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### *' I PROTOCO L FO

RENCODING PROBABILITY JUDGMENT S ABOU T DOSE-RESPONSE CURVES FO RLEAD-INDUCE

D HEMOGLOBI

N DECREMENTS AN

D FO RDISCUSSIN

G POSSIBL

E ADVERSE HEALT H EFFECT S O

F ELEVATE

D E P
1 . INTRODUCTIO N 2
. LEAD-INDUCE D HEMOGLOBI N DECREMENT S 2. 1 Definitio n o f

Hemoglobi n Decremen t a s a n Advers e Healt h Effec t 3
. POPULATIO N A T RIS K 4
. EXPOSURE CONDITION S 5
. PHYSIOLOGICAL CONDITION S 6
. FACTOR S T O CONSIDE R 7
. FACTOR S T O KEEP I N MIN D WHE N MAKIN

G PROBABILITY JUDGMENT S 7. 1 Sequentia l Consideratio n o f Informatio n 7. 2 Effect s of

Memory o n Judgmen t 7. 3 Estimatin g Reliabilit y o f Informatio n 7. 4 Relatio n Betwee n Even t Importanc e an dProbabilit y 7. 5 Estimatio n of

Probabilitie s 7. 6 Recommendation s 8
. POSSIBL

E ADVERS E HEALTH EFFECT S O FELEVATE D ERYTHROCYT E PROTOPORPHYRI N 9
. FINAL PREPARATIO N FO RELICITATIO N O FPROBABILITY JUDGMENT S (T o b e provide ddurin g initia l visit )

Versio n 84.10.1 7P. 3
; A

PROTOCO

L FORENCODIN

G PROBABILIT

Y JUDGMENTS ABOUT DOSE-RESPONS E CURVES FORLEAD-INDUCE D HEMOGLOBI

N DECREMENTS AND FO RDISCUSSIN

G POSSIBL

E ADVERSE HEALT H EFFECT S O F ELEVATE D E P
1 . INTRODUCTIO

N Th e Environmenta l Protectio n Agenc y (EPA ) i s charge db y th e Clea n Ai r Ac t wit h settin g an drevisin g Nationa l Ambien t Ai r Qualit y Standard s (NAAQS ) fo r selecte d pollutants , a t

level s sufficien t

t o protec t

th e publi c healt 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 din criteri adocuments
. I

n suppor t o f th e forthcomin g revie w of th e lea dNAAQS , EPA ha s jus t prepare dane w Ai r

Quality Criteria for

Lead. I t

present s scientifi c evidenc e fro m whic h th e mos t

susceptibl e population s ca n b e determine dan dfro mwhic h variou s advers e healt h effect s ca n b e identified
. Th e criteri adocumen t summarize s an d evaluate s th e availabl e clinical , epidemiological , an danima l o r toxicologica l laborator y evidenc e wit 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 u p 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 pollutant , 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 EPA administrato r

i n selectin g tha t

standar dwhich , i n hi s judgment , protect s th e publi c healt h wit h a n adequat e margi n o f safety
. Becaus e th e ris k estimate s tha tEP A seek s ar e ofte n base d i n parto n dose

respons e relationship s an d lea d exposur e estimate s whic h ar e uncertain , i t i s necessar y t o mak e probabilit y judgment s abou trelevan tdose-respons e function s base d o n th e availabl e evidence , an d t o probabilisticall y estimat e lea d exposur e unde ralternativ eP. 4

