1

UNITED STATES ENVIRONMENTAL PROTECTION AGENCY

NATIONAL CENTER FOR ENIRONMENTAL ASSESSMENT- RTP DIVISION 

Research Triangle Park, NC 27711 

OFFICE OF RESEARCH AND DEVELOPMENT 

May 9, 2014

MEMORANDUM

Subject: Identification and consideration of errors in Lanphear et al. (2005), “Low‐Level Environmental

Lead Exposure and Children’s Intellectual Function:  An International Pooled Analysis”

From: Ellen F. Kirrane, Ph.D. /S/

Molini M. Patel, Ph.D. /S/

EPA, NCEA‐RTP

Through: Steven Dutton, Ph.D.

    John Vandenberg, Ph.D.

EPA, NCEA‐RTP

To: Integrated Science Assessment for Lead Docket (EPA‐HQ‐ORD‐2011‐0051)

This memorandum documents errors in a publication cited in the 2013 Integrated Science Assessment for Lead

(U.S. EPA, 2013, hereafter, 2013 Pb ISA). These errors in Lanphear et al. (2005), “Low‐Level Environmental Lead

Exposure and Children’s Intellectual Function:  An International Pooled Analysis,” were identified after the

completion of the 2013 Pb ISA (see Attachment 1 with Appendix). This memorandum identifies these errors and

provisionally considers whether the changes to aspects of Lanphear et al. (2005) that result from correction of the

errors materially affect the scientific conclusions made in the 2013 Pb ISA about the effects of Pb exposure on

cognitive function or intelligence quotient (IQ).  

The 2006 Air Quality Criteria Document for Lead (U.S. EPA, 2006, hereafter, 2006 Pb AQCD) and the 2013 Pb ISA in

the current review conclude that the concentration‐response relationship between blood Pb and cognitive

function in young children is nonlinear, meaning that the IQ decrement per μg/dL increase in blood Pb level is

larger at lower (versus higher) blood Pb levels. This conclusion is based on the findings from several studies (Tellez‐

Rojo et al., 2006; Kordas et al., 2006; Lanphear et al., 2005; Canfield et al., 2003; Bellinger and Needleman 2003;

Lanphear et al., 2000). Lanphear et al. (2005) conducted a pooled analysis of seven cohorts of children and

reported a log‐linear relationship between IQ and concurrent blood Pb levels; and linear regression coefficients

describing the concentration‐response relationship for linear models that were larger for subsets of children with

peak blood Pb levels less than 7.5 μg/dL or 10 μg/dL, as compared to subsets with higher peak blood Pb levels.

Lanphear et al. (2005) reported these models for concurrent blood Pb, which they state to have the strongest

relationship with IQ as measured by R2

.

1

  The quantitative modeling of Lanphear et al. (2005), focusing on the

shape of the concentration‐response relationship, was subsequently corroborated in a separate analysis of the

same dataset by Rothenberg and Rothenberg (2005).   

                                                           

1 The 2006 Pb AQCD and 2013 Pb ISA also evaluated scientific information regarding critical lifestages and time

periods of Pb exposure and concluded that decrements in cognitive function were found with several different

blood Pb metrics that represent blood Pb during lifestages or time periods from the prenatal period through

adolescence (e.g., 2013 Pb ISA, pp. xciv, 4‐57, 4‐76, 4‐248; 4‐256, Table 4‐14).
2

Since completion of the 2013 Pb ISA, a publication by Crump et al. (2013) reports findings from a re‐analysis of the

data for the seven cohorts studied in Lanphear et al. (2005). Crump et al. (2013) reported “some small errors” in

the dataset analyzed by Lanphear et al. (2005) and presented results based on analysis of the corrected pooled

dataset.2 Two of these errors were identified after the completion of the final 2013 Pb ISA (see Attachment 2),

while EPA had corrected others in the last Pb NAAQS review such that presentations in the 2013 Pb ISA are not

affected. 3

Using a copy of the pooled dataset, we were able to correct the errors and confirm the calculations of Crump et al.

(2013) for specific study results that were affected by these errors (see Attachment 1 with Appendix): (1) the non‐

linear effect estimate for the association between IQ and concurrent blood Pb levels; (2) the linear coefficients for

the regressions of concurrent blood Pb on IQ for four groups of children in the dataset with peak blood Pb levels

below 7.5 μg/dL, at or above 7.5 μg/dL, below 10 μg/dL, and at or above 10 μg/dL; and (3) the R2 values for the

models with concurrent, early childhood, peak, and lifetime average blood Pb levels. We re‐calculated additional

statistics that were not reported in Crump et al. (2013) using the corrected dataset (see Attachment 1 with

Appendix): (1) absolute IQ decrements over various concurrent blood Pb ranges based on the log‐linear model; (2)

statistics on the concurrent blood Pb distribution and number of children in the subsets with peak blood Pb levels

below 7.5 μg/dL, at or above 7.5 μg/dL, below 10 μg/dL, and at or above 10 μg/dL; and (3) the coefficients for the

concurrent blood Pb level‐IQ relationship based on the log‐linear model, leaving one cohort out at a time.

Although the model coefficients based on the corrected dataset differ slightly from those in Lanphear et al. (2005)

(see Attachment 1), the conclusion drawn regarding the finding of a steeper concentration‐response relationship

at lower blood Pb levels is unaffected. Further, the errors in Lanphear et al. (2005) do not affect the conclusion in

the 2013 Pb ISA or the 2006 Pb AQCD, which was based on findings from several studies, that multiple blood Pb

metrics including blood Pb level measured concurrent to IQ, were associated with decrements in cognitive

function. After correcting and re‐analyzing the Lanphear et al. (2005) dataset, Crump et al. (2013) confirmed the

primary findings of Lanphear et al. (2005) stating that, “Although we found some small errors and questionable

decisions by Lanphear et al. that, taken alone, could cause doubt in their conclusions, our reanalysis tended to

support their conclusions.” Further sensitivity analyses performed by Crump et al. (2013), including those designed

to test whether findings were robust to various interim modeling decisions, do not alter conclusions drawn from

the data.

After this provisional consideration of the corrected results for Lanphear et al. (2005) and the publication by

Crump et al. (2013), we conclude that the conclusions drawn in the 2013 Pb ISA are not materially affected by

these newly identified errors.  Accordingly, EPA is not re‐opening the air quality criteria for this review to further

consider these studies.

   

                                                           

2 Errors in the Lanphear et al. (2005) pooled dataset identified by Crump et al. (2013) also apply to Rothenberg and

Rothenberg (2005) who relied on the same original dataset. 3 We have contacted the primary authors and have received confirmation of the two recently identified errors in

the dataset analyzed by Lanphear et al. (2005) (see Attachment 2).  
3

References

Bellinger, D; Needleman, HL. (2003). Intellectual impairment and blood lead levels [Letter]. N Engl J Med 349: 500.

Canfield, RL; Henderson, CR, Jr; Cory‐Slechta, DA; Cox, C; Jusko, TA; Lanphear, BP. (2003). Intellectual impairment

in children with blood lead concentrations below 10 micrograms per deciliter. N Engl J Med 348: 1517‐

1526.

