureveryda y thinking . However , no teveryon e i s awar e o f al l th e source s tha tcontribut e t o thei runcertainty , norar e mos tpeopl e familia rwith th e proces s o f

actuall y expressin g thei runcertaint y i n probabilisti c terms . Whe n a n exper ti s aske d t o make probability judgment s on sociall y importan tmatters , i ti s particularl y importan ttha th e o rsh e conside rth e relevan tevidenc e in asystemati c an d effectiv e manne ran

d provid e judgment s tha trepresen thi s o rhe ropinion s well . Experimenta l psychologist s an d decisio n analyst s hav e amasse d aconsiderabl e amoun to f

dat aconcernin g th e wa y peopl e for

m an d expres s probabilisti c judgments . Th e evidenc e suggest s tha twhen considerin g larg e amount s o f comple x information , mos t peopl e emplo y simplifyin g heuristic s and demonstrat e certai n systemati c distortion s o f thought , i.e. , cognitiv e biases , which adversel y affec tthei rjudgments . Th e purpos e o f thi s sectio n i s t o make you awar e o f thes e biase s an

d heuristic s s o that , a s much a s possible , yo u ca n avoi d the m in making probability judgments . W e wil l firs trevie w th e mos twidesprea d biase s an d heuristics , and the n offe rsom e suggestion s t o hel p yo u mitigat e thei reffects . C.l.7. 1 Sequentia l Consideratio n o f Informatio n Generally , th e orde ri n whic h evidenc e i s considere d influence s th e fina l judgment , althoug h logicall y tha tshoul d no tb e th e case . O f necessity , piece s o f informatio n ar e considere d on e b y on e in asequentia l fashion . However , thos e considere d firs tan

d las tten d t o dominat e judgment . I n part , initia l informatio n ha s it s undue influenc e becaus e i tprovide s th e framewor k tha tsubsequen tinformatio n i s the n tailore d t o fit . Fo rexample , peopl e usuall y searc h fo revidenc e t o confirm thei rinitia l hypotheses ; the y rarely loo k fo revidenc e tha tweighs against them . Th e late revidenc e ha s it s undue effec tsimpl y becaus e i ti s freshe rin memory .P . 1 5 10 9 Relate dt o thes e sequentia l effect s i s th e phenomeno n o f anchorin g an d adjustment
. Base do n earl y partia l information , on e form s a n initia l probabilit y estimat e regardin g th e even t

i n question
. Thi s ancho r judgmen t

i s the n adjuste da s subsequen t informatio n i s considered
. Unfortunately , suc h adjustment 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 n considere 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 n a s awhole
. However , th e specifi c instance s ofte n ar e recalle dprecisel y becaus e the y stan dou t in som e way , suc h a s bein g familiar , unusual , especiall y concrete , o r personall y significant
. Unfortunately , th e specifi c characteristic s of thes e singula r

example s ar e the n attributed , ofte n incorrectly , t o al l th e member s of

th e populatio n of

interest
. Moreover , thes e memor y effect s ar e ofte n combine dwit h th 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 yo u 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

wa s unusua l an dtherefor e stand s out
. Th e tendenc y migh t the n b e t o trea t

th e recalle dstudie s a s typica l o f th e populatio n o f

relevan t

research , ignorin g importan t difference s amon g studies
. Subsequen t

attempt s t o recal l informatio n coul dresul t i n thinkin g primaril y of evidenc e consisten t

wit h th 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 o f information , ignorin g factor s suc h a s samplin g erro r

an dimprecisio n o f

measurement
. Rathe r the y summariz e evidenc e i n term s o f simpl e an ddefinit e conclusions , causin g the mt o b e overconfiden t i n thei r judgments
. Thi s tendenc y i s stronge r whe n on e ha s aconsiderabl e amoun t o f intellectua l and/o r persona l involvemen t

i n aparticula r

field
. I

n suc h cases , informatio n i s ofte n interprete di n away tha t i s consisten t

wit h one' s belief s an dexpectations , result s ar e overgeneralized , an dcontradictor y evidenc e i s ignore do r underestimated
. C . 1.7. 4 Relatio n betwee n Even tImportanc e and Probabilit y Sometime s th e importanc e of
. events , o r thei r possibl e cost s o r

benefits , influence s 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 towar dris 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 ; similarly , 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
.P.1 6



### 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 n level s o f uncertaint y andt o us e appropriat e criteri ao f discriminatio n for

differen t

range s o

f probability
. Peopl e ten dt o estimat e both extrem e an dmid-rang e probabilitie s in
. th e sam e fashion , usuall y doing apoo r jo b i n th e extremes
. It

help s her e t o thin k

i n term s o f odd s a s wel l a s probabilities
. Thus , fo r example , changin g aprobabilit y estimat e fro m 0.51 0 t o 0.50 1 i s equivalen t t o achang e i

n odd s from1.041: 1 t o 1.004:1 , bu t achang e froma n estimat e o

f 0.99 9 t o 0.99 0 change s th e odd s by afacto r o f abou t 1 0 fro m999: 1 t o 99: 1 Th e close r

t o th e extreme s (eithe r 0 or 1 ) tha t on e i s estimatin g probabilities , th e greate r

th e impac t

o f smal l changes
. C.l.7. 6 Recommendations Althoug h extensiv e andcarefu l trainin g wouldb e necessar y t o eliminat e al l th e problem s mentione dabove , some relativel y simpl e suggestion s can help minimiz e them
. Mos t importan t

i s t o b e awar e o

f one' s natura l cognitiv e biase s an dt o tr y consciousl y t o avoi dthem
. To avoi dsequential

effects kee p i

n min dtha t th e orde r

in whic h yo

u think o f informatio n shoul dno t

influenc e your

final judgment
. It

ma y b e helpfu l t o actuall y not e o n pape r th e importan t

fact s yo u ar e considerin g andthen t o reconside r the mi n tw o o r more sequences , checkin g th e consistenc y o f your judgments
. Tr

y t o kee p a

n open min

d unti l yo u hav e gon e throug h al l th e evidence , an ddon' t le t th e earl y informatio n yo u conside r swa y yo u more than i s appropriate
. T o avoi dadvers e memory effects, defin e variou s classe s o f informatio n tha t

yo u dee mrelevan t

andthe n searc h you

r memor y for example s o

f each
. D o no t restric t your thinkin g only t o item s tha t stan dou t

for specifi c reasons . Mak

e aspecia l attemp t

t o conside r conflictin g evidenc e andt o think o f dat atha t

ma y b e inconsisten t

with a particula r theory
. Also , b e carefu l t o concentrat e o n th e give n probabilit y judgmen t an d do no t le t your ow n value s (ho

w yo u wouldmak

e th e decisio n yourself

) affec t thos e judgments
. T o accuratel y estimate Vie reliability of information, pay attentio n t o suc h matter s a s sampl e siz e andpowe r o f th e statistica l tests
. Kee p i n mindtha t

dat aar e probabilisti c i

n nature , subjec t

t o element s o

f rando merror , imprecis e measurement , and subjectiv e evaluatio n andinterpretation
. I n addition , th e farthe r

on e mus t

extrapolate , o r generalize , fromaparticula r stud y t o asituatio n o

f interest , th e les s reliabl e i s th e conclusio n andth e les s certaint y shoul db e attribute dt o it
. Rely more heavil y o n informatio n tha t

yo u conside r

more reliable , bu t

d o no t trea t i t a s "absolut e truth. " Kee p i n 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 n outcom e influenc e th e poin t

a t which actio n i s take n wit h respec t t o it , bu t no t th e judgmen t

tha t i s made abou t

th e outcome' s likelihood
.Finally , i n makin g probabilit y judgments , thin k primaril y i n term s o f

th e measur e (probabilit y o r

odds ) wit h whic h yo u fee l mor e comfortable , bu t sometime s translat e t o a n 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)
. 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 in term s of

odds , whic h ar e unbounded , instea do f probabilities , whic h ar e bounded
. Fo r

example , on e ca n mor e easil y conceptualiz e odd s o f 1:20 0 tha n a probabilit y of

0.005
. C.1.8 Fina l 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

d o no t allo w exac t

predictions
. Ou r

goa l i s t o hav e yo u represen t probabilisticall y you r

ow n uncertaint y abou t th e experimenta l outcome s base do n you r expertis e an dth e availabl e knowledge
. I n respondin 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 n reviewe di n th e CD , 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 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 n of larg e amount s of comple x evidence
. Yo

u ma y fin di t

helpfu l t o revie w th e sectio n o 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 o f

lea dexposur e o n mea n decremen t i n I Q (relativ e t o th e mea n I Q o f childre n sheltere dfro mPb B exposure ) ca n b e represente d probabilisticall y in tw o differen t ways . 1
. Uncertaint y abou t

th e mea n I Q decremen t tha t woul dresul t

whe n th e expose dgrou p ha s agive n Pb B concentration
. 2
. Uncertaint y abou t

th e Pb B concentratio n tha t woul db e require dt o caus e agive n mea n I Q decrement
. W e wil l concentrat e o n on e way a t atime , focusin g primaril y o n th e firs t one . Fo r thes e purpose s recal l tha t everyon e i n th e expose dpopulatio n ha s aspecifie d Pb B level , whil e everyon e i n th e zer o Pb B populatio n ha s negligibl e PbB , a s describe d above
. Then , i n orde r

fo r u s t o determin e you r

uncertaint y abou t

th e mea n I Q decremen t o f th e expose dgrou p wit h agive n Pb B leve l relativ e t o th e negligibl e Pb B group , w e mus t introduc e adefinition
. Le t L b e th e give n Pb B concentratio n i n question , the n Definition : D(L) i s th e mea n I Q decremen t of th e expose dgrou p wit h Pb B leve l L relativ e t o th e negligibl e group . Th e valu e o f

D(L) fo r

agive n L 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

D(L) b y specifyin g aparticula r mea n I Q decremen t

d an dhavin g yo u conside r ho w likel y i t

i s tha t D(L) i s les s tha n tha t value
. T o hel p yo u mak e you rP.1 8



### probabilit y judgments , w

e will mak

e use o f adevic e calle d aprobabilit y wheel , whic

h ha s adjustabl e sector s o

f blu e an d orange . W

e ca n rea d o n th e bac

k o f th e wheel th e percentag e o

f th e whee

l thati s each color . I

n makin g you rjudgment

s yo u ar e to imagine thatth e whee

l i s aperfectl y fai rrando m device , an

d thattherefore th e probabilit y o f its . stopping wit

h th e pointe ro

n blu e i s exactl y represente d b y th e relativ e are athatis blue . W e will then proceed a

s follows . Fo

reach Pb B concentratio n L , we will specif y a particularmea

n I Q decrementd

, an d als o se tth e probabilit y wheel t o hav

e aspecifi c relativ e areao

f blue . The

n yo u ar e to considercarefull y th e question : D o yo u consideritmor

e probabl e tha tD(L ) i s les s tha

n d o rthatth e whee

l woul d stop wit h the pointero

n blu e (o n arando m spin) ? Yo u ca n giv e on e o f thre e responses : 1 . Yo u judg e i tt o b e mor

e probabl e thatD(L

) i s les s tha

n d, 2 . Yo u judg e i tt o b e mor e probabl e thatth e whee

l woul d sto p wit

h th e pointero

n blue , o r 3 . Yo u cannotjudg

e eithe reventa

s mor e probabl e tha n th e other . Fo raparticularconcentratio n L an d mea n I Q decrementd, some wheel setting s wil l hav e asmall enoug

h relativ e areao

f blu e thatyo u will fee l confidentmakin g the firs tresponse . Othe

rwhee l setting s wil

l hav e alarge enoug

h relativ e areao

f blu e that yo u will fee l confidentmakin g th e second response . Th e intermediate setting s will be mor e difficul tto judge . However, forafixed Pb B L , an d mea n I Q decrementd

, w e will manipulat e th e whee

l setting s t o fin

d the on e forwhic

h yo u fee l mostcomfortabl e makin g th e thir d response . Onc e w e hav e determined th e poin

ta twhic h yo u ar e mostcomfortabl e wit

h th e thir d response , an

d stil l focusin g o

n th e given Pb

B concentratio n L, we will specif y ane w mea n I Q decrementd' , rese tth e whee l to ane w relativ e areao

f blue , an d procee d t o obtain you

rjudgment

s regardin

g th e probabilisti c relatio n betwee n d ' an d D(L) . This will continu e forth e given L unti l w e hav e obtained comparisons o f various mea

n value s t o D(L) . The

n w e will hav

e elicite d th e probabilisti c representatio n o f you runcertaint

y abou tthe mea

n I Q decrementfo ron

e Pb B level . W

e will obtai n th e probabilisti c representatio n o

f you runcertaint

y forth e outcom e o

f anotherexperimentb

y specifyin g ane w L an d continuing a

s before . W

e will d o thi s fo ranumbe

rof value s o f L. I tfrequently happen

s thata n expert' s judgment

s alte rsomewha

tove rth e cours e of asessio n suc

h as this , a

s h e orsh e considers th e evidenc e fro m various perspective s an d think s abou tth e various responses calle d for . Hence , w e will grap

h you rresponse s and, a tappropriat

e times , sho

w the- , to yo

u foryou rconsideratio n an

d comparison . A

t thes e time s yo

u ma y wis h t o change some of

th e judgment

s yo u gav e earlier . Also , althoug

h th e probabilit

y judgment

s ar e entirel y you

rown , w

e mus t introduce on

e logical constraint : namely , thatyou rfina l judgment

s are coheren ti

n a sens e thatw

e ca n explain a

s w e go along . I

ti s quit e commo n forinitia l judgment

s toP.1 9

exhibi tsom e incoherences . Thati s anothe rreaso n w e wil l conside rtogethe rth e graph s o f yourjudgments . Ou robjectiv e i s t o obtai n acoheren tse to f judgment s tha t represent s you ropinion s wel l b y th e en d o f thi s elicitatio n process . Yo u ar e no texpecte d t o giy e u s suc h ase timmediately . Al l o f thi s wil l becom e cleare ra s w e g o along . W e shoul d emphasiz e tha tth e judgment s w e ar e askin g you t o make ar e no t simpl e ones , no ro f

cours e ar e ther e know n correc tanswers . Rather , w e wan tyou rbes t an d mos tconsidere d judgmen tin ligh to f th e availabl e relevan tscientifi c data . Therefore , pleas e reflec ton th e availabl e dat acarefully , feelin g fre e t o consul tth e lea d CD o rothe rsource s a s yo u wis h a s you formulat e you rjudgments . (Encod e judgment s fo rtw o Pb B concentrations , then continu e with instructions. ) Recal l tha tuncertaint y abou tth e experimenta l outcome s ca n als o b e expresse d in term s o f

th e Pb B concentratio n necessar y t o produc e agive n mean I Q decremen tD , i

f th e entir e expose d populatio n ha d th e sam e Pb

B concentration , establishe d in th e manne r discusse d earlier . Mor

e specifically , proceedin g a s before , le tus introduc e adefinition : Definition : L(D) i s th e Pb B leve l tha twoul d caus e amean I Q decremen tD i

n a n expose d group relativ e t o th e negligibl e group . Th e valu e o f

L(D ) i s uncertai n fo ragive n D , an d w e wan tt o obtai n you rjudgment s abou t it s possibl e values . Analogousl y t o whatw e hav e alread y don e in obtainin g th e D(L) judgments , fo ragive n D w e wil l specif y concentration s I

an d as k you t o conside rho w likel y i ti s tha tth e L(D) i s les s tha n th e specifie d 1. Mor e 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 ri tmore likel y tha tL(D) i s les s tha n I o rtha tth e whee l woul d sto p wit h th e pointe ron blu e (o n arandom spin) ? You ca n giv e on e o f

thre e responses : 1 . You judg e i tmore probabl e tha tL(D) i s les s tha n I, 2 . You judg e i tmore probabl e tha tth e whee l woul d sto p with th e pointe ron blue , o r 3 . You canno tjudg e eithe reven ta s more probabl e tha n th e other . Afte rdeterminin g th e whee l settin g a twhic h yo u fee l mos tcomfortabl e wit h th e thir d response , w e wil l specif y ane w I

and repea tth e process . A s before , fo reac h D w e wil l elici tyou rcomparativ e judgment s fo rvariou s value s o f 2, . W e mus tencod e you rprobabilisti c judgmen tabou tth e mean I Q o f childre n i

n th e population , o rin th e tw o SE S groups , wh o hav e anegligibl e Pb B leve l underth e exposur e condition s describe d previously . W e star twith adefinition : Definition : Le £ y b e th e tru e populatio n mean I Q fo rchildre n with negligibl e PbB . (Or , le ty . b e th e tru e populatio n mean I Q fo rchildre n with negligibl e Pb B in SE S grou p i. )_ _ _P.2 0 