NAAQS
. Obtainin g th e healt h ris k estimate s the n involve s combinin g dose-respons e an d exposur e probabilit y estimates
. .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
. In tha t cas e i t i s necessar y t o us e scientifi c judgmen t t o extrapolat e fro mth e dat at o mak e abes t decisio 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 t certai n and , therefore , w e wil l ai dyo u t o represen t you r 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 wil l hav e differen t judgments
. Fo r

eac h healt h effec t

w e 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 mode l fo r estimatin g risk s wil l no t merg e thes e judgment s int o asingl e averag e judgment , bu t

rathe r wil l estimat e th e rang e o f risk s base do n th e rang e o f judgments
. I

f w e a s ris k

analyst s d o ou r

jo b properly , the n no t

onl y wil l w e b e abl e t o sho w th e EPA administrato r th e rang e of

estimate s base don th e rang e of judgments , bu t
w e wil l 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 t of thi s exercis e i n whic h w e prob e you r knowledg e in astructure dmanne r ma y b e t o hel p identif

y source s o f

greates t disagreement
. Base do n th e evidenc e i n th e lea dcriteri adocument , tw o population s hav e bee n identifie da s bein g mos t susceptibl e t o th e effect s o f lea dintoxication
. On e i s childre n fro mbirt h throug h th e sevent h birthday , an dth e othe r i s pregnan t

women , o r

mor e precisely , th e fetuse s bein g carrie db y th e pregnan t women . A numbe r

o f advers e healt h effect s hav e bee n identifie dfo r whic h w e woul dlik e t o estimat e dose-respons e function s includin g th e on e discusse dbelow
.
2 . LEAD-INDUCED HEMOGLOBI N DECREMENT S W e woul dlik e t o represen t i n probabilisti c for myou r opinio n abou t

th e locatio n an dshap e o f

dose-respons e function s fo r certai n wel l define dlevel s o f lead-induce dP. 5

hemoglobi n reductio n i n th e populatio n o f U.S
. childre n fro mconceptio n throug h th e sevent h birthday
. W

e realiz e tha t

availabl e dat ad o no t

full y defin e thes e functions ; i f the y did , the n i t

woul db e unnecessar y t o obtai n you r an dothe r

experts ' opinion s abou t them
. Nevertheless , if th e population , th e exposur e conditions , an dth e healt h effect s ar e al l precisel y defined , the n suc h function s i n fac t exis t an dw e woul dlik e you r bes t judgmen t abou t wha t the y woul dloo k

lik e i f th e dat acoul db e collected
.
2. 1 Definitio n o f

Hemoglobi n Decremen ta s a n Advers e Health Effec t Ther e ar e difference s of opinion , o f

course , a s t o wha t

degre e o f

reductio n i n hemoglobi n leve l constitute s ahealt h risk
. Th e Clea n Ai r Ac t make s i t

clea r tha t EPA shoul dse t

it s standard s t o protec t agains t advers e healt h effects
. However , th e reductio n in hemoglobi n leve l considere dt o b e advers e ma y b e differen t

fo r regulator y purpose s tha n fo r

clinica l action
. Sinc e i t i s generall y agree dfo r childre n tha t

a hemoglobi n leve l o f

abou t 1 2 gram s pe r

decilite r

i s norma l an dabou t

9 gram s pe r decilite r i s anemic , w e wil l specif y tw o hemoglobi n level s in tha t interval , namel y 9. 5
an d1 1 gm/dl , an dtrea t eac h a s th e physiologica l effec t fo r purpose s o f

specifyin g a dose-respons e function
. W e wil l elici t

fro myo u probabilit y judgment s abou t th e shap e an dlocatio n o f

th e dose-respons e curv e fo r eac h o f th e tw o level s o f

effect s i n th e sensitiv e population
.
3
. POPULATIO

N A T RIS

K W e ar e definin g th e mos t susceptibl e grou p a s al l Unite dState s childre n fro m conceptio n throug h thei r sevent h birthday
. However , yo u may believ e o n variou s ground s tha t younge r an dolde r

childre n i n thi s gr,ou

p hav e differen t

dose-respons e function s fo r lead-induce dhemoglobi n reduction
. I f so , the n w e wil l elici t

you r judgment s separatel y fo rth e ag e group s 0- 3 an d 4-6
.P. 6

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 blood-lea dlevels
. Assum e tha t th e blood-lea dleve l unde r consideratio n fo r

agive n judgmen t i s i n equilibriu ma s aresul t o f asufficientl y long-ter mconstan t lea dexposur e withou t gros s excursion s above o r belo w th e state dlevel
.
5
. PHYSIOLOGICA

