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UNITE D STATE S ENVIRONMENTA L PROTECTIO N AGENCYJJ^ - ft ~£~ 

# USB, 1 ''<.*&*• SUBJECT : MODELINGTH E PERCENT O F CHILDRE NWIT H HIGH BLOO D LEA D LEVEL S FROM : Joe l Schwart z CVc ^ (j

Offic e o f Polic yAnalysi s VJ p<-H f 

### ( j \ flnr, ? I 198 5 TO : Vi c Hasselbla d

Alla n Marcu s Jef f Cohe n Th e distributio no f bloo d lead level s i nU.S
. childre ni s a broad one , becaus e ther e i s a distributio no f exposure s thos e childre nface , a distributio no f behavio r pattern s tha t affec t th e uptak e o f tha t exposure , an d a distributio no f biologica l absorbtio nan

d excretio nrates
. Observationa l dat a bases , suc h a s NHANE S II , reflec t al l o f thos e contribution s t o th e varianc e o f th e distribution
. I believ e tha t th e issu e w e hav e bee n grapling wit ho n ho wt o determin e wha t ai r lead standar d wil l protec t a give n percen t o f childre nfrom exceeding som e cutof f bloo d lea d leve l i s th e issu e o f ho wt o dea l wit hthos e varianc e components , an

d ho wtheymigh t change
.
I believ e tha t Vi c an d Allan' s poin t i s tha t th e varianc e o f th e distributio ni s partiall ydu e t o th e varianc e i nai r lead levels ; therefor e th e percen t o f childre na t hig hbloo d lead level s i f al l area s wer e a t a give nambien t standar d shoul d b e estimate d i na wa ytha t remove s tha t variance
. I believ e tha t tha t poin t i s a fai r one . Mypoin t ha s bee ntha t th e techniqu e chose nals o remove s som e o f th e varianc e i nnon-ai r exposure , thereb yunderestimatin g th e varianc e a t uniformai r lead , an d tha t th e assumptio ntha t th e tai l o f th e distributio ni s wel l modele d b

yfitting a lognorma l distributio nt o th e overal l distributio ni s les s robus t tha nsom e othe r technique s fo r estimatin g th e siz e o f th e tail
. I wil l discus s thes e furthe r i n th e hope s tha t w e ca nreac ha nagreemen t o nth e bes t wa yt o d o th e modeling
.
Myfirs t poin t i s tha t muc ho f th e varianc e associate d wit h som e o f th e demographi c variable s reflect s variatio ni nbaselin e exposure , behavio r pattern s o r biologica l factors , an d no t ai r lead , an

d therefor e adjusting th e distributio nfo r thema s a techniqu e fo r removin g th e varianc e du e t o variatio ni nai r lead level s i s excessivel yconservative
. Fo r example , conside r race . Black s hav e highe r bloo d lead level s tha nwhites , howeve r th e NHANE S dat a indicate s tha t black s hav e highe r bloo d lead level s tha nwhite s eve nafte r controlling fo r degre e o f urbanization , income , residenc e insid e th e centra l city , parent s educationa l level , an

d an yothe r variabl e tha t appear s t o tes t whethe r tha t differenc e i s soleydu e t o differentia l exposur e t o highurba n ai r lead
. Indeed , som e o f thos e variable s als o tes t whethe r th e racia l differenc e i s du e t o differentia l exposur e t o pain t lead
.P. 3

Afte r controlling fo r al l o f thos e factor s ther e i s stil l a substantia l differenc e betwee nth e race s i nthei r bloo d lead levels
. Indeed , whe nw e di d ou r gasolin e lead regressions , whic h contro l fo r th e majo r sourc e o f ai r lea d exposure , a s wel l a s ag e sex , incom e , degre e o f urbanization , regio no f th e country , educationa l level , dietaryconsumption , etc , black s stil l ha d significantl yhighe r bloo d lead levels
. Thi s differenc e reflect s tru e difference s i nth e othe r factor s affecting bloo d lead levels , an

d therefor e shoul d remai na s a rea l facto r tha t contribute s t o th e GSD
. Locatio n i s anothe r facto r tha t represent s mor e tha njus t differenc e i nai r lead exposure . Whil e th e estimate s o f mea n baselin e exposur e i n th e criteri a documen t ar e reasonable , an d th e bes t dat a w e have , clearl yfood lead levels , dus t lead , wate r lead , an