### 11 4

* ie 

### Th e valu e of

y o ru . i s uncertain , an

d w e will obtain you

rjudgmen

tabou tit s possibl e values . Analogousl

y t o wha tw e hav e already done , w

e will specif

y amea n y an d as k you . t o conside rho

w likel y i ti s thaty o

ry . i s les s tha

n y . W e will elici tyou

rjudgment

s abou tvarious value s o

f y wit h the aid o

f th e probabilit

y wheel , i

n th e sam e manne

ra s wa s don e previously . I f yo u fel ti tnecessary to conside rseparate experiments fo rtw o SE S groups , then yo u ma y believ e thatth e within-group I Q standar d deviatio n i s differen tfro m 15 . I f so , w e mus tencode you

rprobabilisti c judgmen

tabou tthatvalue . I

f yo u agree , w

e will assume thatth e standar

d deviatio n i s unaffecte d b y Pb B level . However , yo

u ma y fee l thatth e standar

d deviatio n is differen tfo rth e two SE S groups . I

f so , w e mus tencod e you ropinion separatel y abou teach case . As before , w

e star twit

h adefinition : * 

### Definition : Le

to . be th e true I

Q standar d deviatio n fo rSE

S grou p i . * 

### Th e valu e o f o . i s uncertain , an

d w e will obtain you

rjudgmen

tabou tit s possibl e values . Analogousl

y t o wha tw e hav e alread y done , w e will specif

y astandar

d deviatio n a an

d as k yo u t o conside rho

w likel y i ti s tha

to . is les s tha

n o . W e will elici tyou

rjudgment

s abou tvarious values o

f o wit h the ai d o f th e probabilit

y wheel , i

n th e sam e manne

ra s wa s don e previously . C.2 FURTHE

RMATHEMATICA

L FORMULATION

S FO RI Q ASSESSMENT

S NOL O probabilit

y functions were fi tt o all o f th e judgment

s o f th e H b experts . Becaus e o

f th e divers e natur

e o f th e judgment

s obtained fro

m th e I Q experts , i twa

s necessary t o choos e amon g normal , lognormal , an d NOL O probabilit

y function s t o adequately representthos e judgments . Fittin g norma l an d lognorma

l distribution s t

o judgment s i s a n intermediate ste p i

n th e proces s o

f fittin g aNOL

O distribution , s o i ti s unnecessar

y t o repeatthos e detail s here . Th e readerca

n refe rt o Sec. B.2 fo rth e necessary information . I n fittin g lognorma

l distributions t o judgments , th e variabl e o f interes ti s thatdesignated X i n Sec . B.2.2 ; forfittin g norma l distributions , th e variabl e o f interes ti s thatdesignated Y. Distributions forrespons e rate (increase d occurrenc e o f IQ s les s tha n orequa l t o acritica l leve l IQ*

) wer e derived fro

m th e distributions fo rI Q , o TO 

### , an d Ayp rthat wer e encoded fro

m th e I Q experts . Numerica

l methods wer

e used t o obtai n th e distributions . Th

e firs tste p wa

s to chang e th e PDF

s fo rI Q , a , an

d A^ o into discret e probabilit y mass functions (PMFs

) wit h areasonable numbe

rof point s (seve n were use

d i n mos tcases) . Fo ron e expert , on

e SE S level , an

d on e Pb B level , an

d foraspecifi c combination of mea n IQ, standar

d deviation , an

d I Q decrement , th e increase d probabilit y (converte d t o arespons e rate , expressed i n percent) o

f havin g I Q value s < IQ* wa

s calculated . Th

e respons e rate an

d th e probabilit

y fo rth e particularvalue s o f I Q , o T



### _ , an

d A-

—wer e recorded . Thi

s process , whic

h wa s repeate d fo reac h possibl e combinatio n o f I Q , OJQ , an d A— , resulte d i

n ase to f points t o whic

h adistribution functio n (eithe rnorma l• a a-3 ' P.2 1

o rNOLO) wa s fi tin orde rt o facilitat e furthe rcalculations . One functio n wa s obtaine d fo reac h Pb

B and SES combination . Th e proces s wa s repeate d fo reac h o f th e expert s excep tExpertI . T o illustrat e th e process , conside rth e followin g hypothetica l example . Le t

= 95 105 ! 0.5 , fo rI

Q = 0.5 , fo rI

Q = (0.5 , fo ro = 1 4 P(0 I Q ) = ) I Q (0.5 , fo ro I Q u 1 C (0.5, fo rAJQ = i y (0.5 , fo rA

— = I Q = 1 5

= 5 1 0 I Q Thes e ar e discret e PMFs havin g onl y tw o possibl e outcome s i n eac h case , eac h o f

whic h i s equall y likely . Ther e ar e eigh tcombination s o f th e thre e variable s t o consider , an d eac h combinatio n i s equall y likely . Fo rI Q = 95 , o = 14 , and A

—= 5 , th e increase d probabilit y o f havin g IQ

s < 7 0 i s
A P= • ( 7 0 - 95 • 5

1 4 ) -• (

= 0.07 7 - 0.03 7

= 0.0 4 70-95 - 1 4

whic h correspond s t o arespons e rat e o f 4% . I n asimila rfashion , arespons e rat e ca n b e calculate d fo reac h o f

th e othe rseve n combinations . The result s ar e respons e rate s o f 0.1% , 1.2% , 3.1% , 3.8% , 4.3% , 10.5% , an d 11.1% . Thes e values , alon g wit h thei r associate d probabilities , defin e aprobabilit y distributio n havin g amea n o f 4.9 % and a standar d deviatio n o f

3.6% . C. 3 RESULT S Th e results , whic h ar e presente d in Table s C.1-C.8 , ar e explaine d usin g th e judgment s o f

ExpertF a s a

n example . Exper tF believe d tha tSE S leve l doe s no t significantl y influenc e th e effect s o f lea d o n IQ ; therefore , h e o rsh e provide d onl y on e se to f judgments . ExpertF judge d a0. 5 probabilit y tha tth e mean I Q o f th e unexpose d group woul d b e < 100.5 , a0. 8 probabilit y tha ti twoul d b e < 101.5 , and s o on (se e Tabl e C.l) . Exper tF als o believe d tha tusin g aprobabilit y distributio n t o characteriz e populatio n standar d deviatio n wa s unnecessar y an d simpl y gav e apoin testimat e o f 1 5 fo r OJ Q (se e Tabl e C.2) . A s show n in Tabl e C.3 , Exper tF provide d judgment s on I Q difference s a tfiv e Pb

B levels . Fo rexample , a taPbB leve l o f 6 5 yg/dL , Exper tF judge dP.2 2



### TABL E C. l Encode dJudgment s aboutth e Mea n I Q of Childre n Unexposed t o Lea

d

Exper t F lQ 0 a F b
Both SES Level 10 0 0.0 1 100. 5 0.0 5 10 1 0.6 5 101. 5 0.8 0 10 2 0.9 9 Low SES Level

High SES Level Exper t G

IQ o F

s

9 0 9 3 9 4 9 6 9 8 10 0

10 0 10 4 10 6 10 8 11 0 0.0 1 0.2 5 0.5 0 0.7 6 0.9 2 0.9 9

0.0 1 0.1 5 0.5 0 0.8 5 0.9 9 Exper t H iQ 0 F

9 2 9 4 9 8 9 9 10 2

10 0 10 2 10 4 10 6 10 8 U O 0.0 1 0.2 0 0.5 0 0.6 5 0.9 9

0.0 2 0.1 1 0.3 0 0.4 9 0.7 5 0.9 6 Exper t J

^ 0

90. 0 93. 5 95. 0 96. 0 98. 0

10 0 10 2 10 4 10 6 10 8 11 0 F

0.0 1 0.2 5 0.5 0 0.7 5 0.9 0

0.00 1 0. 1 0.7 7 0.9 0 0.9 9 0.99 9 Exper t K

iQ 0 * F

7 8 0.0 1 8 3 0.2 5 8 5 0.5 0 8 8 0.7 5 9 1 0.9 9

10 0 0.0 1 10 2 0.1 7 10 4 0.4 2 10 6 0.6 0 10 8 0.8 5 11 0 0.9 9

a I Q denote s mea

n I Q of childre

n unexpose

d t o lead . F denote s cumulativ e probability .



### a0.95 probabilit y tha t

th e mea n I Q differenc e wouldb e < 3. 7 points
. Figur e 1 5 show s tha t Expert Fi s increasingl y uncertai n abou t th e magnitud e o

f I Q difference s a s Pb

B leve l increases
. Also , Expert Fdi dno t

provid e judgment s o

n I Q difference s havin g cumulativ e probabilitie s les s than 0. 5 a t th e lowes t

thre e Pb

B level s (se e Tabl e C.3) , indicatin g tha t

h e o r sh e experience ddifficult y i n providin g judgment s on wha t would hav e bee n very smal l I

Q differences
. Fo r th e reason s presente di n Sec
. 1 , mathematica l function s wer e fi t t o th e judgment s o

f Expert F
. The y wer e obtaine db y fittin g regressio n line s t o transformation s o f th e judgments
. Th e transformatio n use dwa s th e natura l lo g (In ) transformation
. A

sTABL E C. 2 Encode d Judgment s abou tPopulatio n Standar d Deviatio n

Exper t F 

### °I Q F Exper t G

"I Q F Exper t H



### °I Q F Exper t J



### °I Q F Exper t K

a I Q F Both SES

Levels 1 5 1 Low SES Level 1 4 1 0

11 1 2 1 3 1 4 0.0 4 0. 1 0.3 5 0. 5 0.8 5 1

1 1 2 13 1 4 1 5 0.00 1 0.12 5 0. 5 0.87 5 0.99 9 1 0

1 1 1 2 13 14 0.0 1 0.0 5 0.1 4 0.5 3 0.9 3 1 5 0.99 9 1 5 0.99 9 High SES Level

1 4 1 1 3

13. 5 1 4 14. 3 1 5 15. 5 0.0 4 0.0 7 0.27 5 0. 5 0. 9 0.9 9 1

1 1 2 13 1 4 1 5 0.00 1 0.12 5 0. 5 0.87 5 0.99 9 12

1 3 13. 5 1 4 1 5 0.0 2 0.2 5 0. 5 0.7 5 0.9 9

a o T ndenote s standar d deviatio

n i n IQ values . 'I Q Fdenote s cumulativ e probability
.

wa s tru e fo r

th e H b case , thi s transformatio n le dt o distribution s tha t ar e norma l distributions , wit h ahig h degre e of accuracy . Fo r

Exper t F , th e mathematica l representation s of

th e CDF s fo r

I Q difference s conditiona l o n Pb B leve l ar e guarantee d neve r t o cross . Th e fitte ddistribution s ar e lognorma l distributions , whic h ar e uniquel y define d b y th e mea n an dvarianc e o f th e underlyin g norma l distribution s an dth e transformatio n function
. Th e propertie s o f th e lognorma l distribution s ar e summarize di n Tabl e B.l
. A variet y o f

distribution s wer e fi t t o th e judgments , an dth e one s reporte dher e wer e determined , wit h inpu t

fro mth e experts , t o b e best
. Table s C.4-C. 6 summariz e relevan t informatio n abou t

th e fi t o f th e distribution s t o th e judgment s o f

th e experts
. Tabl e C. 4 identifie s th e functiona l form ; th e definin g parameter s y an da, i f atransformatio n i s used ; th e mea n E[I Q ] an dstandar d deviatio n SD[I Q ] of

th e I Q distributions ; an dr fo r th e regressio n of

fitte dcumulativ eP.2 4



### TABL E C. 3 Encode

d Judgment

s abou tMea n I Q Decrements of Childre n Expose d t o Lea d

Pb B Leve l (ug/dL )
5

15

2 5

3 5

4 5

5 5

6 5 Exper t F

Bot hSE S 

### *I Q

0 . 1

0 . 2

0 . 1 2 3

1 2 3 4

1 2 3 4 5 2 5

5

9 F

0. 5 0.99 9

0. 5 0.99 9

0. 5 0.5 5 0.9 3 0.9 9

0. 2 0. 8 0.9 5 0.9 9

0.1 5 0. 5 0. 9 0.9 6 0.9 9 Lo

w 

### *T Q
0. 2 0. 3 0. 5 1 3 O. S 0. 7 1. 5 2 5
1 1. 3 3 4 8. 5

2 2. 5 3. 5 5 1 0
3. 5 4 5 7 1 2
4 5 7 1 0 IS Ex

p SE S F

0.0 1 0.2 5 0. 5 0.7 5 0.9 9 0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 (.9 9

0.0 1 0.2 5 O. S 0.7 5 0.9 9 ert C

Hig h 4 

### lQ

0. 3 0. 4 0. 5 1 3
0. 5 0. 7 1 2 4

1 1. 5 2. 5 4 8
2 2. 5 3. 5 5 1 0
3. 5 4 5 7. 5 1 2 SE S

F

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 0.9 9

0.0 1 0.2 5 0. 5 0.7 5 0.9 9 Lo

w
*I Q
1 2 3 4 5 2 3 4 5 6
2 4 6 8 1 0

4 6 8 1 0 1 2
6 8 1 0 1 2 1 4
8 1 0 1 2 1 4 1 6 Exper t H SE S F

0.0 3 0. 4 0.5 5 0. 9 0.9 9 0.0 6 0. 5 0. 6 0.7 5 0.9 3

0.0 1 0.3 5 0. 6 0.8 4 0.9 9

0.0 2 0.2 5 0.4 6 0.7 9 0.9 5

0.0 2 0.3 5 0.5 5 0.8 5 0.9 5

0.0 2 0. 4 0.7 7 0. 9 0.9 5 High

4 l Q "
0.5 . 1 1. 5

1 2 2. 5 3 3. 5 4 2. 4 3. 4 4. 4 4. 5 5. 4 6. 4 7. 4 3. 8 4. 8 5. 5 5. 8 6. 8 8. 3 4. 8 5. 8 6. 5 6. 8 7. 8 8. 8 6 7 8 9 1 0 SE S

F

0.4 5 0. 8 0.9 8

0.0 3 0. 3 0. 5 0. 6 0.7 3 0.9 3 0.0 2 0.1 3 0.4 7 0. 5 0. 7 0.9 3 0.9 9 0.0 4 0. 3 0. 5 0.6 1 0.8 6 0.9 9 0.0 1 0.0 9 0. 5 0. 7 0.8 5 0.9 9 0.0 1 0. 1 0. 5 0.8 5 0.9 9TIT

TABL E C. 3 (Cont'd )
' Pb B Leve l (ug/dL )

5

1 5

2 5

3 5

4 5

S S

6 5 Lo

w 

# m

0.00 1 0. 5 0. 7 1. 1 2

1 1. 9 2. 3 3. 2 5
2 3. 1 3. 6 5. 1 7
3 4. 5 S. 3 6. 9 1 0
4 5. 5 6. 3 8. 2 1 2 Exper

t SE S F

0.02 5 0.2 5 0. 5 0.7 5 0.97 5

0.02 5 0.2 5 0. 5 0.7 5 0.97 5
0.02 5 0.2 5 0. 5 0.7 5 0.97 5
0.02 5 0.2 5 0. 5 0.7 5 0.97 5
0.02 5 0.2 5 O. S 0.7 5 0.97 5 I Hig

hSE S
4 I Q

0. 2 0. 3 0. 5 1

0. 7 1 2 3

1 1. 9 2. 3 3. 2 5
2 3. 1 3. 6 4. 7 7
2 3. 5 4. 3 5. 8 9 F

0.2 5 0. 5 0.7 5 0.97 5

0.2 5 0. 5 0.7 5 0.97 5

0.02 5 0.2 5 0. 5 0.7 5 0.97 5
0.02 5 0.2 5 0. 5 0.7 5 0.97 5
0.02 5 0.2 5 0. 5 0.7 5 0.97 5 Lo

w 

# m
0.00 1 1 2 3 5 0.00 2 2.2 5 3. 5 4. 5 6. 5

0.00 3 4 5 5.7 5 8
2 6 7 8 1 0
4 7. 5 9 10. 5 1 2
6 9 11 12. 5 1 4 Exper

t SE S F
0.000 1 0.2 5 0. 5 0.7 5 0.99 5 0.00 1 0.2 5 0. 5 0.7 5 0.99 5

0.00 1 0.2 5 0. 5 0.7 5 0.9 9
0.00 1 0.2 5 0. 5 0.7 5 0.9 9
0.00 1 0.2 5 0. 5 0.7 5 0.9 9
0.00 1 0.2 5 O. S 0.7 5 0.9 9 J Hig

h *I Q

0. 5 1.2 5 2. 3

2.7 5 3. 5

3. 5

4. 5 5.7 5 8
5 6. 5 7 7. 5 1 0 SES F

•
0.01 4 0.1 4 0.2 5 0. 5 0.7 5 0.9 5 0.9 9 0.99 9 0.0 1 0.2 5 0. 5 0.7 5 0.99 9
0.0 5 0.2 5 0. 5 0.7 5 0.99 9
0.00 5 0.2 5 0. 5 0.7 5 0.9 9
0.0 1 0.2 5 0. 5 0.7 5 0.9 9 Lo

w *T Q

0.2 5 1 1. 5 2

0. 5 1 2 3 4 5 1 2 3 4 5 6 4 5 6 7 8 9 5 6 7 8 9 1 0 7 8 1 0 1 2 1 4 Exper t K SES F

0.0 1 0.3 6 0. 5 0.9 7

0.0 1 0.0 6 0.2 7 0.4 7 0. 8 0.9 8 0.0 1 0.0 5 0.1 8 0. 5 0.8 6 0.9 9 0.0 2 0.1 1 0. 5 0.6 4 0.8 2 0.9 9 0.0 2 0. 1 0.2 8 0.4 7 0.8 2 0.9 7 0.0 1 0.0 9 0. 5 0.7 9 0.9 9 Hig

h
4 l Q

0. 5 1 1. 5 1

1. 0 1. 5 2. 0 2. 5 3
2 3 3. 5 4 5
3 4 4. 5 5 6
4 5 6 7 8 SE S

F

0.0 1 0.3 5 0. 5 0.9 9

0.0 1 0.1 1 0. 5 0. 9 0.9 9
0.0 1 0. 2 0. 5 0.7 5 0.9 9
0.0 2 0.2 5 0. 5 0.7 8 0.9 8
0.0 1 0.1 7 0. 5 0.8 2 0.9 9
*4J Q denote s th e mea nI Q decremen t amon g childre nwit hth e specifie d PbB Levels , reference d t o : 

### 9 nex unexpose d children .
* F denote s cumulativ e probability .P.2 6

..,.,. . ww r^— • 12 0 TABLE C. 4 Function s Fi t t o Judgment s abou tMea n I Q Level s amon g Childre n Unexpose d t o Lea d

Functiona l Exper t For

m Definin g

Parameters 3 Measure s o f

Distributio n ove r IQ Q b E[IQ J SDUQ J r 2 fo r Regressio

n o f F o n F
Both SES Levels F Lognorma l Low SES Level 4.6 1 0.00 5 100. 9 0. 5 0.8 8