L CONDITION S Becaus e th e effec t

o f lea do n hemoglobi n leve l depend s o n man y parameter s o f a person' s system , i t

i s necessar y t o specif y assumption s abou t

thos e parameter s in th e population
. Th e effec t o f lea din th e syste mdepend s on th e person' s nutritiona l an d metaboli c status
. Th e incidenc e of iro n deficienc y i s greate r i n childre n tha n in adults , an dgreate r

ye t i n childre n ag e 0- 3 tha n ag e 4-6 , wit h awid e rang e o f iro n level s i n childre n u p 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 o f lea dals o depend s o n th e level s of zinc , copper , vitamin s A , C , D , an dE , calcium , phosphorou s an d magnesium
. Assum e i n al l case s tha t thes e nutrient s ar e distribute di n 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 wel l established , o f course , tha t

erythrocyt e protoporphyri n (EP ) leve l i s positivel y correlate dwit h blood-lea dlevel
. However , th e correlatio n i s no t perfect , an d ther e i s arang e o f

E P value s a t

an y give n bloo dlead
. You ma y 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 blood-lea dleve l a s yo u believ e i t

i n fac t is
.
6 . FACTOR

S T O CONSIDE

R In 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 i n orde r t o hel p u s t o interpre t you r judgments , w e woul dlik eP. 7 1

6
t o ask yo u t o discus s briefl y yourinterpretation s o f variou s aspect s o f

th e literature . Firs to f all , coul d yo u tel

j u s somethin g abou thow , i n yourjudgment , lea d and iro n interac tt o reduc e hemoglobi n level s an d somethin g abou tth e relatio n betwee n iro n an d lea d level s i n th e body ? Similarly , w e woul d b e intereste d i n you ropinion s abou tth e sam e question s wit h regar d t o zin c an d lea d an d t o calciu m an

d lead . I tappear s tha tlea d affect s hemoglobi n level s throug h thre e somewha tseparat e routes : interferenc e with hem e synthesis , interferenc e with globi n synthesis , an d decrease d lif

e expectanc y o f erythrocytes . Briefly , whati s yourinterpretatio n o f th e literatur e o n thes e variou s effect s o f

lead ? E

P leve l increase s with iron deficiency , buti tals o increase s wit h bloo d lea d an d i s considere d t o b e a proxy measur e fo rth e amoun to f lea d recentl y cumulate d in bod y tissue . Considerin g only tha tportio n o f E P elevatio n du e t o lead , i n you r judgment , i s th e relationshi p betwee n bloo d lea d an d hemoglobi n differen ta tdifferen t E P levels ? Finally , w e kno

w tha tsom e group s o f

childre n ar e a tgreate rris k of exposur e t o lea d due t o thei rlivin g i n deterioratin g pre-195 0 housin g o rin urba n area s with larg e amounts o f

vehicula rtraffic . Thes e childre n woul d ten d t o hav e high lea d levels , bu td o yo u believ e tha tther e ar e als o independen treason s t o think tha tthei rdose-effec tcurve s wil l b e differen tfrom childre n who liv e i n othe rcircumstances ? Fo rexample , thes e may b e th e sam e childre n wh o ten d t o hav e poore rdiet s an d les s acces s t o medica l care . Wha ti s you ropinio n regardin g th e possibilit y o f a correlatio n betwee n increase d exposur e and increase d susceptibility ? Ar e ther e othe rfactor s t o conside ri n thinkin g abou tth e dose-respons e function s fo rlead-induce d hemoglobi n decrement s tha tw e shoul d discus s now ?

