Document Yjay4JdQR3G022j4bDoyZXKb0

E. 1. pu Po n t d e Ne mo u r s & Co mp a n y WILMINGTON, DELAWARE 10898 ENGINEERING DEPARTMENT LOUVIERS BUILDING October 26, 197? bee: D. R, Diggs - Orchm,PetLab A. J, Pahnke - Orchm,Wilm S, S. Jacobs - Orchm, PetL'ab W. H. Walsh R. W. Kennard D. W. Marquardt J. M. Lucas IC 31 - Applied Statistics Dr> P. Gordon Hueter, Associate Director . Health Effects Research Laboratory," MD-51 Environmental Protection Agency Research Triangle Park, NO 27711 Dear Dr. Hueter: At the October 7, 1977, meeting of the EPA Science Advisory Board Subcommittee on Lead, Dr. Piomelli and others expressed concern that the slope of the blood lead-air lead relationship may be larger at low air lead levels (i.e. <1,0 pg/m3) than at high air lead levels. Their concern was based on the predictions of the log-log model for the relationship between blood lead and air lead. 1 have studied this question, comparing the results obtained when the Azar data are modeled using both a log-log model and a model similar to that used by Yankel and von Lindern in the Idaho study. Both models fit the data equally well; however, the log-log model predicts blood lead-air lead slopes for air lead levels ssl.O pg/m3 which are two to three times larger than the predicted slopes of the other model* In my judgment the large blood lead slope obtained with the log-log model at low air lead values is an artifact of the model and is not consistent with the actual situation. For instance* the log-log model predicts minus infinity blood lead for zero air lead (log-log form) or zero blood lead for zero air lead (exponential form)'. Neither result is correct, hence the log-log model cannot be considered valid for low air lead values. It should be noted that originally we used the log-log model in the analysis of the Azar data so that we could compare our results with those of Goldsmith and Hexter and test the statistical significance of the blood lead-air lead relationship. We did not intend for this log-log model to be used for predicting at low air lead levels. Philosophically, the principal objective of any analysis is to find a model which gives a good fit to the data and is consistent with the biological response being studied. X believe the "lead exposure" model, which has been discussed in several of our reports on the Air Quality Criteria Document for Lead (see attached discussion) is the most realistic model for the Azar data. TEH 0470669 2 Dr. F. Gordon Hueter October 26, 1977 A discussion of the analyses described above is attached. Please contact me if you have any questions concerning this work. Very truly yours, ENGINEERING SERVICE DIVISION R. D. Snee, Consultant Supervisor Applied Statistics qhro Atch cc: Dr. Sergio Piomelli Dr. Victor Hasselblad TEH 0470670 DUP050083487 TABLE X Azar Blood Lead-Air Lead Data Air Lead Range 0.2-6.0 fig/m3 ------------ - I'Qg-X-og Model in (Blood Pb) = Bj. + .1936 in (Air Pb) Group B Philadelphia Cab Drivers Starke, Florida Barksdale, Wisconsin Los Angeles Cab Drivers Los Angeles Office Workers Model Goodness of Fit (!) 