G H J K Lognorma l Lognorma l Norma l Norma l 4.5 5

4.5 8 0.0 2 0.0 2 94. 6

97. 2 94. 8 85. 0 2. 2

2. 4 1. 9 2. 9 0.9 9

0.9 7 0.9 9 0.9 9 High SES Level G H J K Lognorma l Lognorma l Lognorma l Norma l 4.6 6

4.6 6 4.6 5 0.0 2 0.0 3 0.0 2 105. 6

105. 6 104. 1 104. 9 2. 2

2. 8 1. 7 2. 4 0.9 9

0.9 9 0.9 6 0.9 9
*Th e functio n Y = ln(IQ 0 ) i s normall y distribute dwit h mea n y an d standar ddeviatio n a . Ther e ar e n o entrie s i n thes e column s whe n I Q i s normall y distributed
. 5 Fo r lognorma l distributions , y , o , an dth e equation s i n Tabl e B. l ar e use dt o calculat e th e mea n E[I Q ] an dth e standar d deviatio n SD[I Q ] o f

th e distributio n ove r I Q
. o o probabilit y value s Pversu s encode dvalue s F
. I n Tabl e C.5 , E[OJQ ] denote s th e mea n an dSD[OJQ ] denote s th e standar ddeviatio n o f th e distributio n fo r

populatio n standar d deviation
. I

n Tabl e C.6 , E[A-=Q ] an dSD[AYQ ] denot e th e mea n an dstandar ddeviatio n of probabilit y distribution s fo r th e I Q decrement s fo r differen t

Pb B levels
. Fo r Exper t F , th e fitte ddistributio n of th e uncertai n mea n I Q o f th e unexpose d grou p i s alognorma l distributio n wit h amea n valu e o f 100.9 , astandar ddeviatio n of 0.47 , an da n r

valu e o f

0.88 3 (se e Tabl e C.4)
. Th e definin g parameter s y an do ar e 4.6 1 an d0.005 , respectively
. Thes e value s ar e neede dt o calculat e point s o n aCD Ffo r th e mea n I Q variable
.X rx*ur *



### TABL E C.5 Functions Fi tt o Judgment s abou tPopulation Standar

d Deviatio n fo rI Q Level s

Exper t Functiona l

For m Definin g

Parameters *
y o y y Measure s o f

Distributio n ove r o I Q b

E[o I Q ] SD[o IQ ] r 2 fo r Regressio n o f F o n F

Bot A SES Levels Poin t 15. 0 Low SES Level G H J K Poin t Lognorma l Norma l Norma l 2.505 6 0.091 5 14. 0 12. 3 13. 0 12. 6 1. 1

0. 7 0. 9 0.9 5

0.9 9 0.9 7 High SES Level G H J K Poin t Lognorma l Norma l Norma l 2.654 1 0.041 6 14. 0 14. 2 13. 0 13. 5 0. 6

0. 7 0. 7 0.9 9

0.9 9 0.9 9

a Th e functio n Y= ln(ojQ > i s normall y distribute d wit hmea n y an d standar d deviatio n a . There ar e n o entrie s i n thes e column s fo r norma l o r poin t distributions . Fo r lognorma l distributions , y y , o y , an d th e equation s i n Table B. l ar e use d t o calculat e th e mea n E[OJQ ] an d th e standar d deviatio n SD[o I Q ] . 

### Lognorma l distribution s provide dth e bes t fit s o f Expert F' s judgment s abou t

I Q differences
. Thus , al l o

f th e column s i

n Tabl e C. 6 hav e entries
. The mea n value s o

f th e distribution s ove r

I Q decremen t

vary from0. 3 a t

aPb B leve l o f 25 yg/d L t o 1.9 a t 6 5 yg/dL
. I

n general , th e fitte dfunction s represen t th e judgment s quit e well , havin g r value s o f 0.99
. Tabl e C. 7 compare s encode djudgment s andcorrespondin g point s o n th e function s fi t t o th e judgment s o

f eac h expert
. It

can als o b e use dt o compar e th e judgment s o f th e differen t experts
. Table s like thi s on e were use dt o help th e expert s understan dth e implication s o

f thei r judgment s andt o choos e th e mathematica l function s tha t bes t represente dthos e judgments
.P.2 8



### TABL E C. 6 Functions Fi tt o Judgment s abou tMea n I Q Decrements amon

g Childre n Expose d t o Lead 3

Pb B Leve l (yg/dL ) Functiona l

For m Definin g Parameter s Measure s o f

Distributio

n ove r A^ c
E[AJQ ] SD[AJQ ] r * fo r Regressio

n o f F o n F

Bot hSES Levels Expert F 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. 3

0. 5 1. 1 1. 6 1. 9 0. 1

0. 3 0. 5 0. 8 0. 9 0.9 9

0.9 9 0.9 9 0.9 9 0.9 9 Low SES Levels Expert G 5 1 5 2 5 3 5 4 5 5 5 Expert H 5 1 5 2 5 3 5 4 5 5 5 Expert I 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l 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

0.826 8 1.248 1 1.586 0 2.032 3 2.242 2 2.404 5

-0.327 6 0.849 5 1.336 1 1.700 9 1.904 1 0.642 2

0.542 9 0.522 9 0.380 7 0.301 1 0.317 4

0.403 7 0.398 9 0.374 9 0.308 7 0.236 6 0.188 7

0.535 1 0.411 0 0.328 2 0.308 8 0.284 5 0. 8

1. 6 3. 0 4. 1 5. 9 7. 7

2. 5 3. 8 5. 2 8. 0 9. 7 11. 3

0. 8 2. 5 4. 0 5. 7 7. 0 0. 5

0. 9

. 1. 7 1. 6 1. 8 2. 5

1. 1 1. 6 2. 0 2. 5 2. 3 2. 1

0. 5 1. 1 1. 4 1. 8 2. 0 0.9 8

0.9 8 0.9 7 0.9 8 0.9 7 0.9 8

0.9 7 0.9 8 0.8 8 0.9 9 0.9 9 0.9 9

0.9 9 0.9 9 0.9 9 0.9 9 0.9 9TABLE C. 6 (Cont'd )

' Pb B Leve l (yg/dL ) Expert J 5 1 5 2 5 3 5 4 5 55 Functiona l

For m

Norma l Norma l Norma l Norma l Norma l Norma l Definin g

Parameter s
yo M yO y -Measure s o f Distributio n ove r

EIAIQ ]

2. 4 3. 5 4. 8 6. 8 8. 8 10. 7 *I

Q
SD[AJQ ]

0. 9 1. 2 1. 5 1. 5 1. 6 1. 6 Re

g o f r 2 fo r ressio n F o n F

0.9 6 0.9 9 0.9 9 0.9 9 0.9 9 0.9 8 Expert K 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. 3 2. 9 3. 8 6. 4 7. 8 10. 4 0. 4

1. 1 1. 1 1. 2 1. 3 1. 6 0.9 5

0.9 9 0.9 9 0.9 8 0.9 9 0.9 9 High SES Levels Expert G 1 5 2 5 3 5 4 5 5 5 Expert H 5 1 5 2 5 3 5 4 5 5 5 Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l

Lognorma l 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

-0.576 7 0.896 0 1.478 5 1.687 3 1.885 9 2.068 8 0.567 1

0.504 5 0.484 7 0.380 7 0.306 8

0.520 7 0.449 8 0.260 7 0.195 5 0.129 7 0.110 3 0. 8

1. 4 2. 9 4. 2 6. 0

0. 6 2. 7 4. 5 5.5 - 6. 6 8. 0 0. 5

0. 8 1. 5 1. 6 1. 9

0. 4 1. 3 1. 2 1. 1 0. 9 0. 9 0.9 5

0.9 7 0.9 9 0.9 8 0.9 6

0.9 9 0.9 8 0.9 9 0.9 9 0.9 8 0.9 9P.3 0

TABL E C. 6 (Cont'd )

Pb B Leve l (yg/dL ) Expert I 1 5 2 5 3 5 4 5 5 5 Expert J 1 5 2 5 3 5 4 5 5 5 Expert K 2 5 3 5 4 5 5 5 6 5 Functiona l

For m

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l

Lognorma l Lognorma l Lognorma l Lognorma l Lognorma l

Norma l Norma l Norma l Norma l Norma l Definin g

Parameter s

u y

-1.180 0 0.063 7 0.849 5 1.319 8 1.471 9

0.454 2 1.006 9 1.308 2 1.628 0 1.948 9 

### °

y

0.619 1 0.602 2 0.411 0 0.329 3 0.383 9

0.450 2 0.364 0 0.276 2 0.199 1 0.146 6 Measure s o f

Distributio n ove r
EUTQ ]

0. 4 1. 3 2. 5 3. 9 4. 7

1. 7 2. 9 3. 8 5. 1 7. 1

1. 3 2. 0 3. 5 4. 5 6. 0 A 

### I Q SD[Ajp ]

0. 3 0. 8 1. 1 1. 3 1. 9

0. 8 1. 1 1. 1 1. 0 1. 0

0. 3 0. 4 0. 6 0. 7 0. 9 - r 2 fo r Regressio n o f F o n F

0.9 9 0.9 9 0.9 9 0.9 9 0.9 9

0.9 6 0.9 4 0.9 6 0.9 9 0.9 9

0.9 3 0.9 9 0.9 9 0.9 9 0.9 9
Th e distribution s ar e eithe r norma l o r lognorma l i n form . I f th e distributio n ove r AJ Q i s lognormal , the n the functio n Y = ln(AYg ) i s normall ydistribute d wit h mea n yan d standard deviatio n o . Ther e ar e n o entrie s i n thes e column s whe n A-=- r i s normall ydistributed
.

c Fo r lognorma l distributions , y, a , an d the equation s i n Tabl e B. l ar e use d t o calculat e th e mea n E[A

—] an d th e standard deviatio n SD[A— ] o f th e response-rat e distributio n ove r ATQ . Calculation s involving norma l distribution s ove r A-=r » ar e mor e straightforward
.TABL E C. 7 Compariso n o f Judgment s an d Fitte d Function s Concernin g Lead-Induce d I Q Effect s

AJ Q a tPb

B Leve l
Inde x. IQ . 'I Q 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 Expert F, Both SES Levels Encoded Judgments Media n 50 Z CI a 90 % CI 100. 5

100.2 , 101. 3 100.1 , 101. 9 1

5 0.2 5 b , 0. 6 b , 0. 9 0. 5

b , 1. 2 b , 1. 9 0. 9

b , 1. 5 b , 2 1. 5

1.1 , 1. 9 b , 3 2

1.3 , 2. 6 b , 4 Fitted Functions Media n 50 Z C I 90 Z CI 98 Z C I 100. 9

100.6 , 101. 2 100.1 , 101. 7 99.8 , 10 2 1

5 0.2 5 0.2 , 0. 3 0.1 , 0. 5 0.1 , 0. 7 0. 5

0.4 , 0. 7 0.2 , 1. 1 0.2 , 1. 4 1. 0

0.7 , 1. 3 0.5 , 2. 1 0.3 , 2. 8 1. 4

1.0 , 1. 9 0.7 , 3. 0 0.5 , 4. 1 1. 7

1.3 , 2. 4 0.8 , 3. 7 0.6 , 5. 1TABL E C. 7 (Cont'd )

Inde x 

### IQ , 'I Q AJ Q a t PbB Leve l

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 Expert G, Low SES Level Encoded Judgments Media n 50 % C I 90 % CI 9 4

93 , 9 6 91 , 9 9 Fitted Functions 1 4 0. 5 0.3 , 1 0.2 , 3 1. 5

0.7 , 2 0.5 , 5 3. 0

1.3 , 4 1 , 8. 5 3. 5

2.5 , 5 2 , 1 0 5. 0

4 , 7 3.5 , 1 2 7. 0

5 , 1 0 4 , 1 5

Media n 50 % CI 90 % C I 98 % C I 94. 6

93.1 , 96. 1 91.0 , 98. 3 89.6 , 99. 8 1 4 0. 6 0.4 , 0. 9 0.2 , 1. 8 0.1 , 2. 8 1. 4

1 . 2 0.6 , 3. 5 0.4 , 4. 9 2. 7

1.9 , 3. 8 1.1 , 6. 3 0.8 , 9 3. 9

3 , 5 2.1 , 7. 3 1.6 , 9. 4 5. 7

4.6 , 7 3.5 , 9. 3 2.8 , 11. 4 7. 3

5.9 , 9. 1 4.3 , 12. 3 3.5 , 15. 3 Expert G, High SES Level Encoded Judgments Media n 50 % C I 90 % C I 10 6

105 , 10 7 103 , 10 9 Fitted Functions Media n 50 % CI 90 % C I 98 % C I 105. 5 104.1 , 107. 0 102.0 , 109. 2 100.6 , 110. 7 1 4

1 4 0. 5

0.4 , 1 0.3 , 3 1. 0

0.7 , 2 0.5 , 4 2. 5

1.5 , 4 1 , 8 3. 5

2.5 , 5 2 , 1 0 5. 0

4 , 7. 5 3.5 , 1 2

0. 7 0.5 , 1 0.3 , 1. 8 0.2 , 2. 7 1. 2

0.9 , 1. 7 0.5 , 2. 8 0.4 , 4 2. 6

1.9 , 3. 6 1.2 , 5. 8 0.8 , 8 3. 9

3 , 5 2.1 , 7. 3 1.6 , 9. 4 5. 8

4.7 , 7. 1 3.5 , 9. 5 2.8 , 11. 7TABL E C. 7 (Cont'd )

AJ Q a t Pb B Leve l
Inde xIQ Q o I Q 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 Expert H, Low SES

Level Encoded Judgments Media n 50 % C I 90 % C I 9 8

95 , 10 0 92 , 10 2 1 3

12 , 1 4 10 , 1 5 2. 6

1.6 , 3. 4 1.1 , 4. 5 3. 0

2.6 , 5 1.9 , 6. 1 5. 2

3.4 , 7. 2 2.4 , 9. 2 8. 2

6 , 9. 7 4.2 , 1 2 9. 5

7.4 , 11. 3 6.2 , 1 4 10. 5

9.7 , 11. 8 8.2 , 1 6 Fitted Functions Media n 50 % C I 90 % C I 98 % C I 97. 2

95.5 , 98. 8 93.3 , 101. 2 91.7 , 102. 9 12. 3

11.5 , 13. 0 10.5 , 14. 2 9.9 , 15. 2 2. 3

1.7 , 3 1.2 , 4. 5 0.9 , 5. 9 3. 5

2.7 , 4. 6 1.8 , 6. 7 1.4 , 8. 8 4. 9

3.8 , 6. 3 2.6 , 9 2 , 11. 7 7. 6

6.2 , 9. 4 4.6 , 12. 7 3.7 , 15. 7 9. 4

8 , 1 1 6.4 , 13. 9 5.4 , 16. 3 11. 1

9.7 , 12. 6 8.1 , 15. 1 7.1 , 17. 2 Expert H, High SES

Level Encoded Judgments Media n 50 % C I 90 % C I 10 6

104 , 10 8 101 , 11 0 14. 3

13.8 , 14. 7 13.2 , 15. 2 0. 6

b , 0. 9 b , 1. 3 2. 5

1.8 , 3. 5 1.2 , 4. 1 4. 5

3.8 , 5. 6 2.7 , 6. 7 5. 5

4.4 , 6. 4 3.9 , 7. 8 6. 5

6.1 , 7. 1 5.3 , 8. 4 8. 0

7.4 , 8. 7 6.4 , 9. 6 Fitte d Functions Media n 50 % C I 90 % C I 98 % C I 105. 6

103.7 , 107. 5 101.1 , 110. 3 99.3 , 112. 3 14. 3

13.8 , 14. 6 13.3 , 15. 2 12.9 , 15. 6 0. 6

0.4 , 0. 8 0.2 , 1. 3 0.2 , 1. 9 2. 4

1.8 , 3. 3 1.2 , 5. 1 0.9 , 7 4. 4

3.7 , 5. 2 2.9 , 6. 7 2.4 , 8 5. 4

4.7 , 6. 2 3.9 , 7. 5 3.4 , 8. 5 6. 6

6 , 7. 2 5.3 , 8. 2 4.9 , 8. 9 7. 9

7.3 , 8. 5 6.6 , 9. 5 6.1 , 10. 2TABL E C. 7 (Cont'd )

Inde x IQ Q o I Q Expert I, Low SES Level Encoded Judgments Media n 50 % CI 90 % C I Fitted Functions Media n 50 % C I 90 % C I 98 % C I Expert J, High SES Level Encoded Judgments Media n 50 % C I 90 % CI Fitted Functions Media n 50 % C I 90 % C I 98 % C I 5 yg/d L 1 5 yg/d L

0. 7 0.5 , 1. 1 0 , 2

0. 7 0.5 , 1. 0 0.3 , 1. 7 0.2 , 2. 5

0. 3 0.2 , 0. 5 0 , 1

0. 4 0.2 , 0. 5 0.1 , 0. 9 0.1 , 1. 3 AJ Q a t
2 5 yg/d L

2. 3 1.9 , 3. 2 1 , 5

2. 3 1.7 , 3. 1 1.2 , 4. 6 0.9 , 6. 1

1. 0 0.7 , 2 0 , 3

1. 1 0.6 , 1. 7 0.1 , 2. 8 0.1 , 4. 3

1 PbB Leve l

3 5 yg/d L

3. 6 3.1 , 5. 1 2 , 7

3. 8 3.0 , 4. 7 2.2 , 6. 5 1.8 , 8. 2

2. 3 1.9 , 3. 2 1 , 5

2. 4 1.8 , 3. 2 1.2 , 4. 5 0.9 , 6. 1 4 5 yg/d L

5. 3 4.5 , 6. 9 3 , 1 0

5. 5 4.4 , 6. 7 3.3 , 9. 1 2.7 , 11. 3

3. 6 3.1 , 4. 7 2 , 7

3. 8 3.1 , 4. 7 2.2 , 6. 3 1.8 , 7. 9 . •

5 5 yg/dL

6. 3 5.5 , 8. 2 4 , 1 2

6. 7 5.5 , 8. 1 4.2 , 10. 7 3.5 , 13. 1

4. 3 3.5 , 5. 8 2 , 9

•
4. 5 3.4 , 5. 7 2.3 , 8. 0 1.8 , 10. 6 0TABL E C. 7 (Cont'd )

AJ Q a tPb B Leve l
Inde x iQ

c OJ Q 5 yg/d L 1 5 yg/d

L 2 5 yg/d

L 3 5 yg/d

L 4 5 yg/dL 5 5 yg/dL Expert J, Low SES Level Encoded Judgments Media n 50 % C I 90 % C I 9 5

94 , 9 6 91 , 9 9 1 3

12 , 1 4 11 , 1 5 2

1 , 3 0.2 , 5 3. 5

2.3 , 4. 5 0.4 , 6. 4 5

4 , 5. 8 1 , 8 7

6 , 8 3 , 9. 6 9

7.5 , 10. 5 5 , 11. 7 1

1 9 , 12. 5 6.6 , 13. 7 1 Fitted Functions Media n 94. 8 50 % C I 93.5 , 96. 1 90 % C I 91.6 , 98. 0 98 % C I 90.3 , 99. 3 Expert J, High SES Level Encoded Judgments Media n 103. 1 50 % C I 102.5 , 103. 9 90 % C I 100.5 , 107. 0 Fitted Functions Media n 104. 1 50 % C I 103.0 , 105. 2 90 % CI 101.4 , 106. 8 98 % C I 100.4 , 108. 0 1 3 12.5 , 13. 5 11.9 , 14. 1 11.4 , 14. 6

1 3 12 , 1 4 11 , 1 5

1 3 12.5 , 13. 5 11.9 , 14. 1 11.4 , 14. 6 1 .

