Reference Doses 



• The coefficient of the maximum linear term, designated as qi*, 

 is set equal to the slope of the dose-response function at low 

 doses 



• The resulting estimate of qi* is used as an upper-bound es- 

 timate of the Carcinogenic Potency Factor (termed Slope Fac- 

 tor in U.S. EPA 1987a). 



qi* is usually calculated as the upper 95 percent confidence limit of 

 the estimate of the coefficient qi in Equation 1. 



The model commonly used to estimate plausible-upper-limit risk for 

 low levels of exposure over a lifetime is therefore: 



R (d) = qi* d 



(2) 



where: 



R (d) = Upper-bound estimate of excess lifetime risk of cancer 

 (dimensionless) 



qi* = Upper-bound estimate of carcinogenic potency (kg day 



mg-^) 

 d = Dose (mg kg' day" ). 



Equation 2 represents a linear approximation of the multistage model. 

 Because the slope of the dose-response function at high doses could 

 be different from that at low doses, the use of qi* as an upper-bound 

 estimate of potency is not valid at high levels of exposure. Thus, qi* 

 should not be used as the upper-bound estimate of potency at ex- 

 posures corresponding to excess lifetime risks greater than ap- 

 proximately 10'" per individual (i.e., one excess tumor per 100 exposed 

 individuals). 



If a potency factor is derived from nonhuman data, as is usually the 

 case, it must be extrapolated to humans. Before being applied to 

 humans. Carcinogenic Potency Factors derived from animal data are 

 corrected using surface-area differences between bioassay animals and 

 humans (U.S. EPA 1980b, 1986a). The rationale for using surface-area 

 extrapolations is detailed in Pinkel (1958), Freireich et al. (1966), 

 Dedrick (1973), and Mantel and Schneiderman (1975). The relation- 

 ship between surface-area extrapolation and body-weight extrapola- 

 tion approaches is discussed in the Introduction above (see 

 Background, Relationship of EPA Risk Assessment Methods to FDA 

 Risk Assessment Methods). 



Current methods for predicting human health effects from exposure 

 to noncarcinogenic chemicals rely primarily on the concept of an RfD 

 (U.S. EPA 1987a). The RfD is derived from an observed threshold 

 dose (e.g., NOAEL or LOAEL if the NOAEL is indeterminate) in a 

 chronic animal bioassay by applying an uncertainty factor, which usual- 

 ly ranges from 1 to 1,000 (Dourson and Stara 1983). The relationship 

 between the NOAEL, the RfD, and the uncertainty factor are il- 

 lustrated in Figure 2 above. The uncertainty factor accounts for dif- 

 ferences in threshold doses among species, among intraspecies groups 

 differing in sensitivity, and among toxicity experiments of different 



26 