7 . FACTOR

S 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 tha tw e dra w fro m research , an

d more generall y in oureveryda y thinking . However , no teveryon e i s awar e o f al l th e source s tha tshoul d contribut e t o thei runcertainty , no rar e mos tpeopl eP. 8

familia rwith th e proces s o f actuall y expressin g thei runcertainty in probabilisti c terms . Whe n a n exper ti s aske d t o mak e probability judgments on sociall y importan tmatters , i t i s particularl y importan ttha th e o rsh e conside rth e relevan tevidenc e i n a systemati c an d effectiv e manneran

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 a considerabl e amoun to f

dat a concernin g th e way peopl e for m an d expres s probabilisti c judgments . Th e evidenc e suggest s tha twhen considerin g larg e amounts o f comple x information , mos t peopl e emplo y simplifyin g heuristic s an d demonstrat e certai n systemati c distortion s o f thought , i.e. , cognitiv e biases , which adversel y affec tthei rjudgments . The purpos e o f this 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 muc h a s possible , yo u ca n avoi d the m in making probabilit y judgments . W

e wil l firs trevie w th e mos twidesprea d biases an d heuristics , an

d the n offe rsom e suggestion s t o hel p yo u mitigat e thei reffects .
7. 1 Sequentia l Consideratio n o f Informatio n Generally , th e orde rin 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 a sequentia 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 framework which subsequen tinformatio n i s then 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 tweigh s against them . Th e late revidenc e ha s it s undu

e effec tsimpl y becaus e i ti s freshe ri n memory . Relate d t o thes e sequentia l effect s i s th e phenomeno n o f anchorin g and adjustment. Base d o n earl y partia l information , on e form s a n initia l probability estimat e regardin g th e even ti n question . Thi s ancho rjudgmen ti s the n adjuste d a s subsequen t informatio n i s considered . Unfortunately , suc h adjustment s ten d t o b e to oP. 9

8 conservative
. In 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 o f

th e initia l judgment
.
7. 2 Effect s o f

Memor y o n Judgmen t Iti 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 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 som e way , suc h a s bein g familiar , unusual , especiall y concrete , o r o f persona l significance
. 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 of

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
. Fo r 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 migh t naturall y firs t

thin k o f 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
.
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 in term s of 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
. In suc h cases , informatio n i s ofte n interprete di n awa y whic h 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
.P.1 0

7. 4 Relatio n Betwee n Even tImportanc e and Probability Sometime s th e importanc e o f events , o r

thei r possibl e cost s o r

benefits , influenc e 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 toward s ris k ten dt o affec t one' s abilit y t o mak e accurat e probabilit y judgments
. Fo r example , man y physician s ten d t o overestimat e th e probabilit y o f ver y sever e diseases , becaus e the y fee l i t i s importan t t o detec t an dtrea t

them ; an dsimilarly , man y smoker s underestimat e th e probabilit y o f advers e consequence s of smoking , becaus e the y fee l tha t th e odd s d o no t

appl y t o themselve s personally
.
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 uncertainty , an dt o us e appropriat e criteri aof discriminatio n fo r

differen t

range s of probability
. On e resul t o f thi s fac t

i s tha t peopl e ten dt o estimat e bot h extrem e an d mid-rang e probabilitie s i n th e sam e fashion , usuall y doin g apoo r jo b i n th e extremes
. I t help s her e t o thin k

in term s of

odd s a s wel l a s probabilities
. Thus , fo r example , changin g aprobabilit y estimat e fro m0.51 0 t o 0.50 1 i s equivalen t t o achang e i n odd s fro m1.041: 1 t o 1.004:1 , bu t

achang e fro man estimat e o f 0.99 9 t o 0.99 0 change s th e odd s b y afacto r o f abou t 10 ? fro m999: 1 t o 99: 1 Th e close r t o th e extreme s (eithe r 0 o r 1 ) tha t on e i s estimatin g probabilities , th e greate r th e impac t

o f smal l changes
.
7. 6 Recommendation s 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 , som e relativel y simpl e suggestion s ca n hel p minimiz e them
. Mos t importan t

i s t o b e awar e o f

one' s natura l cognitiv e biases , an dt o tr y consciousl y t o avoi dthem
.P.1 1