0 . 0 . 2 . 8 , 9 , 3 , 4 3. 0 3. 9 4. 5 3. 5 2.7 , 4. 3 1.5 , 5. 4 0.7 , 6. 2

2 1.3 , 2. 3 0.7 , 3

1. 6 1.2 , 2. 2 0.7 , 3. 4 0.5 , 4. 6 4. 8

3.8 , 5. 8 2.3 , 7. 2 1.3 , 8. 2

3 2.8 , 3. 5 1.4 , 6. 4

2. 7 2.1 , 3. 5 1.5 , 5. 0 1.2 , 6. 4 6. 8

5.8 , 7. 8 4.4 , 9. 3 3.3 , 10. 3

4 3.5 , 5 2 , 6. 7

3. 7 3.0 , 4. 4 2.3 , 5. 8 1.9 , 7. 0 8. 8

7.8 , 9. 9 6.3 , 11. 4 5.2 , 12. 5

5 4.5 , 5. 8 3.3 , 7. 6

" ' 5. 0 4.4 , 5. 8 3.6 , 7. 0 3.2 , 8. 0 10. 7

9.7 , 11. 8 8.1 , 13. 4 7.0 , 14. 5

7 6.5 , 7. 5 5.3 , 9. 7 i 7. 0 j 6.4 , 7. 8 ' 5.5 , 8. 9 5.0 , 9. 9

;TABL E C. 7 (Cont'd )

Inde xIQ Q Expert K, Low SES Level Encoded Judgments Media n 8 5 50 % C I 83 , 8 8 90 % C I 79 , 90. 4 Fitted Functions Media n 8 5 50 % C I 83.0 , 87. 0 90 % C I 80.2 , 89. 8 98 % C I 78.2 , 91. 8 

### °I Q

1 3 12.2 , 13. 5 11 , 1 4
12. 6 12.0 , 13. 2 11.1 , 14. 1 10.4 , 14. 8 1 5 yg/d L

1. 5 0.8 , 1. 7 0.3 , 2
1. 3 0.7 , 1. 6 0.5 , 1. 8 0.2 , 2. 3 2 5 yg/d L

3. 1 2 , 3. 8 1 , 4. 8
2. 9 2.1 , 3. 6 1.1 , 4. 7 0.3 , 5. 5 A

### I Q

3 5 yg/d L

4 3.2 , 4. 7 2 , 5. 8
3. 8 3 , 4. 5 2 , 5. 5 1.3 , 6. 3 a t PbB Leve l

4 5 yg/d L

6 5.4 , 7. 5 4.5 , 8. 8
6. 4 5.6 , 7. 3 4.4 , 8. 4 3.6 , 9. 3 5 5 yg/d L

8. 1 6.8 , 8. 6 5.5 , 9. 8

7. 8 6.9 , 8. 6 5.6 , 9. 9 4.7 , 10. 8 6 5 yg/d L

1 0 8.8 , 11. 8 7.5 , 13. 7
10. 4 9.3 , 11. 4 7.8 , 1 3 6.7 , 1 4 Expert K, High SES Level Encoded Judgments Media n 50 % C I 90 % C I 104. 9

102.6 , 107. 2 100.6 , 109. 4 tte d Functions Media n 50 % C I 90 % C I 98 % C I 104. 9

103.3 , 106. 5 101 , 108. 8 99.4 , 110. 4 1 3

13 , 12.2 , 1 3 13 , 12.3 , 11.9 , . 5 1 4 14. 8

. 5 1 4 14. 6 15. 1 1. 5

0.8 , 1. 7 0.6 , 1. 9
1. 3 1 , 1. 5 0.7 , 1. 9 0.5 , 2. 1 2

1.6 , 2. 3 1.2 , 2. 9

2 1.7 , 2. 3 1.3 , 2. 7 1 , 3 3. 5

3.1 , 4 2.2 , 4. 8
3. 5 3.1 , 4 2.5 , 4. 6 2 , 5 4. 5

4 , 4. 8 3.1 , 5. 9
4. 5 4 , 5 . 3.3 , '5. 7 2.8 , 6. 2 6

5.2 , 6. 8 4.3 , 7. 8
6 5.4 , 6. 6 4.5 , 7. 5 3.9 , 8. 1

a C I denote s credibl e interval
. Lowe r C I limi t coul d no t be calculate d becaus e Expert s F an d H di d no t mak e probabilit yjudgment s o n A-TT T value s les s than th e media n a t thi s Pb B level . I QU i JJ > O J iV » H U l U I U I U I U I U I

a s * a t a s a s a s o o o o o o r r * f r t
- r ; o o o o o o

i i i i i i N > r o ts > *s > O J u i

..... . o t o u i o o * » o O J s o u i o u i v o K > V O O J > O O K J O S O O 0 0 0 0

o o o o o o

..... . K > 0 J O J * » U i O s I O H M

M v O U

~ J * » O 0 0 - J 0 0 0 J J > J > Is

J «« l * »

H - v O * J O s O

J O

..... . 0 0 J > O s •- • O s - J

O J K> N> N I N I O

..... . N> * J O s * > O * » h

o I A o o U I

O Q t r C A P I C A f f t < i t U I * » 0 J |S

J H- " U I U I U I U I U I U I

o o o o o o S O V O s O v O v O s O s O v O V O s o - J U i a s s e a s a s a s a s

o o o o o o c c r * r1 r * r * o o o o o o

i i i i i i O H H H M N

..... . ^ J O O

J V O 0 J 0 0 V O * » 0 J O

J O s «» l U i K » O s V O - J 4 S vl(T>0>UiM H
o o o o o o

..... . O J J > J > U I U I U I U I 00 0 U M H u i o o o o o o o o K

> 0 0 U I O

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—O J S O U l * • O s 0 0 «»

J J > V O

v l V 0 0 0 > { > M

. o . . . . OOiOOOUv l

o o o o o o v o v O v O vO v O v O v O v O V O 0 0 0 0 0 0 ?

> X • o r t h r t a : ^ H O I A o o U I " • f o « M P I C A r f t < a !- • U I U I

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1 ls > • jJ N V O O J K > K >0.4721

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K > H - O J J > U I

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a s a s s s s s a s o o o o o 1111 1 

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o o o o o vO s o s o V

O s o s O 0 0 S O V O - O o o o o o o

S O s o s o v O s o s o S O 0 0 0 0 s o s o v O o o o o o vO s o s o s o vO v O S O s O 0 0 - g o o o o o o s O s o s o s o v O s o S O s o s o 0 0 0 0 O 0 c f 0 0 f t - V

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### §

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e •* •f t c o to r t c a 1 C f " 1 C T I t C c o r t H - O O M s 9

PP O H b I t O Q 1 »*J> 1 r o I t O c o i- h 9 c o O f . 1 * n o 9

c o o oTABL E C. 8 (Cont'd )

i PbB

. Leve l "(yg/dL ) Expert 5 1 5 2 5 3 5 4 5 5 5 Exper t 1 5 2 5 3 5 4 5 5 5 Exper t 5 1 5 2 5 3 5 4 5 5 5 Expert 5 1 5 2 5 3 5 4 5 5 5 Expert 5 1 5 2 5 3 5 4 5 5 5 

### o,

G,

H,

H,

J, Functiona l For m IQ < 70 , NOL O NOL O NOL O NOL O NOL O NOL O IQ S 70 , NOL O NOL O NOL O NOL O NOL O IQ < 70 , NOL O NOL O NOL O NOL O NOL O NOL O IQ S 70 , NOL O NOL O NOL O NOL O NOL O NOL O IQ * 70 , NOL O NOL O NOL O NOL O NOL O NOL O Lo

w 13 T

Defining Parameter s

w y
SE S Leve l -5.412 3 -4.582 5 -3.820 1 -3.367 3 -2.882 3 -2.487 7 

### °

y

0.760 8 0.713 7 0.720 4 0.556 0 0.493 4 0.549 0 High SE S Leve l

Lo w -6.899 0 -6.307 2 -5.415 0 -4.916 4 -4.357 7 SE S Leve l -4.764 5 -4.218 6 -3.733 2 -3.039 2 -2.695 8 -2.393 0 0.738 9

0.718 9 0.742 1 0.653 0 0.602 4

0.770 6 0.779 6 0.778 9 0.729 2 0.640 6 0.584 4 High SE S Leve l

Lo w -7.107 5 -5.443 9 -4.747 1 -4.466 6 -4.178 8 -3.879 0 SE S Leve l -4.420 6 -3.920 7 -3.455 6 -2.862 7 -2.423 5 -2.062 5 0.794 7

0.786 0 0.634 8 0.579 5 0.529 0 0.507 1

0.665 2 0.608 7 0.571 8 0.452 8 0.407 6 0.377 9 Measure s o f

Distributio n EI*IQ ]

0. 6 1. 3 2. 7 3. 8 5. 8 8. 5

0. 1 0. 2 0. 6 0. 9 1. 5

1. 1 1. 9 3. 0 5. 6 7. 4 9. 4

0. 1 0. 6 1. 0 1. 3 1. 7 2. 3

1. 5 2. 3 3. 5 5. 8 8. 6 11. 7 SD[R IQ ]

0. 4 0. 9 1. 8 1. 9 2. 6 4. 1

0. 1 0. 2 0. 4 0. 6 0. 9

0. 8 1. 4 2. 2 3. 7 4. 1 4. 7

0. 1 0. 4 0. 6 0. 7 0. 9 1. 1

0. 9 1. 3 1. 9 2. 4 3. 1 3. 9 r 2 fo r

Regressio n o f F on F

0.9 4 0.9 5 0.9 7 0.9 8 0.9 9 0.9 8

0.9 6 0.9 7 0.9 8 0.9 8 0.9 9

0.9 7 0.9 7 0.9 8 0.9 8 0.9 8 0.9 8

0.9 7 0.9 8 0.9 9 0.9 9 0.9 9 0.9 9

0.9 6 0.9 7 0.9 8 0.9 9 0.9 9 0.9 9 . P.3 9

"•- ^P.4 0



### TABL E C. 8 (Cont'd

)

Pb B Leve l (yg/dL ) Expert J, 1 5 2 5 3 5 4 5 5 5 Expert K, 1 5 2 5 3 5 4 5 5 5 6 5 Expert K, 2 5 3 5 4 5 5 5 6 5 Functiona l

For m IQ < 70 , NOL O NOLO NOL O NOLO NOLO IQ S 70 , Norma l Norma l Norma l Norma l Norma l Norma l IQ S 70 , NOLO NOL O NOLO NOLO NOLO H

i Lg h

Lo w

H ] Lg h Definin

g Parameter s

y y 

### ° y
SE S Leve l -6.183 8 -5.521 6 -5.169 0 -4.721 2 -4.192 7 SE S Leve l 0.717 1

0.652 9 0.588 7 0.519 1 0.475 1

SE S Leve l -6.569 0 -6.026 8 -5.294 6 -4.945 9 -4.496 9 0.648 5

0.612 2 0.592 6 0.572 3 0.554 8 Measure s o f

Distributio

n EIRIQ I

0. 3 0. 5 0. 7 1. 0 1. 6

2. 4 5. 9 7. 7 14. 0 17. 5 24. 9

0. 2 0. 3 0. 6 0. 8 1. 3 SD[R IQ ]

0. 2 0. 3 0. 4 0. 5 0. 7

1. 0 2. 7 2. 9 4. 2 4. 9 6. 2

0. 1 0. 2 0. 3 0. 5 0. 7 r 2 fo

r Regressio

n 6'f F o n F

0.8 8 0.9 8 0.9 8 0.9 9 0.9 9

0.9 6 0.9 5 0.9 6 0.9 8 0.9 8 0.9 9

0.9 8 0.9 8 0.9 8 0.9 8 0.9 8



### Th e mai n poin t

o f th e tabl e i s t o show tha t th e fitte dfunction s matc h th e judgment s quit e well
. Th e fitte dmedia n value s ar e generall y quit e clos e t o th e assesse d median values
. The 50%

- an d90%-C I value s ar e als o quit e close
. Fo r example , Expert G * judge dth e media

n valu e fo r

th e mea n IQ leve l fo r

unexpose dchildre n i

n th e lo w SE

S categor y t o b e 9

4 (se e Tabl e C.l) , andth e media n o f th e fitte ddistributio n i s 94.6
. The encode dmedian s fo r

I Q decremen t

ar e 0.5 , 1.5 , 3.0 , 3.5 , 5.0 , and7. 0 fo r Pb B level s o

f 5 , 15 , 25 , 35 , 45 , an d5 5 yg/dL , respectively
. Th e respectiv e median s o f th e fitte d distribution s ar e 0.6 , 1.4 , 2.7 , 3.9 , 5.7 , and7.3
. Th e lower end s o f th e 50 % CI s (0.2 5 point s o n th 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 , and0.4 , 1 , 1.9 , 3 , 4.6 , and5. 9 for th e fitte dfunctions
. Th e uppe r

•Becaus e Expert

Fdi dno t

provid e judgment s a t

0.2 5 cumulativ e probabilit y for thre e o f th e fiv e Pb

B levels , th e followin g discussio n o f CI s i s base do

n Expert G' s judgments
.P.4 1

end s of th e 50 % CI s (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 dth e mea n I Q of childre n unexpose dt o lea dt o b e abou t 10 1 wit h a hig h .degre e o f

certainty , whic h i s indicate db y astandar ddeviatio n o f abou t 0.5
. Th e othe r expert s judge dth e mea n I Q o f th e unexpose dhig h SE S grou p t o b e thre e t o fiv e point s higher , bu t

wit h muc h les s certainty , whic h i s indicate db y standar ddeviation s that

- range dfro m1. 7 t o 2.8
. Exper t Fals o judge dmuc h smalle r I Q decrement s attributabl e t o lea dexposur e tha n di dth e othe r experts
. Tabl e C. 8 summarize s distribution s fo r populatio n respons e rate , i n percent , fo r th e occurrenc e of

I Q level s belo w 7 0 an d8 5 (i.e. , increase dpercentag e o f occurrenc e o f I Q level s belo w 7 0 o r

8 5 amon g childre n expose dt o lea dversu s thos e sheltere dfro m lead)
. Thi s tabl e i s identica l i n forma t t o earlie r

tables , an dentrie s wer e obtaine db y combinin g informatio n o n I Q , a , an dA—
. Th e tabulate dvalue s ar e fo r function s fi t t o intermediat e result s obtaine dthroug h th e step s outline di n Sec
. C.2
. Fo r Exper t F , smal l respons e rate s wer e calculate dfo r bot h o f thes e critica l I Q levels
. I n addition , norma l distribution s provide dth e bes t fit s a t bot h I Q levels
. Fo r

I Q = 85 , mea n respons e rate s range dfro m0.5 % a t Pb B = 2 5 yg/d L t o 4 % a t 6 5 yg/dL ; fo r

I Q = 70 , result s range dfro m0.1 % t o 1 % a t th e correspondin g Pb B levels
. Th e r value s fo r regression s of

intermediat e numerica l result s an dcorrespondin g fitte ddistribution s ar e hig h (th e smalles t

i s 0.95)
. Uncertaintie s i n thes e result s ar e small , evidence db y th e smal l (relativ e t o th e mea n values ) standar ddeviatio n values , an dexpecte dbecaus e of th e smal l degre e o f

uncertaint y expresse db y Exper t Ffo r I Q , o , an dA—
. Whil e th e judgment s o f th e expert s ar e interestin g i n an do f themselves , the y tak e o n adde dmeanin g whe n include di n ahealt h ris k assessment
. Thus , th e result s o f Sec
. 5 provid e furthe r

insigh t int o th e significanc e of th e difference s i n judgment s amon g th e experts
. C. 4 DISCUSSION SUMMARIES Th e followin g summarie s ar e base do n note s take n durin g th e interview s wit h th e experts
. A t

times , th e point s mad e ar e fragmentar y an dhighl y specialized
. Eac h exper t ha s ha da t

leas t on e opportunit y t o revie w hi s o r he r section
. C.4. 1 Exper tF

• Lo w Pb B level s (

< 30-4 0 yg/dL ) d o no t

hav e adiscernibl e deleteriou s effec t o n IQ
. Studie s tha t purpor t t o sho w suc h a n effec t hav e methodologica l an dbia s problems
.