Crump KS, Van Landingham C, Bowers TS, Cahoy D, Chandalia JK. (2013). A statistical reevaluation of the data used

in the Lanphear et al. ( 2005 ) pooled‐analysis that related low levels of blood lead to intellectual deficits

in children. Crit Rev Toxicol 43:785‐799.

Kordas, K; Canfield, RL; Lopez, P; Rosado, JL; Vargas, GG; Cebrian, ME; Rico, JA; Ronquillo, D; Stoltzfus, RJ. (2006).

Deficits in cognitive function and achievement in Mexican first‐graders with low blood lead

concentrations. Environ Res 100: 371‐386.

Lanphear, BP; Hornung, R; Khoury, J; Yolton, K; Baghurst, P; Bellinger, DC; Canfield, RL; Dietrich, KN; Bornschein, R;

Greene, T; Rothenberg, SJ; Needleman, HL; Schnaas, L; Wasserman, G; Graziano, J; Roberts, R. (2005).

Low‐level environmental lead exposure and children's intellectual function: An international pooled

analysis. Environ Health Perspect 113: 894‐899.

Rothenberg, SJ; Rothenberg, JC. (2005). Testing the dose‐response specification in epidemiology: Public health and

policy consequences for lead. Environ Health Perspect 113: 1190‐1195.

Téllez‐Rojo, MM; Bellinger, DC; Arroyo‐Quiroz, C; Lamadrid‐Figueroa, H; Mercado‐Garcia, A; Schnaas‐Arrieta, L;

Wright, RO; Hernandez‐Avila, M; Hu, H. (2006). Longitudinal associations between blood lead

concentrations lower than 10 microg/dL and neurobehavioral development in environmentally exposed

children in Mexico City. Pediatrics 118: e323‐e330.

U.S. EPA (U.S. Environmental Protection Agency). (2013). Integrated science assessment for lead [EPA Report].

(EPA/600/R‐10/075F). Research Triangle Park, NC.

U.S. EPA (U.S. Environmental Protection Agency). (2006). Air quality criteria for lead: Volume I of II [EPA Report].

(EPA/600/R‐05/144aF). Research Triangle Park, NC.

ATTACHMENT 1: Errors Identified in Lanphear et al. (2005)

ATTACHMENT 2: Emails from R. Hornung  (May 1, 2014) and B. Lanphear (February 24, 2014)

   
4

ATTACHMENT 1

Errors Identified in Lanphear et al. (2005)  

Two aspects to the dataset for the Boston cohort were not accurately represented in the analyses

reported in Lanphear et al. 2005.4

  They are as follows (see Attachment 2).

 The IQ data analyzed were for performance IQ rather than full‐scale IQ.   

 The blood Pb measurements at 6, 12, and 24 months were transformed incorrectly.   

Selected Crump et al. (2013) calculations that were confirmed by NCEA with the Boston cohort data

correctly represented5 and statistics from Lanphear et al. (2005) that were re‐calculated by EPA are

summarized below  and presented in detail in Table 1.   

a. The log‐linear coefficient for concurrent blood Pb changes from ‐2.70 to ‐2.65.   

b. The model with early childhood blood Pb (rather than concurrent) would have highest

R2

, although the values are still very similar (0.6433 as compared to 0.6414 for

concurrent metric).  

c. The linear coefficient for concurrent blood Pb with IQ for the subgroup of children with

peak blood Pb levels <7.5 μg/dL changes from ‐2.94 to ‐2.53.   

d. The number of children in each of the four linear subset analyses (peak blood Pb below

7.5 μg/dL, at or above 7.5 μg/dL, below 10 μg/dL, and at or above 10 μg/dL) changes as

do the descriptive statistics for concurrent blood in these subsets. For example for the

subgroup with peak <7.5 μg/dL, the sample size changes from 103 to 118 and the mean

blood Pb concentrations from 3.24 to 3.3 μg/dL.

   

                                                           

4 During the 2008 Pb NAAQS review, three typographical errors were identified in Lanphear et al. (2005) and

corrections considered. One set of errors pertained to the two numbers associated with the confidence intervals

reported at the top of the first column on page 897 (corrections reported in docket number EPA‐HQ‐OAR‐2006‐

0735‐5905).  The two numbers were the lower bound on the confidence interval for the linear coefficient for the

relationship of IQ with concurrent blood Pb levels for the subgroup of children with peak blood Pb levels ≥ 7.5

μg/dL and the lower bound on the confidence interval for linear coefficient for the relationship of IQ with

concurrent blood Pb for the subgroup of children with peak blood Pb ≥ 10 μg/dL. These errors were recognized

during development of the 2006 Pb AQCD and corrected in the 2006 Pb AQCD (p. 6‐70). The other errors were in

the values of the two rightmost columns of Table 4 (corrections reported in docket number EPA‐HQ‐OAR‐2006‐

0735‐5512). These errors were recognized after the final 2006 Pb AQCD was released but prior to the conclusion of

the review.

5 Full‐scale IQ was miscoded as verbal IQ. Boston IQ data were corrected by substituting the variable coded as

verbal IQ. Boston blood Pb level data for age 6, 12, and 24 months were corrected by subtracting 2 μg/dL from the

blood Pb level. Investigators had incorrectly un‐transformed data from log form by adding 1 μg/dL to the anti‐log

of blood Pb instead of subtracting 1.
5

Table 1. Statistics associated with Lanphear et al. (2005) that were recalculated by EPA

6 Results reported in Crump et al. (2013) and confirmed by NCEA calculations using the corrected dataset (see Appendix). Other result

only on NCEA calculations using the corrected dataset.

7 8/19/2008 and 2/11/2008 emails from Richard Hornung to Jee‐Young Kim (docket number EPA‐HQ‐OAR‐2006‐0735‐5814).

Finding from Lanphear et al. (2005) Corrected information Previously reported information Pa

IS

Log-linear model coefficient for blood Pb metrics and IQ, adjusted for site, HOME score, birth weight, maternal IQ, and maternal education (Table 4) 

Early childhood: -2.21 (-3.38, -1.04) Peak: -2.86 (-4.10, -1.61) Lifetime average: -3.14 (-4.39, -1.88) Concurrent: -2.65 (-3.69, -1.61)6

Early childhood: -2.04 (-3.27, -0.81) Peak: -2.85 (-4.10, -1.60) Lifetime average: -3.04 (-4.33, -1.75) Concurrent: -2.70 (-3.74, -1.66) 

4-

IQ decrement over different concurrent blood Pb ranges based on the log-linear model 

2.4 to 30 μg/dL: 6.7 IQ pts (4.1-9.3) 2.4 to 10 μg/dL: 3.8 IQ pts (2.3-5.3) 10 to 20 μg/dL:1.8 IQ pts (1.1-2.6) 20 to 30 μg/dL: 1.1 IQ pts (0.7-1.5) 

2.4-30 μg/dL: 6.9 IQ pts (4.2-9.4) 2.4-10 μg/dL: 3.9 IQ pts (2.4-5.3) 10-20 μg/dL: 1.9 IQ pts (1.2-2.6) 20-30 μg/dL: 1.1 IQ pts (0.7-1.5) 

4-

Linear coefficient, sample size (n) and concurrent blood Pb level measurements (mean, minimum, 5th and 95th percentiles, 

and maximum) for subset with peak blood Pb levels <7.5 μg/dL 

-2.53 (-4.48, -0.58 )6

N=118 (3.3, 0.9, 1.1, 6.7, 7.4 μg/dL) 

