Document bBbDdVz7pODjENj0XOw4bMZVk

...- Health and Welfare Sante et Bien-etre social Canada Canada Health Protect1on Branch Direction generale de Ia protection de Ia sante Room 843 Environmental Health Centre Tunney's PastUR Ottawa. Ontario KIAOL2 JuJy 26, 1993 Dr. Mary Paxton American Petroleum Institute 1220 L Street, Northwest Washington. D.C. 20005 Dear Mary, As requested. I have read over the material you sent us on benzene risk estimation by C. Brown and R. SpiJtas as well as the reply by K. Crump. My comments follow. Spirtas and Brown1 were asked to review Paxton et al.2 Specifically...Jbey addressed three issues: (J) the risk-group stratification, (2) the dose-response function and (3) combining data from Akron and St Mary's locations. K. Crump' commented on the differences between analyses by Paxton et al.2, crump and Brown aDd Spirtas1 aAs pointed out by Crump'. higher log-likelihood does not necessarily mean a better fit. It only means that in total, the curve Is-closer to the observed points. However. this does not address potential lack-of-fit, particularly systematic departw'es of the estimated model from the observed data, and there could be other models with even higher log-likelihoods. One method for assessing lack of fit is to add more parameters to the model. If there- is a significant increase in the Iog-..likelibood. then the original model is not fitting_ the data as well as the oew_model It would also be helpful if Crump' had provided standard errors for the parameter estimates of the expanded models. Brown C. and Spirtas R. (1993) A re-analysis of the leukemogenic risk associated with occupational benzene exposure in tb pliofilm cohort. Unpublished. s.2 ~ton M, Chinchilli V., Brea Rodricks J. (1993) Leukemia risk associated with benzene exposure iD the pliofilm cohort. I. Mortality updata an-a- exposure distribution, and II. Risk estimates, to appear in Risk Analysis. J Crump K. (1993) Reconciliation of results of tluee statistical analyses of the risk of benzene exposure based-on data from the pliofilm cohort. Unpublished. Crump K. (1993) Risk of benzene-induced leukemia derived from pliofilm cohort: effect of additional follow-up and new exposure estimates. J; Tox. Environ. Health, submitted. Canada BP-00011894 , ..::: . 4- .1' Mike Walker of the Biostatistics Section_grapbed the five curves fit by K. Crump' for cumulative doses up to SO ppm-years to view the diffezeoces for low doses and up to 3000 ppm-years to obtain a more global view. ID the first figure. three of the models are quite similar. 'The exponential curve is somewhat flatter than thesethree though stallS rising quickly at- around 1000 ppm-years. 1be power curve raises quickly from the beginning and is much higher than the other four until- 2500 ppmyears when the exponential curve overtakes it._ It is puzzling that the power curve is so different from the others especially since the cumulative exposure for cases is DOt likely to exceed 3000 ppm-years. A graJ:il of data would go a long way to clarify this issue. What about a plot of the relative risk in 500 ppm-year dose intervals? If you can provide this data. we would be happy to do some graphical comparisons. My FAX number is (613) 952-9798. The method of stratifying risk-group did not lead to appreciable differences in parameter estimates for the exponential model and some small differences for the power function model (Paxton'. 1993). For all tbree sets of exposure estimates arid for both models. the Spirtas strata yielded higher maximum log-likelihoods. It would be useful to know oow the differences in parameter estimates translate into differences in estimated relative risks at specific cumulative cxposwes. 1be only comment we have about the Akron and Combined analyses is that we believe that acute myelogenous leukaemia is the response of interest and would prefer to focus on that response. I hope these comments are helpful to you. Please give me a call with any questions that arise.. Sincerely. A{~ Sheryl Bartlett. PhD Head. Biostatistics Section Environmental Health Directorate (613) 954-7787 cc. Dr. D. Krewski Paxton. M. (1993) Exponential vs. Power function as dose-response-in prqportional hazards model. Unpublished table. BP-00011895 Benzene: relative risk vs. dose .0,... co -i - - Exponential: r=exp(px) - Power; r=(1+x)~ r=1-.,.-+ .. - Linearr +Px 1 ---:-'Linear-quadratic: r=1+P1 x+f~ - - - Expanded pow~r: r={1 +ax) '- co .::tt'.~ cw: G) :>; Q) 0: "'t t\1 0 -: 0 ttl ""0 I 0 0 0............ 00 \0 0\ 1o 20 30 40 Dose, x (ppm-years) , . \. ' 50 Benzene: relative risk vs. dose '. .~~. g - - Exponential: r=exp(~x) r Power: r=(1+x)~ ----- Linear: r=1+~x --- Linear-quadratic: r=1+~1x+~~ -~- Expanded power: r=(1+ax) , I' .... 8 T"" ~ (/) 'C ~ ~ I a'CD: 0 lO 0 ...~..... ...../ '.................---==~__..-- ----~=--- ! ~-- ---------__________ ...- ~...::--- 0 500 1000 1500 2000 2500 3000 ttl Dose, x (ppm-years) '"0 I 0 0 0............ 00 \0 -..]