1 0 T o avoi d sequential

effects kee p i n min

d tha tth e orde ri n which yo u think o f informatio n shoul d no tinfluenc e yourfina l judgment . I tma y b e helpfu l t o actuall y not e o n pape rth e importan tfact s you ar e considerin g an d the n t o reconside rthe m in tw o o r mor e sequences , checkin g th e consistenc y o f you rjudgments . Tr

y t o kee p a

n ope n min

d unti l you hav e gon e throug h al l th e evidence , an

d don' tle tth e earl y informatio n you conside rswa y yo u more than i s appropriate . T o avoi d advers e memory effects, defin e variou s classe s o f informatio n tha tyou dee m relevant , an

d the n searc h you rmemor y fo rexample s of

each . Don' trestric tyou r thinkin g onl y t o item s tha tstan d ou tfo rspecifi c reasons . Mak e a specia l attemp tt o conside rconflictin g evidence , an d t o thin

k of dat a tha tma

y b e inconsisten twit h a particula rtheory . Also , b e carefu l t o concentrat e o n th e give n probability judgmen tan d d o no tle tyou row

n value s (ho

w you woul d make th e decisio n yourself ) affec tthos e judgments . To accuratel y estimate the reliabilit y of information, pa

y attentio n t o suc h matter s a s sampl e siz e an d powe rof

th e statistica l tests . Kee p in min d tha tdat a ar e probabilisti c in nature , subjec tt o element s of rando m error , imprecis e measurements , an d subjectiv e evaluatio n an d interpretation . I

n addition , th e furthe ron e mus t extrapolate , o rgeneralize , fro m a particula rstud y t o a situatio n o f interest , th e les s reliabl e i s th e conclusio n an d th e les s certaint y shoul d b e attribute d t o it . Rel y mor e heavil y on informatio n whic h yo u conside rmor e reliable , butdo no ttrea ti ta s "absolut e truth. " Kee p i n min

d tha tthe importance of an event o ra n outcome should

not influence its judged

probability. Iti s rationa l t o le tth e costlines s orseverit y o f a n outcom e influenc e th e poin ta twhic h actio n i s take n wit h respec tt o it , bu tno tth e judgmen ttha t i s made abou tth e outcome' s likelihood . Finally , i n making probability judgments , think primaril y i n term s of th e measur e (probabilit

y o rodds ) wit h which yo u fee l mor e comfortable , butsometime s translat e t oP.1 2

1 1 th e alternativ e scale , o r eve n t o measure s o f

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 i n term s o f

odds , whic h ar e unbounded , instea dof probabilities , whic h ar e bounded
. Fo r

example , on e ca n mor e easil y conceptualiz e odd s o f 1:200 tha n a probabilit y o f

.005
.


### 8 . POSSIBL

E ADVERS E HEALT H EFFECT S O F ELEVATE D ERYTHROCYT E PROTOPORPHYRI N

(EP ) I t seem s wel l establishe dtha t ther e i s apositiv e dose-respons e relationshi p betwee n bloo dlea dan dEP
. Althoug h thi s elevate dEP ca n b e trace dt o hem e synthesi s interference , ther e i s disagreemen t a s t o what , if

an y advers e healt h effect s ar e associate dwit h lea dinduce 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 hemoglobi n blood-lea ddose-respons e function
. I n you r judgment , i s lead-induce delevate dEP 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 of

EP 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 CN S functions , 2
. Live r

detoxificatio n capabilities , o r 3
. Rena l o r

endocrin e functio n (i n particular , reduce dbiosynthesi s of 1,25-dihydroxyvitami n D)
. I s ther e arelatio n betwee n lea dinduce delevate dEP an danemi aof an y sor t beyon dtha t

whic h ca n b e indexe db y blood-lea dleve 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 ?P.1 3