• Althoug h lo w Pb B level s d o no t hav e independen t

effect s o n IQ , on e canno t rul e ou t

th e possibilit y tha t

lea da t highe r level s interact s wit h othe r

variable s t o affec t

IQ
. No r

ca n w e rul e ou t

completel y th e possibilit y tha t

I Q influence s Pb B level
. Relate dvariable sP.4 2 

### migh tinclude genera

l healt h status , menta

l healt h status , an

d othe r environmenta

l factors . Numerou s covariate s ar

e associate d wit

h lead exposure , man

y o f whic h ar e know n t o b e negativel y relate d t o IQ. I ti s difficul tt o us e regressio n techniques t o determin e whic h of th e variable s ar

e causative . Behavioral , social , an

d cognitiv e measures have some degre e of unreliability , whic

h add s uncertaint

y t o an y conclusions . Cor d Pb B ma y b e relate d t o afe w negativ e birt h outcomes , bu

t directio n o

f causalit y cannotb e inferred fro

m suc h data . Perhap s a distresse d fetu s accumulate s lead . Ther e i s afairl y strong correlatio n (abou t0.8 ) betwee n materna

l Pb B an d cor d PbB . Childre n ar e robus tan d ca n recove rfro

m mino rdisruptions i

n thei r cognitiv e development . I ti s notclea rt o wha

tdegre e the y can recove rfro

m largerdisruptions . Middle-clas s children , i n particular , ma

y be able t o compensate . Th e existenc e o

f athreshold leve l fo rth e effect s o f lea d o n I Q i s notindicate d b

y th e availabl e evidence . Th e assumption o

f norma l I Q distributions within exposur e groups i n th e hypothetical experimenti s reasonable , excep tthata thig h Pb B levels , th e I

Q distribution ma

y b e skewed negatively , s o thatth e percentag e o

f childre n below aspecifie d I Q leve l woul

d b e underestimated . C.4. 2 Exper

tG

• Ther e ar e n o dat at o sugges tthatth e physiologica l respons e t o lea d varie s as afunction o

f SE S level .

• Th e effect s o

f lead o n th e developin g CN

S ar e probabl y lon g lastin g an d irreversible .

• I f ther e i s athreshold forth e effect s o f lead o n IQ , i ti s ver y low .

• Anima l models forris

k assessmen thav

e limite d usefulnes s becaus e of th e difficult

y i n extrapolatin g t o human s i n aquantitativ e manner . Theirimportance i s i

n studying mechanisms o f lea d effect s an d topic s suc

h as th e reversibility of

effect s an

d vulnerabl e period s o f development , no

ti n establishin g dose-respons e relationship s that ar e directl y applicabl e to humans .TTF

• Specifi c neurobehaviora l effect s o f lead , suc h a s attentiona l deficits , shoul d no tb e overlooked .

• I ti s reasonabl e t o assum e normall y distribute d I Q score s withi n exposur e group s a s in th e hypothetica l experiment . C.4. 3 Exper tH

• Lead interact s with othe rfactor s t o affec tIQ . Such factor s includ e SES , materna l stimulation , an d nutrition .

• Th e concep to f

critica l developmenta l period s i s crucia l in understandin g th e effect s o f lea d on IQ . Whe

n opportunitie s fo r intellectua l developmen tar e lost , i ti s ver y har d t o compensat e fo r the m later . Thi s situatio n i s especiall y tru e in lo w SES children . Furthermore , th e effec tca n snowball , in tha tskill s generall y buil d on eac h other .

• Childre n expose d t o lea d als o ten d t o b e expose d t o cadmium , pesticides , etc . Thi s patter n i s especiall y tru e fo rlo w SE S children .

• N o dat aexis ton th e minimu m exposur e tim e necessar y t o produc e a n effect .

• A tagive n dos e level , th e cumulativ e effect s ar e wors e tha n th e immediat e effects . Exposure s earlie rin lif e hav e more effec ttha n thos e late ri

n life .

• Som e effect s o f

lea d ar e reversibl e an

d other s ar e not .

• Ra tstudie s hav e indicate d tha tth e half-lif e o f lea d in th e brai n i s ver y long .

• Som e recen tresearc h suggest s tha tlea d may b e involve d in senility . The amoun tof bon e lea d decrease s wit h age . I tmay b e eliminate d o rrecirculated . I n th e latte rcase , lea d may hav e neurobehaviora l effects .

• I ti s reasonabl e t o assum e tha tI Q i s normall y distribute d withi n exposur e group s a s in th e hypothetica l experiment .

• Importan tresearc h relate d t o behaviora l toxicolog y i s bein g conducted .P.4 4



### C.4. 4 Exper

tI The meta-analyse s occasionall y don e a s par t o f studie s o

n th e effect s o f lea do n I Q ar e inappropriat e becaus e th e studie s diffe r i n s o man y way s —differen t

age s o f th e subjects , differen t

sort s o f contro l groups , differen t methods , anddifferen t exposur e conditions
. It i s reasonabl y certai n tha t Pb B level s abov e 3 0 yg/d

L affec t IQ , bu t i t i s les s clea r

whethe r ther e i s a

n effec t a t lowe r levels
. Ther e i s a

n exposure-sensitivit y interaction , i n tha t childre n wh

o suffe r th e greates t

exposure t o lea dten dt o b e thos e wh o ar e mos t susceptibl e t o it s effects
. Excep t for high acut e exposures , neurobehaviora l effect s ar e more likel y t o resul t

fro mchroni c tha n fromacut e exposures . On e shoul ddistinguis h betwee n th e biological andfunctiona l effect s o f lead , bu t

i n eithe r cas e ther e ar e no dat asuggestin g tha t th e effect s ar e necessaril y irreversible
. Th e dat aar e no t

clea r o n whethe r

athreshol dexist s fo r

th e effect s o f lea do n IQ
. C.4. 5 Expert

J

• Leaddoe s hav e adeleteriou s effec t on neurobehaviora l development
. I

n thi s regard , lea dinteract s wit h die t an dSE S factors
.

• Middle-clas s childre n ar e somewhat buffere dagains t

th e negativ e effect s o f lea db y virtu e o

f thei r bette r diet , higher

genera l healt h status , andriche r

intellectua l resources .

• Lea dcrosse s th e blood-brai n barrier
. Onc e i n brai n cells , i t

stay s ther e andaffect s th e neurotransmitters
. I t canno t b e chelate d out
. Th e effect s ar e irreversible
.

• Researc h wit

h animal s suggest s tha t

lea dcause s demyelination , bu t i t i s no t clea r whethe r thi s effec t

occur s i n children
.

• The implication s o

f th e EE G dat aar e no t

clear
. Th e finding s ar e somewhat inconsistent , an di t

i s no t know n what th e measure s refe r to
.P.4 5 Althoug h som e functiona l effect s o f lea dma y b e reversible , morphologica l effect s ar e not
. Ther e i s probabl y n o threshol dfo r th e effect s o f

lead ; if ther e i s one , i t i s ver y low
. Studie s o n primate s sugges t th e absenc e o f

a threshold
. Th e possibilit y of

racia l difference s i n term s of th e effect s o f

lea d i s aver y complicate dissu e tha t remain s t o b e untangled
. Th e assumptio n tha t

I Q score s ar e normall y distribute dwithi n exposur e group s i n th e hypothetica l experimen t i s reasonable , wit h th e possibl e exceptio n of th e 55-yg/d L group . C.4. 6 Exper tK

• Childre n o f

al l genotype s ar e vulnerabl e t o th e effect s o f lead
.

• Som e neurobehaviora l effect s of lead , suc h a s th e effec t o n attentio n span , ar e reversible
. Thes e effect s ar e generall y associate dwit h lo w level s of exposure . Eve n som e perinata l effect s ca n b e reverse dwit h prope r treatment
.

• Othe r neurobehaviora l effect s ar e irreversible , includin g morphologica l change s an dth e effect s o n som e behavior s tha t depen do n critica l developmenta l periods
.

• Blood-lea dlevel s of 5-5 5 yg/d L hav e adeleteriou s effec t o n I Q i n th e presenc e of

othe r factors
. However , th e interactio n o f lea d wit h othe r

factor s i s onl y i n on e direction , s o tha t amultivariat e analysi s of

varianc e woul dsho w bot h a n interactio n an damai n effect
.

• Som e of

th e factor s tha t

lea dinteract s wit h ar e physica l an d psychologica l hygiene , physiologica l status , parenta l IQ , nutritiona l an dhealt h status , organophosphates , an dpesticides
.

• Early , long-ter mexposur e t o lea dca n lea dt o long-ter meffects ; episodi 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
.

• A threshol dexist s fo r th e effect s o f

lea do n IQ
.

• Th e assumptio n tha t I Q score s ar e normall y distribute dwithi n exposur e group s i n th e hypothetica l experimen t i s reasonable
.^^^p^^^^F^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^w^wrv^^^r^^^^^^^^^^^^^^^^^^^^^-T^ i

APPENDIX D RIS KDISTRIBUTIONS14 3 APPENDI

X D RIS KDISTRIBUTIONS
Th e dose-respons e function s fo r th e differen t

healt h effect s wer e combine dwit h specifie dPb B distribution s t o estimat e ris k distributions
. Th e Pb B distributions , whic h ar e assume dt o b e lognorma l wit h aGS D o f 1.4 2 yg/dL , hav e on e o f 1 1 G M value s tha t increas e in step s of

2. 5 yg/d L fro m2. 5 yg/d L t o 27. 5 yg/dL
. Sectio n D. l describe s th e metho duse dt o combin e th e Pb B distribution s an ddose-respons e function s t o obtai n ris k distributions
. Th e nex t thre e section s presen t th e resultin g ris k

distribution s fo r

lead

induce dEP , Hb , an dI Q healt h effects , respectively
. Thes e las t

thre e section s consis t

mainl y of

table s tha t

lis t fractile s (i.e. , selecte d cumulativ e probabilit y levels) , means , an dstandar ddeviation s o f ris k distribution s fo r th e lead-induce dEP , Hb , an dI Q healt h effect s considere di n thi s report
. Detail s concernin g th e forma t

of th e table s ar e explaine di n th e text
. Th e tabula r materia l provide s th e dat apoint s fo r Figs
. 21-2 4 i n Sec
. 5 an dfo r additiona l analysis
. D. l METHO

D FORCOMBININ

G PbB DISTRIBUTIONS WIT H DOSE-RESPONS E FUNCTION S TO CALCULATE RIS KDISTRIBUTIONS Th e metho duse dt o combin e aPb B distributio n wit h ase t o f dose-respons e function s t o calculat e ris k estimate s i s relativel y simpl e bu t certai n feature s nee d explanation
. First , i n calculatin g ase t of Pb B probabilities , th e populatio n Pb B level s ar e assume dt o b e lognormall y distributed , wit h specifie dG M an dGS D values
. Thus , fo r give n G M an dGS D values , th e fractio n Fof apopulatio n havin g Pb B level s < L i s give n b y F(L ) = •~ 1 [ln(L/GM)/ln(GSD) ]

an dth e fractio n Fhavin g Pb B level s i n th e interva l Lj t o L 2 i s give n b y F(L , < L < L 2 > - F(L 2 ) - F(L X ) wher e • denote s th e invers e of th e CD Ffo r

th e standardize dnorma l distribution
. Fo r example , if

G M = 1 5 yg/dL ; GS D = 1.4 2 yg/dL ; an dth e Pb B interval s ar e 0-10 , 10-20 , 30-40 , 40-50 , an d50-6 0 yg/d L (designate db y thei r midpoint s 5 , ... , 5 5 yg/dL ; the n th e cumulativ e probabilitie s ar e 0.12 , 0.79 , 0.98 , 0.99 , 1 , an d1
. Th e correspondin g fractions , whic h ar e probabilities , ar e 0.12 , 0.67 , 0.19 , 0.01 , 0.01 , an d0 fo r th e si x intervals
. Thes e Pb B probabilitie s ar e denote da s p p ... , pg . T o calculat e th e media n overal l respons e rat e fo r aspecifi c se t

o f dose-respons e functions , th e media n respons e rat e a t eac h Pb B leve l i s multiplie db y th e correspondin gP.4 8



### Pb B probabilit

y an d the n summe d acros s th e Pb

B levels . Mathematically , thi s ste p ca n b e writte n a

s

R 

### 0. 5 = 

### X

P 

### i R 

### 0.5, i f0 r i=1 

### ' i= l wher e R g 5 denote s th e media

n valu e of

th e overal l respons e rate , an d RQ ^ J denote s th e media n respons e rate atPb

B leve l i . Fo

rexample , th e media

n respons e rate s o

f the function s fi tto th e judgment s o f H b Exper tE forchildren aged 0- 3 atH b leve l < 9. 5 g/d

L ar e 1.5% , 2.4% , 3.4% , 5% , 11% , an d 13% (se e Table B.4) . Applyin g th e las tformula yield s 2.5 % forth e media n respons e rate base

d o n the judgment

s o f Exper tE an d a lognorma l Pb B distribution wit

h G M = 15 yg/d

L an d GS D = 1.4 2 yg/dL . I

n asimila r fashion , th e respons e rate a tan y cumulativ e probabilit

y leve l ca

n b e calculated . Agai

n fo rExper tE , th e respons e rate s a t0.9 5 cumulativ e probabilit y are 6%, 9% , 12% , 16% , 32% , an d 36% , wit

h amedia

n respons e rate o

f 9.2% . Atth e 0.05 probabilit y level , the resul ti s 0.2% . Thus , th e 90 % C I i s 0.2-9.2% . Repeate d applicatio n o f th e formulaa

t selecte d cumulative probabilities define s aCD F forthe overall respons e rate . Th e abov e calculation s assume thatth e dose-respons e distribution s fo raspecifi c experta tthe differentPb

B level s ar

e perfectl y an

d positivel y correlated . Fo rexample , i f children wit

h Pb B leve l L

j have arespons e rate corresponding t o cumulativ e probabilit y 0.95 , the

n the response rate s atall othe rPb B level s will correspond t o th e 0.95 cumulativ e probabilities . Thus , continuin g th e exampl e wit h th e judgment

s o f Exper tE , i f th e response rat

e forchildren havin

g aPb B leve l o f 5 yg/dL i s assumed to b e 6% , the n th e response rate s a

tth e othe rPb

B level s ar

e assume d t o be 9%, 12% , 16% , 32% , an d 36 % (forPb B level s o f 15 , ... , 5 5 yg/dL , respectively) . Th e independenc

e assumption ma

y notb e exactl y correct ; however , t o have explored th e matte ri

n an y detai l woul

d hav e required mor

e tim e wit

h eac h exper ttha

n wa s available . Assessmento f a tleas t5-1 0 conditional probabilit y distribution s fo rall bu ton e o f th e Pb B level s woul

d hav e bee n required . Fo

rthatleve l o

f effort , th e likel y resul twoul

d b e afamily o

f distributions havin

g ahig h degre e o

f dependenc

y an d one that closel y approximated th e se to f singl e distributions , one a teach Pb B level . Th e appropriatenes s o

f the approac

h ca n b e furtherargue

d as follows . I

f prob abilit y distributions ha

d bee n encoded atman

y mor e Pb B level s (sa

y atevery 0. 1 yg/dL instead o f atevery 1

0 yg/dL) , the

n th e adjacentcurve s woul d have bee

n ver y close . Fo

r example , th e curve at10. 6 yg/d L woul d hav e been shifte d alittl e t o th e righto f th e curve a t10.5 yg/dL . Th

e metho d woul d certainl y hav

e bee n mor e accurate bu

tno t necessaril y mor

e convincing . Considering amaximu m of si x curve s mean

s tha tth e method i s les s accurate tha n itmigh thav e been . However , w

e argue , withoutproof

, that six curve s ar

e sufficientl y accurate fo rou rpurpose . Th

e sensitivit y analysi s describe d i n Sec . 5. 5 support

s thi s belief

.