-2.94 (-5.16, -0.71) N=103 (3.24, 0.9, 1.3, 6.0, 7.4 μg/dL)7

FiFipp

Linear coefficient, sample size (n) and concurrent blood Pb measurements (mean, minimum, 5th and 95th percentiles, and 

maximum) for subset with peak blood Pb levels ≥ 7.5 μg/dL 

-0.15 (-0.19, -0.11)6

N=1215 (13.0, 0.1, 3.7, 34.2, 71.7) 

-0.16 (-0.24, -0.08) N=1230 (12.9, 0.1, 3.5, 34.0, 71.7)7

Fi

Linear coefficient, sample size (n) and concurrent blood Pb measurements (mean, minimum, 5th and 95th percentiles and 

maximum) for subset with peak blood Pb <10 μg/dL 

-0.77 (-1.65, 0.12)6

N=258 (4.4, 0.1, 1.4, 8.0, 9.8) 

-0.80 (-1.74, 0.14) N=244 (4.3, 0.1, 1.4, 8,0, 9.8)7

Fipp

Linear coefficient, sample size (n) and concurrent blood Pb measurements (mean, minimum, 5th and 95th percentiles, and 

maximum) for subset with peak blood Pb levels ≥10 μg/dL) 

-0.13 (-0.22, -0.04)6

N=1075 (14.0, 0.1,4.4, 35.5, 71.7) 

-0.13 (-0.23, -0.03) N=1089 (13.9, 0.1, 4.3, 35.4, 71.7)7

Fi

Blood Pb metric with the largest R2 for the relationship with IQ 

in the log-linear models 

Early childhood R2: 0.6433 = largest 

Peak R2: 0.6401 

Lifetime average R2: 0.6411 

Concurrent R2: 0.6414 

Concurrent (no quantitative results presented) 

4-

Sensitivity of concurrent blood Pb-IQ association to omitting one cohort 

Slopes ranged from -2.36 to -2.94 Slopes range from -2.31 to -2.94 4-

Number of children from Boston cohort with peak blood Pb levels < 7.5 μg/dL 

Boston = 28 Boston = 13 4-
6

Appendix to Attachment 1

Computer Code for EPA Recalculations

libname pooled '\\AA.AD.EPA.GOV\ORD\RTP\USERS\K-Q\mpatel04\Net 

MyDocuments\Lead\Pooled Dataset'; 

proc format; 

value lgender 0='Male'

 1='Female'; 

value lrace 0='Non-white'

 1='White'; 

value YN 0='No'

 1='Yes'; 

data pooled.BostonPb; set pooled.tablespaper; 

/*tablespaper is the uncorrected SAS dataset */

if site NE "Boston" then delete; 

pbch6m2 = pbch6m-2; 

pbch1y2 = pbch1y-2; 

pbch2y2 = pbch2y-2; 

rename pbch6m2 = pbch3 pbch1y2 = pbch1 pbch2y2 = pbch2 pbch4y = pbch4; 

/*This program was first run without subtracting 2 from the blood Pb metrics. 

The purpose of this first run on the original variables was to check whether 

the calculations in this program could replicate the early childhood and 

lifetime average blood Pb levels reported in the Lanphear paper*/

keep ID pbch6m2 pbch1y2 pbch2y2 pbch4y lead peaklead meanlead6m_concurrent 

meanlead6m_24m pbch6m pbch1y pbch2y peakl10 peakl75; 

run; 

proc sort; by ID; 

run; 

data pooled.BostonPb2; set pooled.BostonPb; 

array pbarray[4] pbch1-pbch4; 

do I = 1 to 4; 

pbch = pbarray[I]; 

if pbch NE . then output; 

end; 

keep ID pbch; 

run; 

proc sort; by ID; 

run; 

proc means noprint; 

var pbch; 

by ID; 

output out = pooled.bostonPb3; 

run; 

data pooled.Bostonmax; set pooled.bostonPb3; 

if _stat_ = "MAX"; 

peak2 = pbch; 

drop _type_ _freq_ _stat_ pbch; 
7

run; 

data pooled.Bostonavg; set pooled.bostonPb3; 

if _stat_ = "MEAN"; 

life = pbch; 

drop _type_ _freq_ _stat_ pbch; 

run; 

data pooled.Bostonearly; set pooled.BostonPb; 

array pbarray[3] pbch1-pbch3; 

do M = 1 to 3; 

pbch = pbarray[M]; 

if pbch NE . then output; 

end; 

keep ID pbch; 

run; 

proc sort; by ID; run; 

proc means noprint; 

var pbch; 

by ID; 

output out = pooled.Bostonpb4; 

run; 

data pooled.bostonearly2; set pooled.Bostonpb4; 

if _stat_ = "MEAN"; 

early = pbch; 

drop _type_ _freq_ _stat_ pbch; 

run; 

data pooled.bostonnewPb; 

merge pooled.Bostonmax pooled.BostonPb pooled.Bostonearly2 pooled.BostonPb 

pooled.Bostonavg; 

by ID; 

if peak2 LT 10 then peakl10_2 = 1; 

if peak2 GE 10 then peakl10_2 = 0; 

if peak2 LT 7.5 then peakl75_2 = 1; 

if peak2 GE 7.5 then peakl75_2 = 0; 

keep ID peaklead peak2 peakl10 peakl10_2 peakl75 peakl75_2 early life; 

run; 

data pooled.Lanphearcorrected; 

merge pooled.bostonnewPb (keep = ID peak2 early life peakl10_2 peakl75_2) 

pooled.tablespaper; 

by ID; 

if Site = "Boston" then iq = wiscr10v; 

if Site = "Boston" then meanlead6m_24m = early; 

if Site = "Boston" then meanlead6m_concurrent = life; 

if Site = "Boston" then peaklead = peak2; 

if Site = "Boston" then if peakl10 = 1 then if peakl10_2 = 1 then peakl10 = 

1; 

if Site = "Boston" then if peakl10 = 0 then if peakl10_2 = 0 then peakl10 = 

0; 
8

if Site = "Boston" then if peakl10 = 0 then if peakl10_2 = 1 then peakl10 = 

1; 

if Site = "Boston" then if peakl75 = 1 then if peakl75_2 = 1 then peakl75 = 

1; 

if Site = "Boston" then if peakl75 = 0 then if peakl75_2 = 0 then peakl75 = 

0; 

if Site = "Boston" then if peakl75 = 0 then if peakl75_2 = 1 then peakl75 = 

1; 

if lead=0 then lead=0.1; 

loglead = log(lead); 

logpeak = log(peaklead); 

logearly = log(meanlead6m_24m); 

loglife = log(meanlead6m_concurrent); 

run; 

proc freq; tables peakl10 peakl75; run; 

proc glm; 

class site; 

model wiscr10t = lead/ solution ss3; 

where site = "Boston"; 

run; 

proc glm; 

class site; 

model wiscr10p = lead/ solution ss3; 

where site = "Boston"; 

run; 

proc glm; 

class site; 

model wiscr10t = pbch2y/ solution ss3; 

where site = "Boston"; 

run; 

proc glm; 

class site; 

model wiscr10p = pbch2y/ solution ss3; 

where site = "Boston"; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

proc glm; 

class site; 

model iq = logpeak site birthwt HOME momiq momeduc/ solution ss3; 

run; 

proc glm; 

class site; 

model iq = logearly site birthwt HOME momiq momeduc/ solution ss3; 
9

run; 

proc glm; 

class site; 

model iq = loglife site birthwt HOME momiq momeduc/ solution ss3; 

run; 

proc glm; 

class site; 

model iq = lead site birthwt HOME momiq momeduc/ solution ss3; 

where peakl10 = 1; 

run; 

proc glm; 

class site; 

model iq = lead site birthwt HOME momiq momeduc/ solution ss3; 

where peakl10 = 0; 

run; 

proc glm; 

class site; 

model iq = lead site birthwt HOME momiq momeduc/ solution ss3; 

where peakl75 = 1; 

run; 

proc glm; 

class site; 

model iq = lead site birthwt HOME momiq momeduc/ solution ss3; 

where peakl75 = 0; 

run; 

proc sort; by peakl10; run; 

proc univariate; var lead; by peakl10; run; 

proc sort; by peakl75; run; 

proc univariate; var lead; by peakl75; run; 

