Carcinogenic Potency Factors and RfD values derived by EPA are 

 listed in the IRIS database. At present, values for these toxicological 

 indices are being standardized for agency-widp use. A brief overview 

 of methods by which these indices are derived is presented below. 



The Carcinogen Assessment Group of EPA currently uses the linear- 

 ized multistage procedure to derive Carcinogenic Potency Factors 

 (U.S. EPA 1980b, 1985a, 1986a, 1987a). The multistage model assumes 

 that carcinogenesis results from a series of interactions between the 

 carcinogenic chemical and DNA, with the rate of interactions linearly 

 related to dose. For example, a chemical may induce a mutation in the 

 DNA of a cell to initiate carcinogenesis. However, a series of further 

 interactions between DNA and the same chemical (or another one) 

 may be necessary to promote carcinogenesis and induce a tumor. The 

 multistage model is the model most frequently used by EPA when there 

 is no convincing biological evidence to support application of an 

 alternative model. Other models include the logit, probit, single-hit, 

 and WeibuU models (Food Safety Council 1980, 1982; Hogan and Hoel 

 1982; Cothern et al. 1986). At high doses (corresponding to lifetime 

 risks greater than about 10"^), all currently used models yield generally 

 similar risk estimates. Below risks on the order of 10'^ the models 

 diverge increasingly as dose declines. In the low-dose range, the 

 linearized multistage model generally predicts risks similar to the 

 single-hit (i.e., linear) model. For many data sets, both of these models 

 yield higher estimates of low-dose risk than do other models (U.S. EPA 

 1980b; Hogan and Hoel 1982; U.S. Office of Science and Technology 

 Policy 1985). 



The mathematical form of the multistage model for a specified car- 

 cinogen is: 



where: 



R(d) 



R(d) = 1 - exp [-(qid + q2d2 + . . . + qtd'')] 



(1) 



= Excess lifetime risk of cancer (over background at 

 dose d) (dimensionless) 



qi values = Coefficients [kg day mg'^ (i.e., the inverse of dose 

 units)] 



d = Dose (mg kg' day" ) 



Jc = Degree of the polynomial used in the multistage 



model. 



U.S. EPA (1987a) described the linearized multistage procedure as 

 follows: 



• The multistage model is fitted to the data on tumor incidence 

 vs. dose 



• The maximum linear term consistent with the dose-response 

 data is calculated, which essentially defines the linear portion 

 of the dose-response function at low doses 



Carcinogenic Potency 

 Factors 



25 