### T W

D. 2 ESTIMATE

S O F RISK S O F LEAD-INDUCE

D E PEFFECT

S AMON G U.S . CHILDRE

N AGE D 0- 6 Probabilisti c dose-respons e function s for tw o E P level s considere dt o b e advers e ( > 3 3 yg/d L and> 5 3 yg/dL ) wer

e considere di n Sec
. 2 an dApp
. A
. Response-rat e probability distribution s fo r population s o

f childre n wer e estimate dby combinin g th e dose-respons e function s for particula r

Pb B level s wit

h Pb B distribution s i

n th e manner describe di

n Sec
. D.l
. The result s for E P ar e liste di

n Tabl e D.l
. Entrie s i

n th e tabl e ar e respons e rate s for

th e occurrenc e o

f E P level s abov e on e o

f tw o ris k level s amon g U.S
. childre n aged 0-6 . Ther e i s acolum n o f number s for

eac h o f th e 1 1 G M Pb B level s con sidere di n thi s analysis
. The firs t fiv e number s i

n eac h colum

n ar e th e 0.05 , 0.25 , 0.50 , 0.75 , and0.9 5 fractile s (cumulativ e probabilities ) o f th e resultan t

ris k distribution
. Th

e nex t tw o number s ar e th e mea n andstandar ddeviation
. Fo r example , fo r

E P > 5 3 yg/d

L andG M = 1 5 yg/dL , th e fractile s ar e 4.1% , 4.9% , 5.5% , 6.0% , and6.8% , th e mea n i s 5.5% , an dth e standar ddeviatio n i s 0.8%
. The 0. 5 fractil e i s th e median , th e 0.2 5 an d 0.7 5 fractile s defin e th e 50% CI , andth e 0.0 5 and0.9 5 fractile s defin e th e 90 % CI
. A t lo w G M Pb B levels , th e ris k

distributions converg e o n th e response-rat e probability distributio n fo r th e lowes t

Pb B leve l considere d(2-1 7 yg/dL ) (se e Tabl e A.l)
. Thus , th e tabulate dris k

distribution s for

G M = 2.5-5. 0 yg/d

L ar e normal , with mea

n 2.4 %
TABL E D. l Ris

k Estimate s fo rLead-Induce d Elevate d E

PLevels , U.S . Childre

n Aged 0- 6

Fractiles , Mean , an

d Standar d Deviatio n
EP > 5 3 vg/dL 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 2. 5

1. 5 2. 0 2. 4 2. 8 3. 3 2. 4 0. 5 Respons e 5. 0

1. 5 2. 0 2. 4 2. 8 3. 3 2. 4 0. 5 7. 5

1. 6 2. 1 2. 4 2. 8 3. 3 2. 4 0. 5 Rat e (Z ) 10. 0

1. 8 2. 3 2. 7 3. 1 3. 6 2. 7 0. 6 a t Ceometri c 12. 5

2. 5 3. 2 3. 6 4. 0 4. 7 3. 6 0. 7 15. 0

4. 1 4. 9 5. 5 6. 0 6. 8 5. 5 0. 8 Mea nPb

B Leve l 17. 5

6. 7 7. 8 8. 5 9. 2 10. 3 8. 5 1. 1 20. 0

10. 4 11. 8 12. 7 13. 6 14. 9 12. 7 1. 4 inu

g 22. 5

15. 0 16. 7 17. 9 19. 0 20. 6 17. 9 1. 7 /d L 25. 0

20. 3 22. 5 23. 9 25. 2 27. 1 23. 8 2. 1 27. 5

26. 2 28. 7 30. 4 32. 0 34. 1 30. 3 2. 4
EP > 3 3 ug/dL 0.0 5 0.2 5 0.5 0 • 0.7 5 0.9 5 Mea n S D 8. 9

10. 0 10. 7 11. 4 12. 5 10. 7 1. 1 8. 9 10. 0 10. 7 11. 4 12. 5 10. 7 1. 1 9. 0 10. 1 10. 8 11. 5 12. 6 10. 8 1. 1 9. 5 10. 6 11. 4 12. 1 13. 2 11. 4 1. 1 11. 3 12. 4 13. 3 14. 1 15. 3 13. 3 1. 2 14. 5 15. 9 16. 8 17. 8 19. 1 16. 8 1. 4 19. 3 20. 8 21. 9 23. 0 24. 5 21. 9 1. 6 25. 1 26. 9 28. 1 29. 4 31. 1 28. 1 1. 8 31. 6 33. 6 35. 0 36. 4 38. 2 35. 0 2. 0 38. 3 40. 6 42. 1 43. 6 45. 6 42. 1 2. 2 44. 9 47. 5 49. 1 50. 7 52. 7 49. 0 2. 4P.5 0

an dS D = 0.5%
. A s G M increases , dose-respons e function s fo r Pb B level s abov e th e threshol d(16. 5 yg/dL ) begi n t o influenc e th e ris k calculations
.
D. 3 ESTIMATE

S O F RISK

S O F LEAD-INDUCE D H b EFFECT S AMON

G U.S . CHILDRE

N AGE D 0- 3 Th e calculatio n o f

ris k estimate s fo r

lead-induce dH b effect s i s almos t identica l t o tha t fo r E P effects
. Th e onl y differenc e i s tha t norma l an dbet adistribution s wer e use dt o represen t

uncertaint y abou t

th e E P dose-respons e functions , wherea s NOLO distribution s wer e use dfo r th e H b functions
. Th e NOL O distribution s bes t represente d th e judgment s o f

th e expert s consulted
. Tabl e D. 2 present s th e ris k estimate s fo r

th e occurrenc e o f

Hb level s belo w on e o f tw o critica l levels
. Th e forma t i s th e sam e a s tha t i n Tabl e D.l , excep t

tha t th e result s fo r

individua l expert s ar e listed
. Recal l tha t

Exper t A judge dtha t

lea dexposur e woul dno t caus e H b level s t o b e < 9. 5 g/d L (se e Fig
. 22) , s o n o result s ar e liste dfo r tha t leve l fo r

Exper t A
. Exper t

B di d no t provid e an y probabilisti c judgments , s o n o ris k result s coul db e calculated
. Exper t C provide djudgment s fo r childre n age d0-6 , explainin g tha t th e difference s betwee n childre n age d0- 3 an d4- 6 wer e smal l an dhar dt o distinguish
. H e agree dtha t hi s judgment s coul db e use dfo r bot h ag e categories
. Expert s D an dE provide djudgment s fo r al l fou r age-H b combinations
. A s wa s tru e fo r

EP , th e ris k

distribution s converg e o n th e response-rat e probabilit y distributio n fo r Pb B = 5 yg/d L a t

lo w G M Pb B values
. Thus , th e Exper t C ris k distribution s a t

G M = 2. 5 yg/d L an d5. 0 yg/d L ar e NOL O distribute dwit h amea n respons e rat e o f

1.9% , an S D o f

0.5% , an dau v o f

- 4 an dao v o f

0.2 8 (se e Tabl e B.3)
. I f desired , th e distribution s conditiona l o n ag e ca n b e combine dt o produc e furthe r ris k distributions
. Tha t

aeross-ag e calculatio n woul db e simpl e t o perfor mi f th e relativ e proportio n o f

childre n i n th e tw o ag e group s wer e specified
. However , tha t proportio n i s sit e specifi c an dwa s no t considere di n thi s analysis
. D. 4 ESTIMATES O F RISK S O F LEAD-INDUCE D I Q EFFECT S AMON

G U.S . CHILDRE N AGE

D 7 Tw o I Q healt h effect s wer e considered : I Q decremen t an dth e increase d probabilit y (expresse da s arespons e rat e i n percent ) o f havin g I Q value s les s tha n a specifie dcritica l leve l IQ*
. Calculation s o f th e ris k o f I Q decrement s ar e quit e simpl e an dsimila r

t o thos e fo r

E P an dHb
. Th e calculate dris k distribution s followe ddirectl y fro mth e encode djudgment s o f th e expert s regardin g I Q decrement
. Calculatin g ris k

distribution s o f

th e secon dtyp e i s mor e complicate dan d include s th e uncertaintie s i n mea n I Q o f population s o f

childre n sheltere dfro mlea d exposure , within-grou p standar ddeviation , an dI Q decrement s amon g childre n expose dt o lead
. Th e probabilisti c judgment s o f expert s regardin g thes e quantitie s wer e obtaine dfo r bot h lo w an dhig h SE S populations
. Th e spiri t o f th e calculatio n i s a s follows
.P.5 1 

### 14 7 TABL E D. 2 Ris

k Estimate s fo rH

b Level s < 9. 5 an

d < 1 1 g/dL , U.S . Childre n Aged 0- 3 an d 4- 6

Fractile s Mean , an d Standar d Deviatio n Expert C, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert D, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD Expert E, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert C, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD >

Hb

Hb

Hb

Hb 2. 5

< 9. 5 1. 1 1. 5 1. 8 2. 2 2. 8 1. 8 0. 5

< 9. 5 0 0 0 0 0 0 0

< 9. 5 0. 5 1. 2 2. 2 4. 2 10. 0 3. 3 3. 3

< 9. 5 1. 1 1. 5 1. 8 2. 2 2. 8 1. 9 0. 5 R

e 5. 0 9/dL, 1. 2 1. 5 1. 8 2. 2 2. 9 1. 8 0. 5 9/dL, 0 0 0 0

. 0 0 0 9/dL, 0. 5 1. 2 2. 3 4. 3 10. 3 3. 5 3. 4 9/dL, 1. 2 1. 5 1. 8 2. 2 2. 9 1. 9 0. 5 spons e Rat e (Z )

7. 5 Ages 0-3 1. 3 1. 7 2. 1 2. 5 3. 2 2. 1 0. 6 Ages 0-3 0. 1 0. 2 0. 2 0. 3 0. 4 0. 2 0. 1 Ages 0-3 0. 6 1. 6 3. 0 5. 5 12. 6 4. 3 4. 1 Ages 4-6 1. 3 1. 7 2. 1 2. 5 3. 2 2. 1 0. 6 10. 0

1. 6 2. 1 2. 5 3. 0 3. 8 2. 6 0. 7

0. 3 0. 4 0. 5 0. 7 1. 0 0. 6 0. 2

0. 9 2. 2 4. 0 7. 4 16. 5 5. 8 5. 3

1. 6 2. 1 2. 5 3. 0 3. 8 2. 6 0. 7 a t Geometri c 12. 5

1. 8 2. 4 2. 9 3. 4 4. 4 3. 0 0. 8

0. 5 0. 7 0. 9 1. 1 1. 6 0. 9 0. 3

1. 1 2. 7 5. 0 9. 1 20. 1 7. 1 6. 4

1. 8 2. 4 2. 9 3. 4 4. 4 3. 0 0. 8 15. 0

2. 0 2. 7 3. 2 3. 8 4. 9 3. 3 0. 9

0. 7 1. 0 1. 2 1. 6 2. 2 1. 3 0. 5

1. 3 3. 2 5. 8 10. 6 22. 8 8. 1 7. 2

2. 0 2. 7 3. 2 3. 8 4. 9 3. 3 0. 9 Mea nPb B Leve l 17. 5

2. 2 2. 9 3. 5 4. 1 5. 4 3. 6 1. 0

1. 0 1. 4 1. 7 2. 2 3. 0 1. 8 0. 6

1. 4 3. 6 6. 6 11. 8 25. 1 9. 1 7. 8

2. 2 2. 9 3. 5 4. 1 5. 4 3. 6 1. 0 20. 0

2. 4 3. 1 3. 7 4. 5 5. 8 3. 9 1. 0

1. 4 1. 9 2. 4 3. 0 4. 1 2. 5 0. 8

1. 6 4. 0 7. 4 13. 1 27. 3 10. 0 8. 4

2. 4 3. 1 3. 7 4. 5 5. 8 3. 9 1. 0 in U R 22. 5

2. 6 3. 4 4. 0 4. 8 6. 2 4. 2 1. 1

1. 8 2. 6 3. 2 4. 0 5. 4 3. 4 1. 1

1. 8 4. 5 8. 2 14. 5 29. 5 11. 0 9. 0

2. 6 3. 4 4. 0 4. 8 6. 2 4. 2 1. 1 /d L

• 25. 0

2. 8 3. 6 4. 3 5. 1 6. 6 4. 4 1. 2

2. 4 3. 4 4. 2 5. 2 7. 0 4. 4 1. 4

2. 1 5. 0 9. 1 15. 9 31. 8 12. 0 9. 6

2. 8 3. 6 4. 3 5. 1 6. 6 4. 4 1. 2 27. 5

2. 9 3. 8 4. 5 5. 4 7. 0 4. 7 i. 2

3. 1 4. 3 5. 3 6. : . 8.f e 5. 5 1. 8

2. 3 5. 6 10. 1 17. 4 34. 1 13, 1 10. 2

2. 9 3. 8 4. 5 5. 4 7. 0 4. 7 1. 2P.5 2

TABL E D. 2 (Cont'd )

Fractiles , Mean , an

d Standar d Deviatio n Expert D, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n S D
Expert E, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Hb

Hb 2. 5

< 9. 5 0 0 0 0 0 0 0

< 9. 5 0. 4 0. 9 1. 5 2. 6 5. 7 2. 1 1. 8 Respons e 5. 0 g/dL, 0 0 0 0 0 0 0 g/dL, 0. 4 0. 9 1. 6 2. 7 5. 8 2. 1 1. 8 7. 5 Ages 4- 0 0 0 0 0 0 0 Ages 4- 0. 5 1. 0 1. 7 3. 0 6. 3 2. 3 2. 0 Rat e

6

6 10 .

0 0 0 0 0 0 0

0 . 1 . 2 . 3 . 7 . 2 2 (Z ) 0

5 2 0 5 3 7 3 a t Geometri c 12. 5

0 0 0 0. 1 0. 1 0. 1 0

0. 6 1. 3 2. 3 3. 9 8. 3 3. 1 2. 6 15. 0

0. 1 0. 1 0. 1 0. 2 0. 3 0. 2 0. 1

0. 7 1. 5 2. 6 4. 4 9. 3 3. 5 2. 9 Mea n Pb

B Leve l 17. 5

0. 2 0. 3 0. 4 0. 5 0. 7 0. 4 0. 2

0. 8 1. 7 2. 9 4. 9 10. 2 3. 8 3. 2 20. 0

0. 5 0. 6 0. 7 0. 9 1. 2 0. 8 0. 2

0. 9 1. 9 3. 2 5. 5 11. 3 4. 3 3. 5 i n ug/d L 22. 5

0. 8 1. 0 1. 2 1. 4 1. 9 1. 2 0. 4

1. 0 2. 1 3. 6 6. 1 12. 5 4. 8 3. 8 25. 0

1. 2 1. 5 1. 8 2. 1 2. 7 1. 8 0. 5

1. 1 2. 4 4. 1 6. 9 13. 9 5. 4 4. 2 . 27. 5

1. 7 2. 1 2. 4 2. 8 3. 6 2. 5 0. 6

1. 3 2. 8 4. 7 7. 8 15. 5 6. 1 4. 7 Expert A, Hb < 11 g/dL, Ages 0-3 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0. 1 0. 1 0. 2 0. 1 0. 1 0. 1 0. 2 0. 3 0. 5 0. 9 0. 4 0. 3 0. 3 0. 5 0. 8 1. 2 2. 1 0. 9 0. 6 0. 5 0. 9 1. 4 2. 1 3. 8 1. 6 1. 1 0. 7 1. 3 2. 1 3. 2 5. 8 2. 5 1. 6 1. 0 1. 8 2. 9 4. 4 7. 8 3. 4 2. 2 1. 3 2. 4 3. 7 5. 6 10. 0 4. 4 2. 8 1. 6 3. 0 4. 6 6. 9 12. 1 5. 4 3. 4 Expert C, Hb < 11 g/dL, Ages 0-3 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD 1. 6

2. 1 2. 5 2. 9 3. 8 2. 5 0. 7 1. 7 2. 2 2. 6 3. 1 4. 0 2. 7 0. 7 2. 5 3. 3 3. 9 4. 6 5. 9 4. 0 1. 0 3. 9 5. 0 6. 0 7. 0 8. 9 6. 1 1. 5 5. 1 6. 5 7. 7 9. 1 11. 5 8. 0 2. 0 6. 0 7. 6 9. 0 10. 6 13. 4 9. 3 2. 3 6. 6 8. 5 10. 0 11. 7 14. 7 10. 2 2. 5 7. 2 9. 2 10. 8 12. 7 15. 9 11. 1 2. 6 7. 8 10. 0 11. 7 13. 7 17. 1 12. 0 2. 8 8. 5 10. 8 12. 6 14. 8 18. 4 12. 9 3. 0 9. 2 11. 6 13. 6 15. 9 19. 7 13. 9 3. 2TABL

E D. 2 (Cont'd ) i.HS Fractile s Mean , an

d Standar d Deviatio n Expert D, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n S D Expert E, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert A, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert C, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD >

Hb

Hb

Hb

Hb 2. 5

< 11 1. 8 2. 9 4. 0 5. 5 8. 6 4. 5 2. 1

< 11 3. 5 6. 0 8. 7 12. 5 20. 4 9. 9 5. 3

< 11 0 0 0 0 0 0 0

< 11 1. 6 2. 1 2. 5 2. 9 3. 8 2. 5 0. 7 Re : 5. 0 spons e Rat e (Z ) 7. 5 g/dL, Ages 0-3 1. 9 3. 0 4. 1 5. 6 8. 7 4. 5 2. 2 2. 1 3. 3 4. 5 6. 1 9. 5 5. 0 2. 4 g/dL, Ages 0-3 3. 5 6. 0 8. 8 12. 6 20. 5 10. 0 5. 4 3. 6 6. 3 9. 2 13. 1 21. 3 10. 4 5. 5 g/dL, Ages 4-6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g/dL, Ages 4- 6 1. 7 2. 2 2. 6 3. 1 4. 0 2. 7 0. 7 2. 5 3. 3 3. 9 4. 6 5. 9 4. 0 1. 0 10. 0

2. 5 3. 9 5. 3 7. 3 11. 2 5. 9 2. 7

3. 9 6. 8 9. 8 14. 0 22. 5 11. 1 5. 9

0 0 0 0 0 0 0

3. 9 5. 0 6. 0 7. 0 8. 9 6. 1 1. 5 at Geometri c 12. 5

3. 0 4. 7 6. 5 8. 7 13. 3 7. 1 3. 2

4. 2 7. 2 10. 4 14. 9 23. 8 11. 7 6. 1

0 0 0 0 0 0 0

5. 1 6. 5 7. 7 9. 1 11. 5 8. 0 2. 0 15. 0

3. 7 5. 8 7. 8 10. 5 15. 7 8. 5 3. 8

4. 4 7. 6 11. 0 15. 6 24. 8 12. 4 6. 4

0 0 0 0 0 0 0

6. 0 7. 6 9. 0 10. 6 13. 4 9. 3 2. 3 Mea n Pb

B Leve l 17. 5

4. 5 7. 0 9. 4 12. 6 18. 5 10. 2 4. 4

4. 7 8. 1 11. 6 16. 4 25. 9 13. 0 6. 6

0 0 0 0 0 0 0

6. 6 8. 5 10. 0 11. 7 14. 7 10. 2 2. 5 20. 0

5. 4 8. 3 11. 1 14. 7 21. 4 12. 0 5. 0

5. 0 8. 5 12. 3 17. 3 27. 1 13. 7 6. 9

0 0 0 0 0 0 0

7. 2 9. 2 10. 8 12. 7 15. 9 11. 1 2. 6 in p

g 22. 5

6. 2 9. 6 12. 8 16. 8 24. 2 13. 7 5. 5

5. 3 9. 1 13. 0 18. 2 28. 4 14. 4 7. 2

0 0 0 0 0. 1 0 0

7. 8 10. 0 11. 7 13. 7 17. 1 12. 0 2. 8 /d L 25. 0

7. 0 10. 8 14. 3 18. 8 26. 7 15. 3 6. 1

5. 7 9. 7 13. 8 19. 3 29. 8 15. 3 7. 5

0 0 0. 1 0. 1 0. 2 0. 1 0

8. 5 10. 8 12. 6 14. 8 18. 4 12. 9 3. 0 27. 5

7. 8 12. 0 15. 8 20. 6 29. 1 16. 8 6. 5

6. 1 10. 4 14. 8 20. 5 31. 3 16. 2 7. 8

0 0. 1 0. 1 0. 2 0. 3 0. 1 0. 1

9. 2 11. 6 13. 6 15. 9 19. 7 13. 9 3. 2P.5 4

TABL E D. 2 (Cont'd )