d othe r factor s varyfrom locatio nt o location
. On e importan t proble m

wit hth e modelin g i nth e staf f pape r i s tha t i t ignore s th e distributio no f cit ymea nbaselin e levels
. Sinc e th e percen t o f childre na t highbloo d lead level s i s nonlinea r i n th e mea nbaselin e assumed , adding a distributio ni nmea nbloo d lead level s abou t th e mea nbaselin e quote d i n th e C D and staf f pape r wil l i nfac t chang e th e estimat e o f th e numbe r o f childre na t highlevels
. Th e probabilit yo f exceeding a give nbloo d lead leve l i s clearl yth e produc t o f th e probabilit yo f th e locatio n havin g a mea nu , give nth e gran d mean , time s th e probabilit yo f having a highbloo d lead , give nu an d th e gs d withi na site
. Sinc e th e produc t o f lo g norma l distribution s i s lognormal , thi s i s equivalen t t o spreading th e gs d b yadding th e varianc e o f th e sit e mean s t o th e varianc e o f th e withi nsit e population
. Th e curren t modelin g ignore s thi s byassumin g tha t th e baselin e i n everylocatio ni s th e same . I f I recal l wha t Vi c tol d m e correctly , th e gsd' s quote d i nth e C D remove d th e variatio ndu e t o sit e effects ; wherea s theyshoul d onl yremov e th e sit e variation s du e t o ai r lead variations , an d leav e th e sit e variation s du e t o variation s i nth e baselin e exposure . Th e NHANE S I I dat a ca nb e use d t o quantif ythi s effect
. Assumin g tha t degre e c f urbanizatio ni s a prox yfo r th e distrib

utio no f ai r lead level s (an d I argue d befor e tha t som e o f th e varianc e du e t o degre e o f urbanizatio ni s du e t o othe r factors) , I regresse d th e lo g o f bloo d lead level s o nth e eigh t leve l degre e o f urbanizatio nvariabl e i nth e NHANE S I I dat a . I the n adde d th e mea nbac k t o th e residual s and too k th e mea nlo g bloo d lead level , b ysite
. Thi s i s th e mea nafte r adjusting al l th e site s t o th e sam e population
. Tabl e 1 show s th e mean , standard deviation , an d "geometri c standard deviation" , whic hi s ex p o f th e stadar d deviatio ni nlo g space . W e ca nse e tha t ther e i s a nexpecte d variatio ni nmea nbloo d lea d level s fo r citie s o f th e sam e size
. Adding th e varianc e o f thi s distributio nt o tha t o f a distributio n wit ha gs d o f 1.3 9 woul d giv e a distributio n wit ha gs d o f 1.462 , whic hi s showni nth e las t column
. Th e nex t lin e carrie s th e analysi s further , b yfirs tP. 4

TABL E 1 LO GMEA N 2.66 5

2.66 6 LO GS D

0.18 9

0.18 3 GS D TOTA L GS D

1.20 8 1.46 2

1.20 0 1.45 8 controlling fo r degre e o f urbanization , income , an d race , befor e taking th e sit e means . Agai nther e i s a noticabl e residua l varianc e i n th e mean s o f location s wit hth e sam e population , racia l mi xan

d incom e levels
. Addin g tha t varianc e t o tha t o f a populatio n wit ha gs d o f 1.3 9 woul d giv e a ne wgs d o f 1.458
. Th e abov e calculation s demonstrat e tha t ther e i s a variatio n i nmea nbloo d lead level s amon g cities , an d tha t correcting fo r demographi c proxie s fo r ai r lead exposur e leave s a residua l variatio ni nsit e mean s du e t o variation s i n non-ai r exposure . Thi s i s a napproximatio nt o th e distributio no f mea nbloo d lead level s acros s site s wit hth e sam e ai r lead exposure . Estimatin g a child s likelihoo d o f having a nelevate d bloo d lead level , o r th e percen t o f childre nabov e a certai nbloo d lead leve l a t a give nai r lead leve l canno t ignor e thi s variatio ni nbackground level
.

CAS E Sit e Means , Controlling Fo r Degre e o f Urbanizatio n Sit e Means , Controlling fo r Urbanization , Rac e an d Income
Ther e ar e likel yt o b e difference s i nbaselin e exposur e tha t ar e a functio no f degre e o f urbanization , sinc e highe r populatio n densit ywil l increas e th e soi l contaminatio nfromothe r source s tha nai r (e.g
. ol d batteries , industria l facilitie s etc.)
. Similarl ysom e o f th e racia l an d income difference s i nbloo d lead level s ar e certainl yno t du e t o airlead exposure . O nth e othe r hand , thes e proxie s ma yno t completel ycontro l fo r ai r variations
. I t woul d clearl yb e bette r t o remov e th e airlead varianc e directly
. T o d o thi s I repeate d th e gasolin e lead regressions , an d use d the mt o remov e th e varianc e du e t o gasolin e lead exposure , whic h i s abou t 85 % o f ai r lead exposure . B yajusting everyindividual s bloo d lea d leve l t o wha t i t woul d b e a t zer o gasolin e lea d exposure , w e arriv e a t a goo d estimat e o f th e distributio no f bloo d lead level s du e t o baselin e exposur e variations , biologica l differences , etc
. T o accoun t fo r th e remainin g 15 % o f ai r lead exposure , th e resulting gs d ca nb e reduce d b y15 % o f th e chang e i nth e gs d i ngoin g fro mth e unadjuste d distributio nt o th e on e expecte d a t zer o gasolin e lead
. Usin g th e gs d fromthi s analysi s incorporate s difference s du e t o variation s i n baselin e exposur e amon g locations , races , etc , whic hmus t b e incorporate d t o correctl ypredic t th e effec t o f o f additiona l exposur e t o ai r lea d o nth e percen t o f childre ntha t wil l hav e hig hbloo d lea d levels
. T o maintai nth e distributio na s lo g normal , th e gasolin e regressio n wa s don e usin g a dependen t variabl e o f lo g bloo d lead
.P. 5