/*The data steps and models below estimate the concurrent blood Pb-IQ 

association for a log linear model, excluding one of the seven cohorts*/

data pooled.noBos; set pooled.Lanphearcorrected; 

if site EQ "Boston" then delete; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

data pooled.noRoc; set pooled.Lanphearcorrected; 

if site EQ "Rochester" then delete; 

run; 
10

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

data pooled.noCle; set pooled.Lanphearcorrected; 

if site EQ "Cleveland" then delete; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

data pooled.noCin; set pooled.Lanphearcorrected; 

if site EQ "Cincinnati" then delete; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

data pooled.noMC; set pooled.Lanphearcorrected; 

if site EQ "Mexico" then delete; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

data pooled.noPir; set pooled.Lanphearcorrected; 

if site EQ "PortPirie" then delete; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run; 

data pooled.noYug; set pooled.Lanphearcorrected; 

if site EQ "Yugoslavia" then delete; 

run; 

proc glm; 

class site; 

model iq = loglead site birthwt HOME momiq momeduc/ solution ss3; 

run;   
11

Output from Statistical Program

The SAS System

The FREQ Procedure 

peakl10 Frequency Percent Cumulative

Frequency 

Cumulative

Percent 

0 1075 80.65 1075 80.65

1 258 19.35 1333 100.00

peakl75 Frequency Percent Cumulative

Frequency 

Cumulative

Percent 

0 1215 91.15 1215 91.15

1 118 8.85 1333 100.00

 
12

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 1 Boston

Number of Observations Read 116

Number of Observations Used 116

The SAS System

The GLM Procedure 

 

Dependent Variable: wiscr10t IQ Child age 10 WISCR Total 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 1 1522.11305 1522.11305 7.95 0.0057

Error 114 21830.80936 191.49833

Corrected Total 115 23352.92241

R-Square Coeff Var Root MSE wiscr10t Mean

0.065179 11.93222 13.83829 115.9741

Source DF Type III SS Mean Square F Value Pr > F

lead 1 1522.113050 1522.113050 7.95 0.0057

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 121.9329247 2.47346534 49.30 <.0001

lead -0.9731371 0.34517001 -2.82 0.0057

 
13

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 1 Boston

Number of Observations Read 116

Number of Observations Used 116

The SAS System

The GLM Procedure 

 

Dependent Variable: wiscr10p IQ Child age 10 WISCR Performance 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 1 921.62895 921.62895 4.25 0.0415

Error 114 24705.33657 216.71348

Corrected Total 115 25626.96552

R-Square Coeff Var Root MSE wiscr10p Mean

0.035963 12.42475 14.72119 118.4828

Source DF Type III SS Mean Square F Value Pr > F

lead 1 921.6289488 921.6289488 4.25 0.0415

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 123.1194954 2.63127536 46.79 <.0001

lead -0.7572314 0.36719226 -2.06 0.0415

 
14

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 1 Boston

Number of Observations Read 116

Number of Observations Used 115

The SAS System

The GLM Procedure 

 

Dependent Variable: wiscr10t IQ Child age 10 WISCR Total 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 1 627.48956 627.48956 3.14 0.0791

Error 113 22580.80610 199.83014

Corrected Total 114 23208.29565

R-Square Coeff Var Root MSE wiscr10t Mean

0.027037 12.17810 14.13613 116.0783

Source DF Type III SS Mean Square F Value Pr > F

pbch2y 1 627.4895565 627.4895565 3.14 0.0791

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 120.1845551 2.66597270 45.08 <.0001

pbch2y -0.4821070 0.27206377 -1.77 0.0791

 
15

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 1 Boston

Number of Observations Read 116

Number of Observations Used 115

The SAS System

The GLM Procedure 

 

Dependent Variable: wiscr10p IQ Child age 10 WISCR Performance 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 1 1077.37320 1077.37320 4.99 0.0275

Error 113 24416.59201 216.07604

Corrected Total 114 25493.96522

R-Square Coeff Var Root MSE wiscr10p Mean

0.042260 12.39602 14.69953 118.5826

Source DF Type III SS Mean Square F Value Pr > F

pbch2y 1 1077.373204 1077.373204 4.99 0.0275

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 123.9631987 2.77222516 44.72 <.0001

pbch2y -0.6317181 0.28290689 -2.23 0.0275

 
16

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 7 Boston Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia 

Number of Observations Read 1333

Number of Observations Used 1333

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 11 327940.4682 29812.7698 214.79 <.0001

Error 1321 183352.3915 138.7982

Corrected Total 1332 511292.8597

R-Square Coeff Var Root MSE iq Mean

0.641395 12.60802 11.78126 93.44261

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 3474.24421 3474.24421 25.03 <.0001

site 6 66081.41209 11013.56868 79.35 <.0001

birthwt 1 2621.37601 2621.37601 18.89 <.0001

home 1 10179.85113 10179.85113 73.34 <.0001

momiq 1 12795.37214 12795.37214 92.19 <.0001

momeduc 1 967.67984 967.67984 6.97 0.0084

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 27.04732556 B 3.76475269 7.18 <.0001

loglead -2.65193533 0.53005952 -5.00 <.0001

site Boston 17.65819126 B 1.90163535 9.29 <.0001

site Cincinnati 12.84631794 B 1.31942912 9.74 <.0001

site Cleveland 11.83109308 B 1.43718597 8.23 <.0001

site Mexico 25.64990185 B 1.51558784 16.92 <.0001

site PortPirie 22.00255364 B 1.21043737 18.18 <.0001

site Rochester 7.11903041 B 1.48288723 4.80 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00286312 0.00065882 4.35 <.0001

home 0.52537002 0.06134603 8.56 <.0001
17

Parameter Estimate Standard Error t Value Pr > |t|

momiq 0.28757382 0.02995124 9.60 <.0001

momeduc 0.42930586 0.16258963 2.64 0.0084

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
18

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 7 Boston Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia 

Number of Observations Read 1333

Number of Observations Used 1333

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 11 327276.4058 29752.4005 213.58 <.0001