Fractiles , Mean , an

d Standar d Deviatio n Expert D, Hb 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mean S D Expert E, Hb 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 2. 5

< 11 0. 9 1. 5 2. 0 2. 8 4. 4 2. 3 1. 1

< 11 2. 1 3. 7 5. 4 7. 9 13. 2 6. 3 3. 5 R

e 5. 0 spons e Rat e (Z ) 7. 5 g/dL, Ages 4-6 0. 9 1. 5 2. 1 2. 8 4. 5 2. 3 1. 1 1. 0 1. 6 2. 2 3. 1 4. 8 2. 5 1. 2 g/dL, Ages 4-6 2. 1 3. 7 5. 5 7. 9 13. 3 6. 3 3. 5 2. 2 3. 9 5. 7 8. 3 13. 8 6. 6 3. 7 10. 0

1. 2 1. 9 2. 6 3. 6 5. 5 2. 9 1. 3

2. 4 4. 2 6. 1 8. 9 14. 7 7. 0 3. 9 a t Geometri c 12. 5

1. 6 2. 4 3. 1 4. 2 6. 2 3. 4 1. 4

2. 6 4. 6 6. 7 9. 6 15. 8 7. 6 4. 2 15. 0

2. 2 3. 1 3. 9 4. 9 6. 9 4. 1 1. 5

2. 9 5. 0 7. 2 10. 4 17. 0 8. 2 4. 5 Mean Pb

B Leve l 17. 5

3. 0 3. 9 4. 7 5. 7 7. 7 4. 9 1. 5

3. 2 5. 4 7. 9 11. 3 18. 4 9. 0 4. 8 20. 0

3. 8 4. 7 5. 5 6. 6 8. 5 5. 7 1. 4

3. 5 6. 0 8. 6 12. 3 19. 8 9. 7 5. 1 i n u

g 22. 5

4. 5 5. 5 6. 4 7. 4 9. 2 6. 6 1. 4

3. 8 6. 5 9. 3 13. 2 21. 2 10. 5 5. 5 /d L 25. 0

5. 2 6. 3 7. 1 8. 2 9. 9 7. 3 1. 4

4. 1 7. 0 10. 0 14. 2 22. 6 11. 3 5. 8 27. 5

5. 8 6. 9 7. 8 8. 9 10. 6 8. 0 1. 5

4. 4 7. 5 10. 8 15. 2 23. 9 12. 0 6. 1

Th e numerica l method s describe di n Sec
. C. 2 wer e use dt o obtai n I Q dose

respons e functions
. Th e firs t ste p wa s t o chang e eac h CD Ffo r I Q , OJQ , an dATT

T int o a discret e PM Fwit h areasonabl e numbe r o f points
. Fo r

ever y combinatio n o f th e abov e thre e variables , adistributio n fo r th e increase dprobabilit y o f havin g I Q value s les s tha n o r equa l t o IQ * wa s calculate da t eac h Pb B leve l fo r

whic h I Q decremen t

judgment s ha d bee n obtained
. T o facilitat e furthe r calculations , distributio n function s (eithe r norma l o r NOLO ) wer e fi t

t o th e results , whic h wer e dose-respons e distribution s conditiona l o n Pb B level
. A t

thi s point , th e calculation s becam e quit e simila r t o thos e fo r

EP , Hb , an dmea n I Q decrement
. Thes e distribution s wer e combine dwit h Pb B distribution s usin g th e metho ddescribe din Sec
. D. l t o produc e ris k distribution s fo r

th e tw o SE S groups . Table s D. 3 an dD.4 , respectively , presen t fo r eac h I Q exper t

consulte dth e ris k distribution s fo r

mea n I Q decremen t

an dincrease dprobabilit y o f childre n havin g I Q level s < 7 0 an d< 85
. Tabl e D. 3 ha s tw o mai n sections , on e eac h fo r lo w an dhig h SE S children , whil e Tabl e D. 4 ha s fou r sections , on e fo r

eac h combinatio n o f

IQ * (7 0 o r

85 ) an dSE S leve l (lo w o r

high)
. I f desired , th e distribution s conditiona l o n SE S ca n b e combine dacros s SE S level s t o produc e furthe r

ris k distributions
. Th e across-SE S calculatio n woul db e simpl e t o perfor mi

f th e relativ e proportio n of lo w an dhig h SE S childre n wer e specified
. However , tha t proportio n i s sit e specifi c an dwa s no t considere di n thi s analysis
.^ ^ ^



### TABL E D. 3 Ris

k Estimate s fo rI

Q Decrement , U.S . Childre n Aged 7

Fractiles , ' Mean , an

d Standar d Deviatio

n Expert F, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 2. 5
Low SES 0 0 0 0 0 0 0 5 .

0 0 0 0 0 0 0 R e 0 spons e 7. 5

0 0 0 0 0 0 0 Rat e 10. 0

0 0 0 0 0 0 0 (Z ) a

t 12. 5

0 0 0 0 0. 1 0 0 Geometri c 15. 0

0 0 0. 1 0. 1 0. 1 0. 1 0 Mean 17. 5

0 0. 1 0. 1 0. 1 0. 2 0. 1 0. 1 Pb B Leve l i

n 20. 0

0. 1 O. i 0. 2 0. 2 0. 4 0. 2 0. 1 22.5 .

0. 1 0. 2 0. 2 0. 3 0. 5 0. 3 0. 1 ug/d

L 25. 0

0. 1 0. 2 0. 3 0. 4 0. 7 0. 3 0. 2 27. 5

0. 2 0. 2 0. 4 0. 5 0. 8 0. 4 0. 2 Expert G, Low SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0. 2

0. 4 0. 6 1. 0 1. 8 0. 8 0. 5 0. 2 0. 4 0. 6 1. 0 1. 8 0. 8 0. 5 0. 3 0. 5 0. 8 1. 2 2. 1 0. 9 0. 6 0. 4 0. 7 1. 0 1. 5 2. 7 1. 2 0. 7 0. 5 0. 9 1. 3 1. 9 3. 2 1. 5 0. 9 0. 7 1. 1 1. 6 2. 3 3. 8 1. 8 1. 0 0. 8 1. 3 1. 9 2. 7 4. 4 2. 2 1. 2 1. 0 1. 6 2. 2 3. 1 5. 0 2. 5 1. 3 1. 2 1. 9 2. 5 3. 5 5. 5 2. 9 1. 4 1. 4 2. 1 2. 9 3. 9 6. 1 3. 2 1. 5 1. 6 2 J: 3. 2 <.. ;
v #
_ 3. 6 1. 6 Expert H, Low SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 1. 2

1. 7 2. 3 3. 0 4. 5 2. 5 1. 0 1. 2 1. 8 2. 3 3. 0 4. 5 2. 5 1. 1 1. 3 1. 9 2. 5 3. 3 4. 9 2. 8 1. 1 1. 5 2. 2 2. 9 3. 8 5. 7 3. 2 1. 3 1. 7 2. 5 3. 3 4. 3 6. 4 3. 6 1. 5 2. 0 2. 8 3. 7 4. 8 7. 0 4. 0 1. 6 2. 2 3. 2 4. 1 5. 3 7. 7 4. 4 1. 7 2. 5 3. 6 4. 5 5. 8 8. 3 4. 9 1. 8 2. 8 4. 0 5. 0 6. 4 9. 0 5. 4 1. 9 3. 2 4. 4 5. 5 7. 0 9. 7 5. 9 2. 0 3. 6 4. 9 6. 1 7. 5 10. 3 6. 4 2. 1 Expert I, Low SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0. 1 0. 2 0. 2 0. 4 0. 2 0. 1 0. 2 0. 3 0. 4 0. 6 0. 9 0. 5 0. 2 0. 3 0. 5 0. 7 1. 0 1. 6 0. 8 0. 4 0. 5 0. 7 1. 0 1. 4 2. 2 1. 1 0. 5 0. 7 1. 0 1. 4 1. 8 2. 8 1. 5 0. 7 0. 9 1. 3 1. 7 2. 3 3. 4 1. 9 0. 8 1. 1 1. 6 2. 1 2. 8 4. 1 2. 3 0. 9 1. 4 2. 0 2. 5 3. 3 4. 7 2. 7 1. 0 1. 6 2. 3 2. 9 3. 7 5. 3 3. 1 1. 1P.5 6 

### 15 2

TABL E D. 3 (Cont'd )

Fractiles , Mean , an

d Standar d Deviatio

n Expert J, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mean S D 2. 5
Low SES 0. 9 1. 8 2. 4 3. 0 3. 9 2. 4 0. 9 R

e 5. 0

0. 9 1. 8 2. 4 3. 0 3. 9 2. 4 0. 9 spons e 7. 5

1. 0 2. 0 2. 6 3. 3 4. 2 2. 6 1. 0 Rat e 10. 0

1. 2 2. 3 3. 0 3. 7 4. 7 3. 0 1. 0 (Z ) a

t 12. 5

1. 4 2. 5 3. 3 4. 1 5. 2 3. 3 1. 1 Geometri c 15. 0

1. 7 2. 8 3. 7 4. 5 5. 7 3. 7 1. 2 Mean 17. 5

1. 9 3. 2 4. 0 4. 9 6. 1 4. 0 1. 3 Pb B Leve l i

n 20. 0

2. 2 3. 5 4. 4 5. 3 6. 6 4. 4 1. 3 22. 5

2. 6 3. 9 4. 8 5. 8 7. 1 4. 8 1. 4 Ug/d

L 25. 0

2. 9 4. 3 5. 3 6. 2 7. 6 5. 3 1. 4 •

27. 5

3. 3 4. 8 5. 7 6. 7 8. 1 5. 7 1. 4 Expert K, Low SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0. 2 0. 3 0. 3 0. 4 0. 3 0. 1 0. 3 0. 5 0. 7 0. 8 1. 1 0. 7 0. 2 0. 5 0. 8 1. 1 1. 4 1. 7 1. 1 0. 4 0. 6 1. 1 1. 5 1. 8 2. 3 1. 5 0. 5 0. 8 1. 4 1. 9 2. 3 2. 9 1. 9 0. 6 1. 0 1. 7 2. 2 2. 7 3. 5 2. 2 0. 8 1. 2 2. 0 2. 6 3. 2 4. 0 2. 6 0. 9 1. 5 2. 4 3. 0 3. 6 4. 5 3. 0 0. 9 1. 7 2. 7 3. 4 4. 1 5. 0 3. 4 1. 0 Expert F, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0 0 0 0 0. 1 0. 1 0. 1 0. 1 0 0 0. 1 0. 1 0. 1 0. 2 0. 1 0. 1 0. 1 0. 1 0. 2 0. 2 0. 4 0. 2 0. 1 0. 1 0. 2 0. 2 0. 3 0. 5 0. 3 0. 1 0. 1 0. 2 0. 3 0. 4 0. 7 0. 3 0. 2 0. 2 0. 3 0. 4 0. 5 0. 8 0. 4 0. 2 Expert G, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0. 1 0. 1 0. 2 0. 4 0. 2 0. 1 0. 1 0. 3 0. 4 0. 5 0. 9 0. 4 0. 3 0. 2 0. 4 0. 6 0. 8 1. 4 0. 7 0. 4 0. 3 0. 5 0. 8 1. 1 1. 9 0. 9 0. 5 0. 4 0. 7 1. 0 1. 4 2. 3 1. 1 0. 6 0. 5 0. 8 1. 2 1. 6 2. 7 1. 3 0. 7 0. 6 1. 0 1. 4 1. 9 3. 1 1. 6 0. 8 0. 8 1. 2 1. 7 2. 3 3. 6 1. 9 0. 9 0. 9 1. 4 2. 0 2. 6 4. 1 2. 2 1. 0--T--*Sd - ' "?7'**-*rr7firfwr~
TABL E D. 3 (Cont'd )

Fractile s Mean , an

d Standar d Deviatio

n Expert H, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 2. 5 High SES 0. 2 0. 4 0. 6 0. 8 1. 3 0. 6 0. 3 R

e 5. 0

0. 3 0. 4 0. 6 0. 9 1. 4 0. 7 0. 4 spons e 7. 5

0. 4 0. 7 1. 0 1. 3 2. 1 1. 1 0. 5 Rat e 10. 0

0. 7 1. 1 1. 6 2. 1 3. 3 1. 7 0. 8 (Z ) a

t 12. 5

1. 1 1. 6 2. 1 2. 8 4. 3 2. 3 1. 0 Geometri c 15. 0

1. 4 2. 0 2. 6 3. 4 5. 0 2. 9 1. 1 Mean 17. 5

1. 8 2. 5 3. 1 3. 9 5. 5 3. 3 1. 2 Pb B Leve l i

n 20. 0

2. 2 2. 9 3. 5 4. 4 6. 0 3. 7 1. 2 22. 5

2. 5 3. 3 3. 9 4. 8 6. 3 4. 1 1. 2 Ug/dL 25. 0

2. 9 3. 7 4. 3 5. 1 6. 6 4. 5 1. 1 27. 5

3. 2 4. 0 4. 7 5. 5 6. 9 4. 8 1. 1
Expert I, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0. 1 0. 2 0. 1 0. 1 0. 1 0. 1 0. 2 0. 3 0. 5 0. 2 0. 1 0. 1 0. 2 0. 3 0. 5 0. 8 0. 4 0. 2 0. 2 0. 3 0. 5 0. 7 1. 2 0. 5 0. 3 0. 3 0. 4 0. 6 0. 9 1. 6 0. 8 0. 4 0. 4 0. 6 0. 9 1. 2 2. 1 1. 0 0. 6 0. 5 0. 8 1. 1 1. 6 2. 6 1. 3 0. 7 0. 7 1. 0 1. 4 1. 9 3. 1 1. 6 0. 8 0. 8 1. 2 1. 7 2. 3 3. 5 1. 9 0. 9
Expert J, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0. 1 0. 1 0 0 0. 2 0. 2 0. 3 0. 4 0. 7 0. 4 0. 2 0. 4 0. 6 0. 8 1. 1 1. 7 0. 9 0. 4 0. 6 1. 0 1. 3 1. 7 2. 6 1. 4 0. 6 0. 8 1. 2 1. 6 2. 2 3. 3 1. 8 0. 8 1. 0 1. 5 2. 0 2. 6 3. 8 2. 1 0. 9 1. 3 1. 8 2. 3 2. 9 4. 2 2. 4 0. 9 1. 5 2. 0 2. 6 3. 3 4. 6 2. 7 1. 0 1. 7 2. 3 2. 9 3. 6 4. 9 3. 0 1. 0 2. 0 2. 6 3. 2 3. 9 5. 2 3. 3 1. 0
Expert K, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0. 1 0. 1 0. 1 0. 2 0. 1 0 0. 2 0. 2 0. 3 0. 3 0. 4 0. 3 0. 1 0. 3 0. 4 0. 5 0. 6 0. 7 0. 5 0. 1 0. 5 0. 6 0. 8 0. 9 1. 1 0. 8 0. 2 0. 6 0. 9 1. 0 1. 2 1. 5 1. 0 0. 2 0. 8 1. 1 1. 3 1. 5 1. 8 1. 3 0. 3 1. 0 1. 4 1. 6 1. 8 2. 2 1. 6 0. 3

### TABL

E D. 4 Ris

k Estimate s fo rI

Q Level s < 7

0 an d < 85 , U.S . Childre

n Aged 7 P.5 8

Fractile s Mean , an

d Standar d Deviatio n Expert F, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n S D Expert G, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n S D Expert H, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD Expert J, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D i

IQ

10

IQ

IQ 2. 5

* 70, 0 0 0 0 0 0 0

S 70, 0. 1 0. 3 0. 4 0. 7 1. 5 0. 6 0. 5

< 70, 0. 2 0. 5 0. 8 1. 4 2. 9 1. 1 0. 9

S 70. 0. 4 0. 8 1. 2 1. 8 3. 5 1. 5 1. 0 Respons e 5. 0

Low SES 0 0 0 0 0 0 0

Low SES 0. 1 0. 3 0. 5 0. 8 1. 6 0. 6 0. 5
Low SES 0. 2 0. 5 0. 9 1. 4 3. 0 1. 1 0. 9

