# OAR Box 1112 Prepped by Ryan Dugan



### Document

Number: 

# 15 ) ll-B- 4

Docket Number: 

# A-83-2 2

Printed 4/16/2008 9:12:06

AM Sheet 15of 97 P. 1P. 2



### ^ 

### AP R2 2 

### 1985 Subject : Draf

tStaf f Pape ro nLea d From : Joe l Schwart z Offic e o f

Polic y Analysi s To : Jef f

Cohe n Offic e o f

Ai rQualit y Plannin gan d Standard s A s I mentione d i n ou rphon e conversatio nyesterday , I thin ktha t w e ca n improv e th e modelin go f th e percen to f

childre n a tris ka s afunctio n o f

geometri cmea n bloo d lea d leve l tha ti s currentl y containe d i nth e draf tstaf f paper . Thi s memorandum repeat s th e problem s wit h th e curren tapproac h tha tI discusse d wit h you , and , I hope , offer s asimpl e solutio nt o them . Th e overridin gsourc e o f th e problem s i s tha tth e distributio n o f bloo d lea d level s i nchildre n i s reall y th e su m o f tw o distributions , on e fro m genera l exposur e t o ai rlead , foo d lead , etc. , an d on e fro m ver y hig h exposur e t o lea d pain to rothe rhig h concentratio n sources . Sinc e th e su m o f lo gnorma l distribution s i s no ti n fac tlo gnormal , on e woul d expec tthi s t o introduc e error s int o th e fi to f th e distributio n a thig h levels . Sinc e on e woul d no texpec tth e bloo d lea d level s o f lea d pain texpose d childre n t o fal l proportionatel y a s th e mea n bloo d lea d leve l falls , (i.e . thei rbloo d lea d level s wil l no tfal l b y 4 o r5 ug/d l fro m areductio ni nai rlea d tha tproduce s a n averag e 1 ug/d l fall ) th e underestimat e o f th e fatnes s o f

th e tai l woul d b e expecte d t o increas e a s th e mea n bloo d lea d leve l fell . Thi s theoretica l poin ti s supporte d b y th e dat aa s well . Fo r example , CD

C an d NCH

S i nthei ranalysi s o f th e NHANE

S I I dat a divide d th e sampl e int o tw o periods , befor e an d afte rth e rat e o f chang e o f

bloo d lea d level s increased . Fo rth e secon d perio d th e geometri cstandar d deviatio no f bot h blac kan d whit e children' s bloo d lea d level s wa s approximatel y 1.43 . However , th e GS D tha t correctl y predicte d th e percen to f childre nabov e 3 0 ug/d l wa s 1.54 , i.e . th e extrem e tai l i s fatte rtha n predicte d b y th e GS D tha tbes tfit s th e entir e distribution . Moreover , th e differenc e i nthes e GSD' s wa s large ri n th e secon d period , whe n mea n bloo d lea d level s wer e lower , tha n i twa s i n th e firs t period . S o th e erro rincrease s a s th e mea n bloo d lea d leve l falls . Sinc e OAQP S intend s t o se tth e standar d o n th e basi s o f protectin g 99.5 % (o r99.2 % o r99.8% ) o f U.S . childre n fro m bein g abov e som e critica l level , we wil l b e settin gth e standar d i n precisel y th e tai l o f th e cumulativ e distributio n functio n wher e we knowbot h tha tth e GS D systematicall y underpredict s th e number o f childre n a thig h bloo d lea d levels , an d wher e we kno wtha tth e erro rappear s t o chang e wit h th e mea n bloo d lea d level . A s a n ancillar y point , whil e I thin ktha tAla n Marcus' s estimate s o f th e GS

D fo rahomogeneou s sub-populatio n o f childre n ar e quit e correct , the y ar e no tth e appropriat e GSD' s t o us e fo ryou r goal . Sinc e th e standar d i s bein gse tb y lookin ga tAL L childre n an d tryin gt o pic kastandar d tha twil l kee p e.g . 99.5 %P. 3

o f AL L childre nbelo wth e critica l level , th e appropriat e GS D t o us e i n an y cas e i s th e GS D fo ral l children . Thi s wa s 1.4 7 i n th e NHANE

S I I survey . Thi s i s no tatrivia l point . Th e Criteri a document' s calculatio n o f th e GS