2.8869 2.8139 2.6355 2.8439 2.7319 Res. Std. Dev. .2640, R2 = .48, r | .46 Air Pb (ug/m3 Predicted Blood Lead faeAoog) Phila. Cab Starke Barksdale LA Cab LA Office 0 13.1 12.2 10.2 12.6 11.2 1 17.9 16.7 14.0 17.2 15.4 2 20.5 19.I 16.0 19.7 17.7 5 24.5 22.8 19.1 23.5 21.0 Slope .2-1* 6.0 Slope .2-2* 4.1 5.6 4.8 3.8 3-2 5.8 5.2 3.9 3.6 Change in blood lead per unit change in air lead over the air lead range 0.2-1.0 and 0.2-2.0 ng/nP, respectively. (1) R2 = fraction of the total sum of squares explained by the model, R2 * adjusted r 2 = fraction of the total variance explained by the model. TEH 0470671 DUP050083488 N42489.01 TABLE 2 Azar Blood Lead-Air Lead Bata Air Lead Range 0.2-6.0 ug/m3 Log-Quadratic Model (1) In (Blood Pb) Bj. + .1752 Air Pb - .00866 (Air Pb)2 Group B Philadelphia Cab Drivers Starke, Florida Barksdale, Wisconsin Los Angeles Cab Drivers Los Angeles Office Workers 2.6730 2.5834 2.3933 2.4033 2.4922 Model Goodness of Fit (2) Res. Std. Dev. - .2640, R2 .48, r | = .46 Air Pb Predicted Blood Lead (ug/100g) Phila. Cab Starke Barksdale LA Cab LA Office 0 14.5 13.2 10.9 12.0 12.1 l 17.1 15.6 12.9 14.2 14.3 2 19-9 18.2 15.O 16.4 16.6 5 28.0 25.6 21.2 23-2 23.4 Slope 0 -1* Slope 0 -2* 2.6 2.7 2.4 2.0 2.5 2.0 2.2 2.2 2.2 2.2 (1) Predicted maximum blood Pb at Air Pb - -(,1752)/(2(-.OO866)) = 10.1 ng/m3. Quadratic coefficient not statistically significant (p > .50). * Change in blood lead per unit change in air lead over the air lead range 0-1 and 0-2 ug/m3, respectively. (2) R2 = fraction of the total sum of squares explained by the model, r - adjusted R2 = fraction of the total variance explained by the model. TEH 0470672 DUP050083489 TABLE 3 Azar Blood Lead-Air Lead Data Air Lead Range 0.2-9.1 ug/m3 Log-Quadratic Model (1) In (Blood Pb) = BL + .1795 (Air Fb) - .0156 (Air Pb)12. Philadelphia Cab Drivers Starke, Florida Barksdale, Wisconsin Los Angeles Cab Drivers Los Angeles Office Workers B 2.7103 2.5889 2.|849 2.6639 2.5473 Res. St.d.. Dev, = .2577, R2 * *50, R| * .48 Air Pb Predicted Blood Lead (Mg/100g) (ug/m3) Phila. Cab Starke Barksdale LA- Cab 0 15*0 I3.3 10,9 14.4 1 17*7 IS*? 12.8 I6.9 2 20.2 17.9 14.6 19*3 5 25*0 22.1 18.0 23*8 10 19*0 16.8 13.7 18.2 LA Offj 12.8 15*0 17.2 21.2 16.2 Slope 0- 1* Slope 0- 2* 2.7 2.6 2.4 1.9 2.3 1.8 2,5 2.2 2.4 2.2 (1) Predicted maximum blood lead at air lead -.1795/(2(-.0156)) * 5*8 ug/m3. Quadratic coefficient statistically significant (P < *05) * Change in blood lead per unit change in air lead over the air lead range 0-1 and 0-2 ug/nP, respectively, (2) R2 * fraction of the total sum of squares explained by the model, Rs = adjusted R2 = fraction of the total variance explained by the model. TEH 0470673 DUP050083490 TABLE 4 Azar Blood Lead-Air Lead Bata Air Lead Range 0.2-9*1 ug/m3 ______Lead Exposure Model in (Blood Pb) 2,4965 + *2669 (Air Bh + Bj.) or Blood PL - 12,1 (Air PL + Bt)-2669 Group B Philadelphia Cab Drivers Starke, Florida Barksdale, Wisconsin Los Angeles Cab Drivers Los Angeles Office Workers Model Goodness of Fit (1) 6.00 1.46 .44 6.26 2.23 Average 3*28 Res * Std. Dev. * .2597, R2 - .49, r | .47 Air Pb (ug/m3") 0 1 2 5 Predicted Blood Lead iug/lOOg) Ehila. Cab Starke Barksdale LA Cab 19-6 13.4 9.8 19-8 20,4 15*4 13,4 20.6 21.1 16.9 15.4 21.3 23.O 20,0 I9.I 23-2 XA Office 15.0 I6.6 17.8 20.6 Slope 0-1* Slope 0-2* 0.8 0.8 2.0 3-6 1.8 2.8 0.8 1.6 0.8 1.4 Change in blood lead per unit change in air lead over the air lead range 0-1 and 0-2 pg/m3, respectively, (1) R2 fraction of the total sum of squares explained by the model, R? = adjusted R2 * fraction of the total variance explained by the model. 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