Low SES 0. 4 0. 8 1. 2 1. 9 3. 5 1. 5 1. 0 7. 5

0 0 0 0 0 0 0

0. 2 0. 3 0. 6 0. 9 1. 9 0. 7 0. 6

0. 3 0. 6 1. 0 1. 6 3. 4 1. 3 1. 1

0. 5 0. 9 1. 3 2. 1 3. 8 1. 6 1. 1 Rat e (Z ) 10. 0

0 0 0 0 0 0 0

0. 2 0. 5 0. 8 1. 2 2. 5 1. 0 0. 7

0. 3 0. 7 1. 2 2. 0 4. 1 1. 6 1. 3

0. 6 1. 1 1. 6 2. 4 4. 4 1. 9 1. 2 a t Geometri c 12. 5

0 0 0 0 0 0 0

0. 3 0. 6 1. 0 1. 6 3. 1 1. 2 0. 9

0. 4 0. 8 1. 4 2. 3 4. 8 1. 8 1. 5

0. 7 1. 2 1. 9 2. 8 4. 9 2. 2 1. 4 15. 0

0 0 0 0 0 0 0

0. 4 0. 8 1. 2 1. 9 3. 8 1. 5 1. 1

0. 5 1. 0 1. 6 2. 7 5. 5 2. 1 1. 7

0. 8 1. 5 2. 1 3. 2 5. 5 2. 5 1. 5 Mea n Pb

B 17. 5

0 0 0 0. 1 0. 1 0 0

0. 5 0. 9 1. 5 2. 3 4. 5 1. 8 1. 3

0. 5 1. 1 1. 9 3. 1 6. 3 2. 5 1. 9

1. 0 1. 7 2. 5 3. 6 6. 1 2. 9 1. 6 Leve l 20. 0

0 0. 1 0. 1 0. 1 0. 1 0. 1 0

0. 6 1. 1 1. 8 2. 8 5. 2 2. 2 1. 5

0. 6 1. 3 2. 2 3. 6 7. 2 2. 9 2. 2

1. 2 2. 0 2. 9 4. 1 6. 8 3. 3 1. 8 in u

g 22. 5

0 0. 1 0. 1 0. 2 0. 2 0. 1 0. 1

0. 7 1. 4 2. 1 3. 2 5. 9 2. 5 1. 7

0. 8 1. 6 2. 6 4. 2 8. 2 3. 3 2. 5

1. 4 2. 3 3. 3 4. 6 7. 5 3. 7 1. 9 /d L 25. 0

0 0. 1 0. 2 0. 2 0. 3 0. 2 0. 1

0. 9 1. 6 2. 4 3. 7 6. 6 2. 9 1. 8

0. 9 1. 9 3. 0 4. 8 9. 2 3. 8 2. 7

1. 7 2. 7 3. 8 5. 2 8. 3 4. 2 2. 1 • 27. 5

0 0. 1 0. 2 0. 3 0. 4 0. 2 0. 1

1. 1 1. 9 2. 8 4. 2 7. 3 3. 3 2. 0

1. 1 2. 1 3. 4 5. 4 10. 2 4. 2 3. 0

2. 0 3. 2 4. 3 5. 9 9. 1 4. 8 2. 2TABL

E D. 4 (Cont'd )

I Fractile s Mean, ' and Standar d Deviatio n Expert K, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert F, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert G, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert H, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D »

IQ

IQ

IQ

IQ 2. 5
i 70, 0 0 0 0 0 0 0

< 70, 0 0 0 0 0 0 0 S 70, 0 0 0 0 0 0 0

S 70, 0 0 0. 1 0. 1 0. 3 0. 1 0. 1 Respons e 5. 0

Low SES 0 0 0. 1 0. 1 0. 1 0. 1 0 Hig h SES 0 0 0 0 0 0 0 High SES 0 0 0 0 0 0 0 High SES 0 0. 1 0. 1 0. 2 0. 3 0. 1 0. 1 7 .

0 . 0 . 0 . 0 . 0 . 0 . 0 .

0 0 0 0 0 0 0

0 0 0 0 0 . 0 0

0 0 . 0 . 0 . 0 . 0 . 0 . 5

2 4 5 6 8 5 2

1

1 2 3 6 2 2 Rat e (Z ) 10. 0

0. 4 0. 9 1. 3 1. 7 2. 2 1. 3 0. 5

0 0 0 0 0 0 0

0 0 0. 1 0. 1 0. 2 0. 1 0. 1

0. 1 0. 2 0. 3 0. 4 0. 9 0. 4 0. 3 a t Geometri c 12. 5

0. 6 1. 5 2. 1 2. 7 3. 6 2. 1 0. 9

0 0 0 0 0 0 0

0 0. 1 0. 1 0. 1 0. 3 0. 1 0. 1

0. 1 0. 2 0. 4 0. 6 1. 3 0. 5 0. 4 15. 0

0. 9 2. 1 2. 9 3. 7 4. 9 2. 9 1. 2

0 0 0 0 0 0 0

0 0. 1 0. 1 0. 2 0. 4 0. 1 0. 1

0. 1 0. 3 0. 5 0. 8 1. 6 0. 6 0. 5 Mea nPb

B 17. 5

1. 1 2. 6 3. 7 4. 7 6. 3 3. 7 1. 6

0 0 0 0. 1 0. 1 0 0

0 0. 1 0. 1 0. 2 0. 5 0. 2 0. 1

0. 2 0. 4 0. 6 0. 9 1. 8 0. 7 0. 5 Leve l 20. 0

1. 4 3. 2 4. 5 ' 5. 8 7. 6 4. 5 1. 9

0 0. 1 0. 1 0. 1 0. 1 0. 1 0

0. 1 0. 1 0. 2 0. 3 0. 6 0. 2 0. 2

0. 2 0. 4 0. 7 1. 1 2. 0 0. 9 0. 6 i nu

g 22. 5

1. 7 3. 8 5. 3 6. 8 8. 9 5. 3 2. 2

0 0. 1 0. 1 0. 2 0. 2 0. 1 0. 1

0. 1 0. 1 0. 2 0. 4 0. 7 0. 3 0. 2

0. 3 0. 5 0. 8 1. 2 2. 2 1. 0 0. 6 /d L 25. 0 *
2. 1 4. 5 6. 2 7. 8 10. 2 6. 2 2. 4

0 0. 1 0. 2 0. 2 0. 3 0. 2 0. 1

. 0. 1 0. 2 0. 3 0. 4 0. 9 0. 4 0. 3

0. 3 0. 6 0. 9 1. 3 2. 4 1. 1 0. 7 27. 5

2. 6 5. 2 7. 0 8. 8 11. 5 7. 0 2. 7

0 0. 1 0. 2 0. 3 0, 4 0. 2 0. 1

0. 1 0. 2 0. 3 0. 5 1. 0 0. 4 0. 3

0. 4 0. 6 1. 0 1. 4 2. 6 1. 2 0. 7TABLE D. 4 (Cont'd ) P.6 0

Fractile s Mean , an

d Standar d Deviatio n Expert J, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D
Expert K, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert F, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D Expert G, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D IQ

IQ

IQ

IQ 2. 5

S 70, 0 0 0 0 0 0 0

* 70, 0 0 0 0 0 0 0

S 85, 0 0 0 0 0 0 0

i 85, 0. 1 1. 5 2. 4 3. 3 4. 7 2. 4 1. 4 5 . High 0 0 0 0 0 0 0 High 0 0 0 0 0 0 0

Low 0 0 0 0 0 0 0
Low 0 . 1 . 2 . 3 . 4 . 2 . 1 Res p 0

SES

SES

SES

SES 1 5 5 4 8 5 4 ons e 7. 5

0 0 0 0. 1 0. 1 0. 1 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0. 3 1. 8 2. 9 4. 0 5. 6 2. 9 1. 6 Rat e (Z ) 10. 0

0 0. 1 0. 1 0. 2 0. 3 0. 1 0. 1

0 0 0 0 0 0 0

0 0 0 0 0 0 0

O. S 2. 4 3. 7 5. 1 7. 0 3. 7 2. 0 at Geometri c 12. 5

0. 1 0. 1 0. 2 0. 3 0. 5 0. 2 0. 2

0 0 0 0 0 0 0

0 0 0. 1 0. 1 0. 1 0. 1 0

0. 7 3. 0 4. 6 6. 2 8. 5 4. 6 2. 4 15. 0

0. 1 0. 1 0. 2 0. 4 0. 7 0. 3 0. 2

0 0 0 0 0. 1 0 0

0 0. 1 0. 1 0. 2 0. 2 0. 1 0. 1

1. 0 3. 6 5. 5 7. 4 10. 1 5. 5 2. 8 Mea nPb

B 17. 5

0. 1 0. 2 "0. 3 0. 4 0. 8 0. 3 0. 2

0 0 0. 1 0. 1 0. 2 0. 1 0

0. 1 0. 2 0. 2 0. 3 0. 4 0. 2 0. 1

1. 3 4. 3 6. 4 8. 6 11. 6 6. 4 3. 1 Leve l 20. 0

0. 1 0. 2 0. 3 0. 5 1. 0 0. 4 0. 3

0 0. 1 0. 1 0. 1 0. 3 0. 1 0. 1

0. 1 0. 2 0. 4 0. 5 0. 6 0. 4 0. 2

1. 6 5. 0 7. 4 9. 7 13. 1 7. 4 3. 5 inu

g 22. 5

0. 1 0. 3 0. 4 0. 6 1. 1 0. 5 0. 3

0 0. 1 0. 1 0. 2 0. 3 0. 2 0. 1

0. 1 0. 4 0. 5 0. 7 0. 9 0. 5 0. 2

2. 1 5. 8 8. 3 10. 9 14. 5 8. 3 3. 8 'd L 25. 0

0. 2 0. 3 0. 4 0. 7 1. 2 0. 5 0. 3

0. 1 0. 1 0. 2 0. 2 0. 4 0. 2 0. 1

0. 2 0. 5 0. 7 0. 9 1. 2 0. 7 0. 3

2. 6 6. 5 9. 3 12. 0 15. 9 9. 3 4. 0 • 27.5 "

0. 2 0. 3 0. 5 0. 7 1. 3 0. 6 0. 4

0. 1 0. 1 0. 2 0. 3 0. 5 0. 2 0. 2

0. 2 0. 6 0. 8 1. 1 1. 5 0. 8 0. 4

3. 2 7. 3 10. 2 13. 0 17. 2 10. 2 4. 2T T T P.6 1

TABLE D. 4 (Cont'd )

Fractiles , 'Mean , an d Standar d Deviatio n 2. 5 Respons e Rat e (Z ) at Geometri c Mea nPbB Leve l i n ug/d L 5. 0 7. 5 10. 0 12. 5 15. 0 17. 5 20. 0 22. 5 . 25. 0 27. 5 Expert H, IQ < 85, Low SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n SD Expert J, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 2. 4

3. 8 5. 3 7. 4 11. 6 6. 0 2. 9 IQ i 85, 2. 2 4. 5 6. 2 7. 8 10. 1 6. 2 2. 4 2. 4 3. 9 5. 4 7. 5 11. 8 6. 0 2. 9
Low SES 2. 2 4. 6 6. 2 7. 9 10. 2 6. 2 2. 4 2. 7 4. 3 6. 0 8. 3 13. 0 6. 7 3. 2

2. 5 5. 0 6. 8 8. 5 11. 0 6. 8 2. 6 3. 1 5. 1 7. 1 9. 7 15. 1 7. 8 3. 8

3. 0 5. 8 7. 8 9. 7 12. 5 7. 8 2. 9 3. 6 5. 9 8. 1 11. 2 17. 3 9. 0 4. 3

3. 6 6. 6 8. 8 10. 9 13. 9 8. 8 3. 1 4. 1 6. 7 9. 2 12. 6 19. 3 10. 1 4. 7

4. 2 7. 4 9. 7 12. 0 15. 3 9. 7 3. 4 4. 7 7. 5 10. 4 14. 1 21. 3 11. 3 5. 2

4. 8 8. 3 10. 7 13. 2 16. 6 10. 7 3. 6 5. 4 8. 6 11. 7 15. 7 23. 4 12. 7 5. 6

5. 6 9. 3 11. 9 14. 4 18. 1 11. 9 3. 8 6. 2 9. 7 13. 1 17. 4 25. 5 14. 1 6. 0

6. 6 10. 4 13. 1 15. 7 19. 5 13. 1 3. 9 7. 1 11. 0 14. 6 19. 2 27. 6 15. 6 6. 3

7. 6 11. 6 14. 3 17. 1 21. 1 14. 3 4. 1 8. 1 12. 3 16. 1 20. 9 29. 7 17. 1 6. 6

8. 8 12. 8 15. 7 18. 5 22. 6 15. 7 4. 2 Expert K, IQ < 85, Low SES 0.0 5 0.2 5 0.5 C 0.7 5 0.9 5 Mea n S D

er t F, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 IQ i 85. 0 0 0 0 0 0 0 0 0. 1 0. 1 0. 1 0. 1 0. 1 0 High SES 0 0 0 0 0 0 0 0 . 0 . 0 . 1 . 1 . 0 . 0 .

0 0 0 0 0 0 0 3 6 8 0 3 8 3 0. 8 1. 6 2. 1 2. 6 3. 3 2. 1 0. 7

0 0 0 0 0 0 0 1. 3 2. 5 3. 3 4. 1 5. 3 3. 3 1. 2

0 0 0. 1 0. 1 0. 1 0. 1 0 1. 8 3. 4 4. 5 5. 6 7. 1 4. 5 1. 6

0 0. 1 0. 1 0. 2 0. 2 0. 1 0. 1 2. 3 4. 3 5. 6 6. 9 8. 9 5. 6 2. 0

0. 1 0. 2 0. 2 0. 3 0. 4 0. 2 0. 1 2. 9 5. 2 6. 7 8. 3 10. 5 6. 7 2. 3

0. 1 0. 2 0. 4 0. 5 0. 6 0. 4 0. 2 3. 6 6. 1 7. 8 9. 6 12. 1 7. 8 2. 6

0. 1 0. 4 0. 5 0. 7 0. 9 0. 5 0. 2 4. 3 7. 1 9. 0 10. 9 13. 6 9. 0 2. 8

0. 2 0. 5 0. 7 0. 9 1. 2 0. 7 0. 3 5. 1 8. 1 10. 1 12. 1 15. 0 10. 1 3. 0

0. 2 0. 6 0. 8 1. 1 1. 5 0. 8 0. 4TABL E D. 4 (Cont'd ) P.6 2

Fractiles , Mean , an

d Standar d Deviatio n 2. 5 Respons e Rat e (Z ) a t Geometri c Mea nPbB Leve l in ug/d L 5. 0 7. 5 10. 0 12. 5 15. 0 17. 5 20. 0 22. 5 25. 0 27. 5 Expert G, IQ < 85, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0. 1 0 0 0. 1 0. 1 0. 2 0. 3 0. 5 0. 2 0. 1 0. 1 0. 3 0. 4 0. 6 1. 2 0. 5 0. 4 0. 2 0. 4 0. 7 1. 0 1. 9 0. 8 0. 5 0. 3 0. 6 0. 9 1. 3 2. 5 1. 1 0. 7 0. 4 0. 7 1. 1 1. 7 3. 0 1. 3 0. 9 0. 5 0. 9 1. 4 2. 1 3. 7 1. 6 1. 0 0. 6 1. 1 1. 7 2. 5 4. 4 2. 0 1. 2 0. 8 1. 4 2. 1 3. 0 5. 2 2. 4 1. 4 1. 0 1. 7 2. 4 3. 5 6. 0 2. 8 1. 6
Expert H, IQ < 85, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5
Mea n S D Expert J, 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n SD 0. 2

0. 4 0. 6 0. 9 1. 7 0. 7 0. 5 IQ $85, 0 0 0 0 0 0 0 0. 2 0. 4 0. 7 1. 0 1. 9 0. 8 0. 5 High SES 0 0 0 0. 1 0. 1 0. 1 0 0. 4 0. 7 1. 1 1. 7 3. 0 1. 3 0. 8

0. 2 0. 3 0. 4 0. 6 1. 0 0. 5 0. 3 0. 7 1. 3 1. 9 2. 8 4. 8 2. 2 1. 3

0. 4 0. 7 1. 0 1. 5 2. 4 1. 2 0. 6 1. 1 1. 8 2. 7 3. 9 6. 5 3. 1 1. 7

0. 7 1. 2 1. 6 2. 3 3. 8 1. 9 1. 0 1. 4 2. 4 3. 4 4. 7 7. 7 3. 8 2. 0

0. 9 1. 5 2. 1 3. 0 4. 8 2. 4 1. 2 1. 8 2. 9 4. 0 5. 5 8. 7 4. 5 2. 2

1. 2 1. 9 2. 6 3. 6 5. 6 2. 9 1. 4 2. 2 3. 4 4. 6 6. 2 9. 5 5. 0 2. 3

1. 4 2. 2 3. 0 4. 1 6. 4 3. 4 1. 5 2. 6 3. 9 5. 2 6. 8 10. 2 5. 6 2. 4

1. 7 2. 6 3. 5 4. 7 7. 0 3. 8 1. 7 3. 0 4. 4 5. 7 7. 4 10. 8 6. 1 2. 4

2. 0 3. 0 3. 9 5. 2 7. 7 4. 3 1. 8 3. 4 4. 8 6. 2 8. 0 11. 4 6. 7 2. 5

2. 3 3. 4 4. 4 5. 7 8. 3 4. 8 1. 9 Expert K, IQ < 85, High SES 0.0 5 0.2 5 0.5 0 0.7 5 0.9 5 Mea n S D 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0. 1 0 0 0. 1 0. 1 0. 1 0. 2 0. 2 0. 1 0. 1 0. 1 0. 2 0. 3 0. 4 0. 6 0. 3 0. 1 0. 3 0. 4 0. 5 0. 7 1. 0 0. 6 0. 2 0. 4 0. 6 0. 8 1. 0 1. 5 0. 9 0. 3 0. 6 0. 8 1. 1 1. 4 2. 1 1. 2 0. 5 0. 8 1. 1 1. 4 1. 8 2. 6 1. 5 0. 6 1. 0 1. 4 1. 7 2. 2 3. 2 1. 9 0. 7