Error 1321 184016.4540 139.3009

Corrected Total 1332 511292.8597

R-Square Coeff Var Root MSE iq Mean

0.640096 12.63083 11.80258 93.44261

Source DF Type III SS Mean Square F Value Pr > F

logpeak 1 2810.18175 2810.18175 20.17 <.0001

site 6 69681.25928 11613.54321 83.37 <.0001

birthwt 1 2606.40484 2606.40484 18.71 <.0001

home 1 10407.36979 10407.36979 74.71 <.0001

momiq 1 13373.90809 13373.90809 96.01 <.0001

momeduc 1 1007.34017 1007.34017 7.23 0.0073

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 27.91970929 B 4.00880180 6.96 <.0001

logpeak -2.85587349 0.63584122 -4.49 <.0001

site Boston 18.36212688 B 1.88672487 9.73 <.0001

site Cincinnati 14.06412178 B 1.28253969 10.97 <.0001

site Cleveland 11.39642871 B 1.44278400 7.90 <.0001

site Mexico 26.51500475 B 1.49312461 17.76 <.0001

site PortPirie 22.91283492 B 1.23280694 18.59 <.0001

site Rochester 8.01829313 B 1.43377664 5.59 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00285535 0.00066011 4.33 <.0001

home 0.53083774 0.06141412 8.64 <.0001
19

Parameter Estimate Standard Error t Value Pr > |t|

momiq 0.29342850 0.02994677 9.80 <.0001

momeduc 0.43788970 0.16283718 2.69 0.0073

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
20

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 7 Boston Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia 

Number of Observations Read 1333

Number of Observations Used 1308

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 11 323379.5236 29398.1385 212.53 <.0001

Error 1296 179272.5926 138.3276

Corrected Total 1307 502652.1162

R-Square Coeff Var Root MSE iq Mean

0.643347 12.58240 11.76128 93.47401

Source DF Type III SS Mean Square F Value Pr > F

logearly 1 1888.26101 1888.26101 13.65 0.0002

site 6 68546.00714 11424.33452 82.59 <.0001

birthwt 1 2390.13312 2390.13312 17.28 <.0001

home 1 10145.18428 10145.18428 73.34 <.0001

momiq 1 13737.96496 13737.96496 99.31 <.0001

momeduc 1 1083.28832 1083.28832 7.83 0.0052

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 24.63768949 B 3.73034439 6.60 <.0001

logearly -2.20591751 0.59705275 -3.69 0.0002

site Boston 18.15626038 B 1.91778407 9.47 <.0001

site Cincinnati 14.27745674 B 1.27856877 11.17 <.0001

site Cleveland 11.46422442 B 1.49254021 7.68 <.0001

site Mexico 26.84805362 B 1.48914619 18.03 <.0001

site PortPirie 23.05313333 B 1.24749405 18.48 <.0001

site Rochester 8.42417190 B 1.42756207 5.90 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00275146 0.00066192 4.16 <.0001

home 0.52954367 0.06183385 8.56 <.0001
21

Parameter Estimate Standard Error t Value Pr > |t|

momiq 0.29979643 0.03008290 9.97 <.0001

momeduc 0.45768747 0.16355034 2.80 0.0052

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
22

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 7 Boston Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia 

Number of Observations Read 1333

Number of Observations Used 1333

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 11 327804.7469 29800.4315 214.54 <.0001

Error 1321 183488.1128 138.9009

Corrected Total 1332 511292.8597

R-Square Coeff Var Root MSE iq Mean

0.641129 12.61269 11.78562 93.44261

Source DF Type III SS Mean Square F Value Pr > F

loglife 1 3338.52290 3338.52290 24.04 <.0001

site 6 69505.74205 11584.29034 83.40 <.0001

birthwt 1 2517.77496 2517.77496 18.13 <.0001

home 1 10236.98947 10236.98947 73.70 <.0001

momiq 1 13381.00079 13381.00079 96.33 <.0001

momeduc 1 961.34341 961.34341 6.92 0.0086

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 28.24337513 B 3.92416837 7.20 <.0001

loglife -3.13865602 0.64020506 -4.90 <.0001

site Boston 17.45724787 B 1.91192335 9.13 <.0001

site Cincinnati 13.56169824 B 1.29159931 10.50 <.0001

site Cleveland 11.69697796 B 1.43791274 8.13 <.0001

site Mexico 26.13585581 B 1.49932438 17.43 <.0001

site PortPirie 22.78026468 B 1.22364122 18.62 <.0001

site Rochester 7.22001411 B 1.48020263 4.88 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00280762 0.00065945 4.26 <.0001

home 0.52671510 0.06135390 8.58 <.0001
23

Parameter Estimate Standard Error t Value Pr > |t|

momiq 0.29347023 0.02990008 9.82 <.0001

momeduc 0.42795513 0.16267152 2.63 0.0086

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
24

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Cleveland Mexico Rochester Yugoslavia

Number of Observations Read 258

Number of Observations Used 258

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 75391.2023 7539.1202 47.95 <.0001

Error 247 38835.9140 157.2304

Corrected Total 257 114227.1163

R-Square Coeff Var Root MSE iq Mean

0.660011 13.09652 12.53916 95.74419

Source DF Type III SS Mean Square F Value Pr > F

lead 1 446.063013 446.063013 2.84 0.0934

site 5 8345.359497 1669.071899 10.62 <.0001

birthwt 1 2038.632694 2038.632694 12.97 0.0004

home 1 906.185584 906.185584 5.76 0.0171

momiq 1 3043.925976 3043.925976 19.36 <.0001

momeduc 1 260.774911 260.774911 1.66 0.1990

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 18.18613910 B 8.59218349 2.12 0.0353

lead -0.76511302 0.45425088 -1.68 0.0934

site Boston 18.85551296 B 4.09764496 4.60 <.0001

site Cincinnati 10.80388499 B 3.63189262 2.97 0.0032

site Cleveland 17.27306085 B 4.78283355 3.61 0.0004

site Mexico 23.71313388 B 3.63731021 6.52 <.0001

site Rochester 6.72724026 B 2.92871503 2.30 0.0225

site Yugoslavia 0.00000000 B . . .

birthwt 0.00602932 0.00167443 3.60 0.0004

home 0.39015482 0.16251621 2.40 0.0171

momiq 0.31503186 0.07159880 4.40 <.0001
25

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.55327718 0.42961372 1.29 0.1990

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
26

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 7 Boston Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia 

Number of Observations Read 1075

Number of Observations Used 1075

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 11 252365.1647 22942.2877 170.54 <.0001

Error 1063 143005.8827 134.5305

Corrected Total 1074 395371.0474

R-Square Coeff Var Root MSE iq Mean

0.638300 12.48649 11.59873 92.89023

Source DF Type III SS Mean Square F Value Pr > F

lead 1 1177.57910 1177.57910 8.75 0.0032

site 6 50057.16148 8342.86025 62.01 <.0001

birthwt 1 1209.19905 1209.19905 8.99 0.0028

home 1 9026.17315 9026.17315 67.09 <.0001

momiq 1 9548.68378 9548.68378 70.98 <.0001

momeduc 1 793.78352 793.78352 5.90 0.0153

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 24.20220118 B 3.86515250 6.26 <.0001

lead -0.13305168 0.04497132 -2.96 0.0032

site Boston 17.80470393 B 2.30699971 7.72 <.0001

site Cincinnati 13.35800457 B 1.53156221 8.72 <.0001

site Cleveland 11.17455053 B 1.58088679 7.07 <.0001

site Mexico 26.43625875 B 1.74854717 15.12 <.0001

site PortPirie 21.98066621 B 1.34566292 16.33 <.0001

site Rochester 7.07573613 B 1.88609692 3.75 0.0002

site Yugoslavia 0.00000000 B . . .