D i s adjusted , b y anova , fo rth e effect s o f

age , race , sex , an d income . Tha tis , i tgive s avalu e tha ton e woul d expec ti f al l childre n wer e th e sam e race , ha d th e sam e famil y income , etc . However , th e broadenin go f th e distributio ndu e t o th e broa d distributio n o f famil y income s i n th e Unite d State s i s area l one . Poore rpeopl e d o ge tmore exposur e t o lead . Therefore , i f ou rgoa l i s t o kee p 99.5 % o f rea l U.S . childre nbelo wsom e critica l effect s level , we mus tus e th e rea l distribution . T o pu tthi s i n bette rperspective , th e NHANE S dat a(Vita l an d Healt h Statistics , serie s 11 , no . 223 ) indicate s tha t4 percen to f U.S . childre n wer e abov e 3 0 ug/d l an d 9.1 % o f the m wer e abov e 2 5 ug/d l i nth e NHANE S I I survey . Usin g th e reporte d geometri cmea n bloo d lea d leve l fo rthos e children , an d th e highe ro f

th e homogeneou s GSD' s (1.39) , th e predicte d numbe ro f

childre nexceedin g3 0 ug/d l o r2 5 ug/d l respectivel y ar e 1.6 8 % an d 5.8. . Thu s th e erro rinvolve d i s substantial . Eve n usin gth e actua l GS D o f 1.4 7 fo rNHANE

S I I childre n give s a predictio n o f

3.46 % abov e 30 , versu s th e actua l 4% . Thi s reflect s th e fa ttai l discusse d earlier . Non e o f thi s i s t o sa y tha tth e calculation s o f th e GSD' s fo rhomogeneou s group s don e i n th e Criteri aDocumen tar e wrong , the y jus tar e no tth e appropriat e one s t o us e i f we ar e targetin g99.5 % o f th e non homogeneou s populatio n o f U.S . children . Not e tha ton e doe s no t hav e t o b e dealin gwit h th e whol e U.S . populatio n t o ge tsuc h hig h GSD's . th e GS D fo rchildre ni nurba n area s wit h population s ove ron e millio n i s 1.46 , fo rblac kchildre n wit h famil y income s unde r$600 0 i s 1.47 , etc . W e deal twit h thi s proble m i n th e gasolin e lea d rul e b y usin g logisti cregressio n analysi s o f th e percen to f

childre n abov e e.g . 30ug/d l t o predic ttha tpercentage , rathe rtha n jus tmovin g th e mea n an d usin gaconstan tGSD . Thi s approac h i s superio r conceptually , an d als o i s partiall y nonparametric , i n tha ti t make s n o assumptio nabou tth e shap e o f th e distributio n curve , bu tmerel y fit s th e tai l are aa tth e appropriat e cutof f t o a logisti cfunctio n o f th e variabl e o f

interest . I thin ktha tth e sam e approac h t o you rproble m wil l als o giv e abette rfit . I n addition , regressio nanalysi s i s mor e robus ttha n othe r techniques , suc h a s rollbac kmodeling . T o implemen tthi s approac h fo ryou rproble m I too kth e NHANE S II data , divide d i tint o seventee nquarters , an d fo reac h quarte r too kth e mea no f

th e lo go f

th e bloo d lead s fo rchildre n age d si x an d under , an d als o compute d th e percen to f thos e childre n wh

o wer e abov e 15ug/dl , 20ug/dl , an d 25ug/dl . Al l o f thes e calculation s wer e weighted . I the n performe d logisti c regression s o nho

wthos e percentage s varie d wit h th e means . Thi s direc testimatio ntechniqu e avoid s th e GS D proble m an d automaticall y incorporate s th e actua l dat ao n childre n abov e thes e targe tlevels , avoidin gth e error s o f th e GS

D approac h note d above . Th e regression s wer e weighte d b y th e siz e o f th e sampl e i n eac h quarter , an d wer e don e usin gmaximu m likelihoo dP. 4

estimator s i n Pro cNlin . Th e result s ar e show nbelow . LOGISTI C REGRESSIO N DEPENDEN T VARIABLE : PROBABILIT Y OF BEIN G OVE R 2 5 ug/d l PARAMETE

R INTERCEP T MEA N LN(LEAD ) COEFFICIEN T -16.20 2 5.05 3 STANDAR D ERRO R 1.75 7 0.63 6 t-STATISTI C 9.2 2 7.9 4

PARAMETE

R INTERCEP T MEA N LN(LEAD ) LOGISTI C REGRESSIO N DEPENDENT VARIABLE : PROBABILIT Y OF BEIN G OVE R 2 0 ug/d l COEFFICIEN T -15.50 6 5.24 2 STANDAR D ERRO R 1.12 3 0.40 9 t-STATISTI C 13.8 1 12.3 3