1 2 9 . FINAL PREPARATION FORELICITATIO N OF PROBABILIT

Y JUDGMENTS Th e shap e an dlocatio n of th e dose-respons e curv e a s w e define di t abov e i s uncertain , becaus e th e existin g dat ad o no t determin e th e dose-respons e relationshi p exactly
. Yet , if

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
. Our 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 criteri adocument , an dconsul t it , th e literature , o r

you r file s a s yo u dee m appropriate
. Th e previou s sectio n suggest s 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 o f 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

ados e respons e relationshi p ca n b e represente d probabilisticall y i n tw o differen t ways . 1
. Uncertaint y abou t

th e percentag e o f

th e define dpopulatio n tha t woul db e affecte db y given blood-lead concentrations ca n b e represente dprobabilistically
. 2
. Uncertaint y abou t

th e blood-lea dconcentration s tha t woul db e require dt o affec t

agiven percentage of

the defined

population ca n b e represente dprobabilistically
. W e wil l concentrat e o n on e way a t atime , focusin g primaril y o n th e firs t one . Fo r thes e purpose s i t

i s helpfu l t o imagin e tha t everyon e i n th e populatio n ha s a specifie dblood-lea dleve l tha t ha s becom e stabilize di n th e manne r describe dabov eP.1 4

1 3 underExposure Conditions. Then , a s a result , som e percentag e o f th e populatio n wil l suffe rth e hemoglobi n response .

- Now , in orde rfo rus t o determin e you runcertaint y aboutth e percentage s of th e populatio n tha twoul d b e affecte d by given blood lead levels w e mus tintroduc e a definition . Le tC b e th e give n blood-lea d concentratio n i n question . Definition : R(C) i s th e percentag e of th e populatio n fo rwhich a blood-lea d leve l
o f C woul d caus e th e define d hemoglobi n healt h effect . Thus , R(C) i s precisel y th e percen tof th e populatio n tha twould sho w a respons e i

f th e entir e populatio n ha

d blood-lea d level s of

C underth 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 of

R(C ) fo ra give n C i s uncertain , an d w e woul d lik e t o obtai n probability judgments 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 a particula rpercentag e an d havin g yo u conside rhow likel y i ti s tha tR(C ) i s les s than tha tvalue . T o hel p yo u mak e you r probability judgments , w e wil l mak

e us e o f a devic e calle d a probabilit 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 whee l th e percentag e o

f th e whee l tha ti s eac h color . I n making yourjudgments yo u ar e t o imagin e tha tth e whee l i s a perfectl y fai rrando m device , an

d tha ttherefor e th e probability o f it s stoppin g with th e pointe ro n blu e i s exactl y represente d by th e relativ e are a tha ti s blue . W e wil l the n procee d a s follows . Fo reac h bloo d lea d concentratio n C , w e wil l specif y a particula rpercen tr , an d als o se tth e probability whee l t o hav e a specifi c relativ e are a of

blue . The

n you ar e t o conside rcarefull y th e question'. D o yo u conside ri tmore probabl e tha tth e tru e populatio n respons e rat e R(C ) i s les s than rortha tth e whee l woul d sto p wit h th e pointe ro n blu e ,(o n a rando

m spin) ? You 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 tha tR(C ) i s les s than r ;P.1 5

1 4 (2 ) Yo u judg e i tt o b e mor

e probabl e tha tth e whee l would sto p with th e pointe ri n blue ;