birthwt 0.00215064 0.00071735 3.00 0.0028

home 0.54576743 0.06662943 8.19 <.0001
27

Parameter Estimate Standard Error t Value Pr > |t|

momiq 0.28269110 0.03355449 8.42 <.0001

momeduc 0.42897703 0.17660106 2.43 0.0153

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
28

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Cleveland Mexico Rochester Yugoslavia

Number of Observations Read 118

Number of Observations Used 118

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 32060.86131 3206.08613 17.10 <.0001

Error 107 20060.90141 187.48506

Corrected Total 117 52121.76271

R-Square Coeff Var Root MSE iq Mean

0.615115 13.92620 13.69252 98.32203

Source DF Type III SS Mean Square F Value Pr > F

lead 1 1208.290980 1208.290980 6.44 0.0126

site 5 2414.540703 482.908141 2.58 0.0306

birthwt 1 1312.897431 1312.897431 7.00 0.0094

home 1 1684.201650 1684.201650 8.98 0.0034

momiq 1 203.024510 203.024510 1.08 0.3004

momeduc 1 372.404312 372.404312 1.99 0.1616

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 25.71242076 B 13.97200329 1.84 0.0685

lead -2.52649591 0.99521329 -2.54 0.0126

site Boston 6.68339913 B 7.20701358 0.93 0.3558

site Cincinnati 28.61890969 B 14.93280507 1.92 0.0580

site Cleveland -7.91036480 B 15.64398146 -0.51 0.6141

site Mexico 10.97187362 B 7.11090999 1.54 0.1258

site Rochester -3.90103867 B 5.82471299 -0.67 0.5045

site Yugoslavia 0.00000000 B . . .

birthwt 0.00678705 0.00256477 2.65 0.0094

home 0.86121562 0.28734139 3.00 0.0034

momiq 0.12432473 0.11947214 1.04 0.3004
29

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 1.04376665 0.74059265 1.41 0.1616

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
30

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 7 Boston Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia 

Number of Observations Read 1215

Number of Observations Used 1215

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 11 295595.2682 26872.2971 201.42 <.0001

Error 1203 160493.5433 133.4111

Corrected Total 1214 456088.8115

R-Square Coeff Var Root MSE iq Mean

0.648109 12.42393 11.55037 92.96872

Source DF Type III SS Mean Square F Value Pr > F

lead 1 1856.41937 1856.41937 13.92 0.0002

site 6 59575.72492 9929.28749 74.43 <.0001

birthwt 1 1731.15356 1731.15356 12.98 0.0003

home 1 8914.66922 8914.66922 66.82 <.0001

momiq 1 12447.67461 12447.67461 93.30 <.0001

momeduc 1 871.14627 871.14627 6.53 0.0107

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 23.53661203 B 3.56150039 6.61 <.0001

lead -0.15329940 0.04109589 -3.73 0.0002

site Boston 18.19392517 B 2.03397309 8.95 <.0001

site Cincinnati 13.11021920 B 1.37249065 9.55 <.0001

site Cleveland 11.72102156 B 1.45049515 8.08 <.0001

site Mexico 26.48978529 B 1.57859524 16.78 <.0001

site PortPirie 21.84772381 B 1.23476009 17.69 <.0001

site Rochester 6.92986243 B 1.61490719 4.29 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00245251 0.00068083 3.60 0.0003

home 0.50965282 0.06234732 8.17 <.0001
31

Parameter Estimate Standard Error t Value Pr > |t|

momiq 0.30003407 0.03106150 9.66 <.0001

momeduc 0.42343226 0.16570453 2.56 0.0107

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
32

The SAS System

The UNIVARIATE Procedure 

Variable: lead 

peakl10=0 

Moments

N 1075 Sum Weights 1075

Mean 14.0349963 Sum Observations 15087.621

Std Deviation 9.73241339 Variance 94.7198704

Skewness 1.92115744 Kurtosis 4.82297042

Uncorrected SS 313483.845 Corrected SS 101729.141

Coeff Variation 69.3438972 Std Error Mean 0.29683583

Basic Statistical Measures

Location Variability

Mean 14.03500 Std Deviation 9.73241

Median 11.10000 Variance 94.71987

Mode 12.00000 Range 71.60000

 Interquartile Range 9.44571

Tests for Location: Mu0=0

Test Statistic p Value

Student's t t 47.28202 Pr > |t| <.0001

Sign M 537.5 Pr >= |M| <.0001

Signed Rank S 289175 Pr >= |S| <.0001

Quantiles (Definition 5)

Level Quantile

100% Max 71.70000

99% 48.90000

95% 35.50000

90% 26.50000

75% Q3 17.04571

50% Median 11.10000

25% Q1 7.60000

10% 5.20000

5% 4.37780

1% 2.00857

0% Min 0.10000

Extreme Observations

Lowest Highest
33

Value Obs Value Obs

0.1 691 56.3 476

0.8 699 60.3 564

0.9 725 63.6 546

1.1 721 68.3 481

1.4 694 71.7 553
34

The SAS System

The UNIVARIATE Procedure 

Variable: lead 

peakl10=1 

Moments

N 258 Sum Weights 258

Mean 4.40229389 Sum Observations 1135.79182

Std Deviation 2.04490428 Variance 4.18163352

Skewness 0.30846374 Kurtosis -0.3937443

Uncorrected SS 6074.76923 Corrected SS 1074.67981

Coeff Variation 46.4508806 Std Error Mean 0.12731018

Basic Statistical Measures

Location Variability

Mean 4.402294 Std Deviation 2.04490

Median 4.300000 Variance 4.18163

Mode 4.000000 Range 9.70000

 Interquartile Range 2.79204

Tests for Location: Mu0=0

Test Statistic p Value

Student's t t 34.57928 Pr > |t| <.0001

Sign M 129 Pr >= |M| <.0001

Signed Rank S 16705.5 Pr >= |S| <.0001

Quantiles (Definition 5)

Level Quantile

100% Max 9.80000

99% 9.50000

95% 8.00000

90% 7.40000

75% Q3 5.79204

50% Median 4.30000

25% Q1 3.00000

10% 1.80000

5% 1.40000

1% 0.10000

0% Min 0.10000

Extreme Observations

Lowest Highest
35

Value Obs Value Obs

0.1 1290 9.0 1271

0.1 1288 9.0 1328

0.1 1266 9.5 1284

0.5 1257 9.7 1182

0.9 1296 9.8 1259

 
36

The SAS System

The UNIVARIATE Procedure 

Variable: lead 

peakl75=0 

Moments

N 1215 Sum Weights 1215

Mean 13.0307607 Sum Observations 15832.3743

Std Deviation 9.59106571 Variance 91.9885414

Skewness 1.99140977 Kurtosis 5.20797771

Uncorrected SS 317981.971 Corrected SS 111674.089

Coeff Variation 73.6032676 Std Error Mean 0.27515584

Basic Statistical Measures

Location Variability

Mean 13.03076 Std Deviation 9.59107

Median 10.10000 Variance 91.98854

Mode 8.00000 Range 71.60000

 Interquartile Range 9.43328

Tests for Location: Mu0=0

Test Statistic p Value

Student's t t 47.35775 Pr > |t| <.0001

Sign M 607.5 Pr >= |M| <.0001

Signed Rank S 369360 Pr >= |S| <.0001

Quantiles (Definition 5)