PARAMETE

R INTERCEP T MEA N LN(LEAD ) LOGISTI C REGRESSIO N DEPENDENT VARIABLE : PROBABILITY OF BEING OVE R 1 5 ug/d l COEFFICIEN T -13.41 8 4.99 8 STANDAR D ERRO R 0.81 8 0.30 4 t-STATISTI C 16.4 0 16.4 4

Usin g thes e regressio n result s w e ca ncalculat e th e mea nbloo d lea d leve l tha tcorrespond s t o agive nchoic e o f critica l lea d leve l an d agive n fractio n o f th e populatio nt o b e hel d belo w tha tcritica l level . Fo rexample , i f th e critica l leve l i s 2 0 ug/d l an d th e critica l fractio ni s 99.5 % o f th e children , w e hav e t h e following . log(p/l-p ) = 15.50 6 + 5.242*mea nlog(lead ) f o rth e 99.5 % leve l p = .005 , an d p/(l-p ) = .00502 5 yieldin g -5.293 3 = -15.50 6 + 5.246«mea nln(lead ) whic h ca n obviousl y b e solve d fo rth e geometri cmea nbloo d lea d level . T o tes tth e results , I predicte d th e percen to f childre n abov e 2 5 ug/d l usin g thi s techniqu e an d usin g aconstan tGSD o f 1.39 . Th e tw o predicte d value s o f th e percen to f childre nabov e thes e level s wer e regresse d o nth e actua l observations . Th e R squar e o f

th e logisti cprediction s wa s higher , indicating , a sP. 5

- . , .>••»

.

expected , abette rfi tt o th e data . I thin ktha tthi s techniqu e i s mor e accurat e an d shoul d b e use d t o replac e th e tabl e o n pag e 7 8 an d th e number s i nth e nex tfe wfollowin gpage s tha tgiv e th e mea n bloo d lea d level s tha tar e associate d wit h variou s choice s o f

p an d o f

critica l effect s level . I d o hav e tw o quic kcomment s t o make o n th e res to f th e Staf f Paper . Whil e th e gasolin e lea d regression s tha twe di d ar e no t directl y relevan tt o you rwork , the y d o provid e considerabl e suppor tfo rth e judgmen ttha tyo u reache d regardin gth e significanc e o f

th e non-direc tinhalatio n pathways . Sinc e thes e result s wer e presente d t o CASA C a tth e las tcriteri adocumen t revie wan d wer e reviewe d favorably , I thin ktha ti twoul d b e usefu l t o cit e them . Th e regression s indicate d tha tgasolin e lead , a n airborn e sourc e o f lead , wa s alarg e contributo rt o bloo d lea d levels . Further , whil e i ti s onl y possibl e t o mak e qualitativ e estimate s o f airborn e lea d level s a ttha ttime , th e siz e effec tindicate d b y th e gasolin e lea d regressio n coefficients , i n th e NHANE S data , th e Ne

wYorkCit y data , and th e Chicag o data , sugges ttha tth e direc tinhalatio n componen twa s no mor e tha n 25 % o f

th e total . Thes e result s ar e simila rt o thos e o f Caro l Angle , an d sinc e the y wer e derive d usin gdifferen tdat a an d differen ttechniques , tha tsimilarit y i s striking . I tmigh t b e worthwhil e mentionin gthis . Moreover , th e regression s indicat e tha tabou t8 ug/d l o f averag e bloo d lea d wa s comin gfro m gasolin e lea d i n 197 6 -1980 . Th e averag e ai rmonito rreadin ga t tha ttim e wa s belo w1 ug/cu . m , althoug h th e averag e monito rwa s site d to o hig h an d therefor e underestimate d exposure . Eve n correctin gfo rtha twoul d appea rt o giv e arati o o f 7-8 , which i s abov e th e hig h en d tha tyo u mentio n i n th e staf f paper . Whil

e thi s calculatio n i s inherentl y rough , I believ e tha ti t qualitativel y support s usin gth e hig h en d o f th e ratio' s tha tyo u discussed , an d tha tthi s rati o deserve s som e attentio n i n settin g you rmargi no f

safety . Secondly , whil e th e bloo d pressur e wor ki s discusse d i n th e healt h appendix , i ti s no tdiscusse d i n th e bod y o f th e pape ro r wit h respec tt o th e settin go f th e standard . I f th e assessmen t i n th e curren tversio no f th e corrigend at o th e criteri adocumen t i s accepte d b y CASA C withou tsubstantia l change , I thin ktha t wil l nee d t o b e changed .