Th e regressio ni s showni n th e appendix
. The neac hindividual s lo g bloo d lead wa s reduce d b yth e gaslea d regressio ncoefficien t time s thei r gasolin e lead exposure , an d a weighte d univariat e wa s performe d o n th e resulting distribution
. Th e result s ar e shown o nth e firs t lin e o f tabl e 2
. Th e estimate d gs d i s 1.428
. More

over , th e principa l reaso ntha t thi s gs d i s highe r tha nthos e i n th e C D i s th e natura l variatio ni n th e baselin e exposur e amon g site s wit hsimila r demographi c characteristics , no t th e variatio n i ndemographi c characteristic s betwee nsites
. T o illustrat e this , th e second lin e i n tabl e 2 show s th e sam e results , afte r adjusting b

yregressio nfo r th e effec t o f degre e o f urbanization
. Eve ni f al l childre nlive d i n town s wit hth e sam e degre e o f urbanization , the ywoul d hav e a gs d o f 1.414
. T o illustrat e thi s further , th e nex t tw o line s sho wth e mea nan d gs d o f locatio n mean s a t zer o gasolin e lead wit han d withou t adjusting fo r degre e o f urbanization
. (Th e mea nreflect s zer o gaslead , bu t no t zer o stationarysourc e lead , th e gs d reflect s ou r correctio nfo r bot h factors. )
TABL E LO GMEAN 1.9 9 2

LO GS D 0.36 0 GS D

1.42 8 CAS E Controlling fo r Airlea d (zer o airlead ) Controlling fo r 1.98 9 0.34 6 1.41 4 Airlea d an

d Degre e o f Urbanizatio n Locatio nMea n1.93 5 0.18 7 1.4 6 * Controlling fo r Airlea d Locatio nMea n1.97 8 0.16 1 1.44 * Controlling fo r Airlea d an

d Urbanizatio n Note : sit e mean s diffe r fromoveral l mean s becaus e th e site s ha d differen t populations , whic hi s controlle d fo r i n th e overal l mean .
* assumin g a GS D o f 1.3 9 afte r controlling fo r sites , and adding th e sit e varianc e du e t o no n ai r source s bac k in
.
I nsummary , i t appear s tha t th e bes t estimat e fo r th e GS D fo r childre nsi xan

d under , i f th e ai r lead wa s zero , i s 1.428
. T o calculat e th e percen t o f childre nwit hbloo d lead level s abov e th e lowes t effec t level , w e shoul d us e thi s GS D an d loo k a t th e effec t o f increasing everyone s airlea d exposur e t o 0.50 , etc
. Thi s wil l giv e th e percen t o f childre nexpecte d t o excee d tha t leve l i f everylocatio ni s a t th e ambien t standard
. I stil l lik e th e ide a o f doin g logisti c regression s t o se e ho wP. 6

th e percen t o f childre n abov e a give nleve l changes
. Regressio n i s a mor e robus t techniqu e tha nfitting distributions , and i t ca n als o b e correcte d t o eliminat e th e varianc e du e t o airlea d exposure . I wil l tryt o d o tha t soo n an d send yo u th e results
.P. 7

REGRESSIONRESULT S LO GBLOO D LEAD , CHILDRE NSI XAND YOUNGE R

VARIABL E INTERCEP T GASLEA D URBANIZATIO N RAC E SE X INCOM E AG E COEFFICIEN T

2.25 6 0.162 4 -0.0265 0.212 9 -0.030 7 -0.121 9 -0.018 5 t-STATISTI C 36.0 1 17.6 7 -10.4 4 11.2 4 2.3 5 -12.6 9 -4.97 4 P-VALU E

0.000 1 0.000 1 0.000 1 0.000 1 0.018 7 0.000 1 0.000 1

NOTE : Regressio nwa s run i nWLS , no t SURREGR , sinc e thi s give s th e identica l coefficients , an d w e alread

ykno wth e significan t variables
.