Level Quantile

100% Max 71.70000

99% 47.40000

95% 34.20000

90% 24.60000

75% Q3 16.00000

50% Median 10.10000

25% Q1 6.56672

10% 4.70000

5% 3.69096

1% 1.78971

0% Min 0.10000

Extreme Observations

Lowest Highest
37

Value Obs Value Obs

0.1 1181 56.3 476

0.1 1168 60.3 564

0.1 691 63.6 546

0.5 1165 68.3 481

0.8 699 71.7 553
38

The SAS System

The UNIVARIATE Procedure 

Variable: lead 

peakl75=1 

Moments

N 118 Sum Weights 118

Mean 3.31388564 Sum Observations 391.038506

Std Deviation 1.54915623 Variance 2.39988502

Skewness 0.55062293 Kurtosis -0.1167017

Uncorrected SS 1576.64344 Corrected SS 280.786548

Coeff Variation 46.7474257 Std Error Mean 0.14261139

Basic Statistical Measures

Location Variability

Mean 3.313886 Std Deviation 1.54916

Median 3.150000 Variance 2.39989

Mode 1.500000 Range 7.30000

 Interquartile Range 2.30000

Note: The mode displayed is the smallest of 4 modes with a count of 6.

Tests for Location: Mu0=0

Test Statistic p Value

Student's t t 23.23717 Pr > |t| <.0001

Sign M 59 Pr >= |M| <.0001

Signed Rank S 3510.5 Pr >= |S| <.0001

Quantiles (Definition 5)

Level Quantile

100% Max 7.40

99% 7.10

95% 6.70

90% 5.30

75% Q3 4.40

50% Median 3.15

25% Q1 2.10

10% 1.50

5% 1.10

1% 0.90

0% Min 0.10
39

Extreme Observations

Lowest Highest

Value Obs Value Obs

0.1 1323 6.8 1244

0.9 1328 7.0 1227

1.0 1305 7.0 1249

1.1 1302 7.1 1317

1.1 1279 7.4 1325

 
40

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Cincinnati Cleveland Mexico PortPirie Rochester Yugoslavia

Number of Observations Read 1217

Number of Observations Used 1217

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 236289.1250 23628.9125 173.27 <.0001

Error 1206 164459.3614 136.3676

Corrected Total 1216 400748.4864

R-Square Coeff Var Root MSE iq Mean

0.589620 12.83549 11.67766 90.97946

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 3316.01053 3316.01053 24.32 <.0001

site 5 64980.50802 12996.10160 95.30 <.0001

birthwt 1 2064.61424 2064.61424 15.14 0.0001

home 1 9235.31461 9235.31461 67.72 <.0001

momiq 1 12385.71930 12385.71930 90.83 <.0001

momeduc 1 613.66271 613.66271 4.50 0.0341

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 28.31031692 B 4.05184024 6.99 <.0001

loglead -2.94149749 0.59650787 -4.93 <.0001

site Cincinnati 13.04475988 B 1.33636189 9.76 <.0001

site Cleveland 12.27990700 B 1.44363380 8.51 <.0001

site Mexico 25.62621387 B 1.51767586 16.89 <.0001

site PortPirie 22.18590267 B 1.20511010 18.41 <.0001

site Rochester 7.11859842 B 1.52466887 4.67 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00266431 0.00068473 3.89 0.0001

home 0.50824816 0.06175976 8.23 <.0001

momiq 0.30374683 0.03187181 9.53 <.0001
41

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.34980816 0.16490002 2.12 0.0341

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
42

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Cleveland Mexico PortPirie Yugoslavia

Number of Observations Read 1151

Number of Observations Used 1151

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 301590.5468 30159.0547 219.39 <.0001

Error 1140 156711.1509 137.4659

Corrected Total 1150 458301.6977

R-Square Coeff Var Root MSE iq Mean

0.658061 12.36916 11.72459 94.78888

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 2322.19475 2322.19475 16.89 <.0001

site 5 59773.32662 11954.66532 86.96 <.0001

birthwt 1 2608.68551 2608.68551 18.98 <.0001

home 1 10457.29282 10457.29282 76.07 <.0001

momiq 1 9406.63788 9406.63788 68.43 <.0001

momeduc 1 739.22161 739.22161 5.38 0.0206

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 26.07614527 B 3.97911701 6.55 <.0001

loglead -2.31061277 0.56217998 -4.11 <.0001

site Boston 18.04273067 B 1.97692421 9.13 <.0001

site Cincinnati 12.77102289 B 1.33566531 9.56 <.0001

site Cleveland 11.18448251 B 1.46074838 7.66 <.0001

site Mexico 25.80176014 B 1.52495154 16.92 <.0001

site PortPirie 21.62285075 B 1.23691384 17.48 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00308899 0.00070909 4.36 <.0001

home 0.58105614 0.06662021 8.72 <.0001

momiq 0.26364705 0.03187155 8.27 <.0001
43

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.39387949 0.16985313 2.32 0.0206

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
44

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Mexico PortPirie Rochester Yugoslavia

Number of Observations Read 1173

Number of Observations Used 1173

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 308275.4062 30827.5406 234.54 <.0001

Error 1162 152729.8828 131.4371

Corrected Total 1172 461005.2890

R-Square Coeff Var Root MSE iq Mean

0.668703 12.14944 11.46460 94.36317

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 3022.54666 3022.54666 23.00 <.0001

site 5 65075.88660 13015.17732 99.02 <.0001

birthwt 1 2307.57510 2307.57510 17.56 <.0001

home 1 6986.65200 6986.65200 53.16 <.0001

momiq 1 11915.16399 11915.16399 90.65 <.0001

momeduc 1 770.11737 770.11737 5.86 0.0156

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 27.51857675 B 3.87345880 7.10 <.0001

loglead -2.54225360 0.53014090 -4.80 <.0001

site Boston 18.55257917 B 1.91467978 9.69 <.0001

site Cincinnati 13.24172997 B 1.30690892 10.13 <.0001

site Mexico 26.05459883 B 1.48350394 17.56 <.0001

site PortPirie 22.59583498 B 1.20903911 18.69 <.0001

site Rochester 7.50313658 B 1.46561772 5.12 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00285799 0.00068209 4.19 <.0001

home 0.47427309 0.06505083 7.29 <.0001

momiq 0.29944622 0.03145052 9.52 <.0001
45

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.40255200 0.16630391 2.42 0.0156

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
46

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cleveland Mexico PortPirie Rochester Yugoslavia

Number of Observations Read 1112

Number of Observations Used 1112

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 313841.9568 31384.1957 218.57 <.0001