" ' (3 ) Yo u canno tjudg e eithe reven ta s mor e probabl e than th e other . Fo ra particula rconcentratio n C an d percen tr , som e whee l setting s wil l hav e a smal l enough relativ e are a o f blu e tha tyo u wil l fee l confiden tmaking respons e (1) . Othe rwhee l setting s wil l hav e a larg e enough relativ e are a of blu e tha tyo u wil l fee l confiden tmaking respons e (2) . Th e intermediat e setting s wil l b e more difficul tt o judge . However , w e wil l manipulate th e whee l setting s t o find th e on e fo rwhich yo u fee l
mos tcomfortabl e making respons e (3) . Onc e w e hav e determine d th e poin ta twhich you are mos tcomfortabl e with respons e (3) , an

d stil l focusin g o

n th e give n bloo d lea d C , we wil l specif y a ne w percen t r' , an d repea tth e procedure . Thi s wil l continu e fo rth e give n C unti l w e hav e specifie d variou s percents . Then w e wil l hav e elicite d on e o f th e probabilisti c representation s o f you runcertaint y abou tth 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 a ne

w C an d continuin g a s before . W e wil l do thi s fo ra numbero f

value s o f

C . I tfrequentl y happen s tha ta n expert' s judgments alte rsomewha tove rth e cours e o f a sessio n suc h a s this , a s h e orsh e consider s th e evidenc e from variou s perspective s an d think s abou tth e variou s response s calle d for . Hence , w e wil l grap h you rresponse s and , a tappropriate times , sho w the m t o yo u fo ryou rconsideratio n an d comparison . A t thes e time s yo u ma

y wis h t o chang e som e o f th e judgment s you gav e earlier . W e shoul d emphasiz e tha tth e judgments w e are askin g yo u t o mak e ar e no t simpl e ones , noro f

cours e ar e ther e know n correc tanswers . Rather , w e wan tyou rbes t
an d mos tconsidere d judgmen ti n ligh to f th e availabl e relevan tscientifi c data , Therefore , pleas e reflec ton th e availabl e dat a carefully , feelin g fre e t o consul tth e lea d criteri a documen to rothe rsource s a s yo u wis h a s yo u formulat e you rjudgments .P.1 6 

## iV:.. /
1 5

(Encod e judgments fo ra tleas ttw o concentration s o f on e dose-respons e function , the n continu e wit h instructions. )

_ - Recal l tha tuncertainty aboutth e dose-respons e functio n ca n als o b e expresse d i n term s o f th e blood-lea d concentratio n necessar y t o produce th e effec tin a give n percentag e o

f th e populatio n r , if

th e entir e populatio n ha d th e sam e blood-lea d concentration , stabilize d a s th e resul to f exposur e in th e manne

rdiscusse d earlier . Mor e specifically , proceedin g a s before , le tu s introduc e a definition : Definition : C(R

) i s th e blood-lea d leve l tha twould caus e th e define d hemoglobi n healt h effec ti

n Rpercen tof

th e population . Th e valu e o f

C(R ) i s uncertai n fo ra give n R , an d w e wan tt o obtai n you r judgments aboutit s possibl e values . Analogousl y t o whatwe hav e alread y done , fo ra give n Rw e wil l specif

y concentration s c an

d ask you t o conside rho w likel y i ti s tha tth e tru e C(R ) i s les s than th e specifie d c . Mor e specifically , utilizin g th e whee l a s before , w e wil l as k you th e question : D o yo u conside ri tmor

e likel y tha tth e tru e concentratio n C(R ) i s les s than c , o r tha tth e whee l woul d sto p wit h th e pointe ron blu e (o n a rando m spin) ? Yo u ca n giv e on e of

thre e responses : (1 ) Yo u judg e i tmor

e probabl e tha tC(R

) i s les s tha

n c ; (2 ) You judg e i tmor e probabl e tha tth e whee l woul d sto p wit h th e pointe r in blue ; (3 ) Yo u 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 you fee l mos tcomfortabl e wit h respons e (3) , w e wil l specif y a new c an

d repea tth e process . A s before , fo reac h Rw e wil l elici tyou rcomparativ e judgment s fo rvariou s value s of c .