Error 1101 158093.1790 143.5905

Corrected Total 1111 471935.1358

R-Square Coeff Var Root MSE iq Mean

0.665011 12.65061 11.98293 94.72212

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 3321.62903 3321.62903 23.13 <.0001

site 5 59842.10955 11968.42191 83.35 <.0001

birthwt 1 2357.38692 2357.38692 16.42 <.0001

home 1 10370.91496 10370.91496 72.23 <.0001

momiq 1 10750.08253 10750.08253 74.87 <.0001

momeduc 1 1078.77503 1078.77503 7.51 0.0062

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 25.48075164 B 4.05088278 6.29 <.0001

loglead -2.76180365 0.57422242 -4.81 <.0001

site Boston 16.22337927 B 2.00273592 8.10 <.0001

site Cleveland 11.13427107 B 1.49803361 7.43 <.0001

site Mexico 25.09169853 B 1.55566677 16.13 <.0001

site PortPirie 21.17719673 B 1.27218362 16.65 <.0001

site Rochester 6.68369193 B 1.54435902 4.33 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00292387 0.00072162 4.05 <.0001

home 0.59096264 0.06953675 8.50 <.0001

momiq 0.27935355 0.03228577 8.65 <.0001
47

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.47313581 0.17261689 2.74 0.0062

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
48

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Cleveland PortPirie Rochester Yugoslavia

Number of Observations Read 1234

Number of Observations Used 1234

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 305942.1337 30594.2134 218.46 <.0001

Error 1223 171274.3136 140.0444

Corrected Total 1233 477216.4473

R-Square Coeff Var Root MSE iq Mean

0.641097 12.82310 11.83404 92.28687

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 3476.10559 3476.10559 24.82 <.0001

site 5 45483.33503 9096.66701 64.96 <.0001

birthwt 1 2414.20185 2414.20185 17.24 <.0001

home 1 10341.08090 10341.08090 73.84 <.0001

momiq 1 11780.92409 11780.92409 84.12 <.0001

momeduc 1 1584.80597 1584.80597 11.32 0.0008

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 25.20951687 B 3.90233377 6.46 <.0001

loglead -2.71812947 0.54557762 -4.98 <.0001

site Boston 16.01877770 B 1.96826866 8.14 <.0001

site Cincinnati 12.29350792 B 1.34303009 9.15 <.0001

site Cleveland 11.24709835 B 1.46550263 7.67 <.0001

site PortPirie 21.35910778 B 1.23659062 17.27 <.0001

site Rochester 6.40031930 B 1.51516383 4.22 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00283174 0.00068202 4.15 <.0001

home 0.55594817 0.06469701 8.59 <.0001

momiq 0.28421399 0.03098765 9.17 <.0001
49

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.59716095 0.17751548 3.36 0.0008

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
50

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Cleveland Mexico Rochester Yugoslavia

Number of Observations Read 1009

Number of Observations Used 1009

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 246690.2118 24669.0212 180.55 <.0001

Error 998 136358.2758 136.6315

Corrected Total 1008 383048.4876

R-Square Coeff Var Root MSE iq Mean

0.644018 13.07309 11.68895 89.41229

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 3223.85781 3223.85781 23.60 <.0001

site 5 45113.93818 9022.78764 66.04 <.0001

birthwt 1 2502.40199 2502.40199 18.31 <.0001

home 1 8590.24972 8590.24972 62.87 <.0001

momiq 1 7888.02907 7888.02907 57.73 <.0001

momeduc 1 1182.19474 1182.19474 8.65 0.0033

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 28.71600442 B 4.05775291 7.08 <.0001

loglead -2.69462287 0.55473495 -4.86 <.0001

site Boston 18.62337754 B 1.96821003 9.46 <.0001

site Cincinnati 12.30165902 B 1.33582155 9.21 <.0001

site Cleveland 11.27614573 B 1.46050926 7.72 <.0001

site Mexico 25.73828816 B 1.51617881 16.98 <.0001

site Rochester 6.67150502 B 1.49897680 4.45 <.0001

site Yugoslavia 0.00000000 B . . .

birthwt 0.00323999 0.00075708 4.28 <.0001

home 0.52255782 0.06590327 7.93 <.0001

momiq 0.25030865 0.03294330 7.60 <.0001
51

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.48953177 0.16642243 2.94 0.0033

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

 
52

The SAS System

The GLM Procedure 

Class Level Information

Class Levels Values

site 6 Boston Cincinnati Cleveland Mexico PortPirie Rochester

Number of Observations Read 1102

Number of Observations Used 1102

The SAS System

The GLM Procedure 

 

Dependent Variable: iq 

Source DF Sum of Squares Mean Square F Value Pr > F

Model 10 208387.6679 20838.7668 143.06 <.0001

Error 1091 158916.8439 145.6616

Corrected Total 1101 367304.5118

R-Square Coeff Var Root MSE iq Mean

0.567343 12.38230 12.06904 97.47005

Source DF Type III SS Mean Square F Value Pr > F

loglead 1 2251.58532 2251.58532 15.46 <.0001

site 5 21482.32642 4296.46528 29.50 <.0001

birthwt 1 1496.10389 1496.10389 10.27 0.0014

home 1 5461.31821 5461.31821 37.49 <.0001

momiq 1 12867.67901 12867.67901 88.34 <.0001

momeduc 1 130.12532 130.12532 0.89 0.3448

Parameter Estimate Standard Error t Value Pr > |t|

Intercept 36.99610669 B 4.36665378 8.47 <.0001

loglead -2.65025139 0.67408623 -3.93 <.0001

site Boston 10.78809989 B 2.16658747 4.98 <.0001

site Cincinnati 5.83336114 B 1.30120035 4.48 <.0001

site Cleveland 5.27530315 B 1.68870552 3.12 0.0018

site Mexico 18.19553876 B 1.68636293 10.79 <.0001

site PortPirie 14.88475591 B 1.73534651 8.58 <.0001

site Rochester 0.00000000 B . . .

birthwt 0.00242194 0.00075571 3.20 0.0014

home 0.43765670 0.07147554 6.12 <.0001

momiq 0.33599202 0.03574798 9.40 <.0001
53

Parameter Estimate Standard Error t Value Pr > |t|

momeduc 0.22179064 0.23465774 0.95 0.3448

Note: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by 

the letter 'B' are not uniquely estimable. 

  

   
54

Derivation of IQ Decrements over Various Blood Pb Ranges

A B C D E F G H I J K L Model coefficient for concurrent blood Pb 

lower confidence limit 

upper confidence limit 

minimum blood Pb in range of interest 

maximum blood Pb in range of interest 

ln of minimum blood Pb 

ln of maximum blood Pb 

difference in ln of blood Pb 

difference in maximum and minimum blood Pb of interest 

slope over the blood Pb range of interest 

lower confidence limit for slope over the blood Pb range of interest 

upper confidence limit for slope over the blood Pb range of interest 

-2.65 -3.69 -1.61 2.4 30 0.88 3.40 2.53 27.6 -0.24 -0.34 -0.15 -2.65 -3.69 -1.61 2.4 10 0.88 2.30 1.43 7.6 -0.50 -0.69 -0.30 -2.65 -3.69 -1.61 10 20 2.30 3.00 0.69 10 -0.18 -0.26 -0.11 -2.65 -3.69 -1.61 20 30 3.00 3.40 0.41 10 -0.11 -0.15 -0.07 Formula for cell =LN(D) =LN(E) =G-F =E-D =A*H/I =B*H/I =C*H/I 
55

ATTACHMENT 2  

Emails from R. Hornung  (May 1, 2014) and B. Lanphear (February 24, 2014)