**Suggested Citation:**"2.1 Measures of Carcinogenic Potency." National Research Council. 1993.

*Issues in Risk Assessment*. Washington, DC: The National Academies Press. doi: 10.17226/2078.

Since the maximum dose tested (MDT) in carcinogen bioassay may not always correspond to the maximum tolerated dose (MTD), we note that it may be more appropriate to claim that carcinogenic potency is correlated with the MDT rather than the MTD. However, since highest dose tested in most studies approximates the MTD, we will not always distinguish between the MDT and the MTD in what follows.

Carcinogenic potency has also been shown to be correlated with various measures of toxicity and mutagenic potential (Travis et al., 1990a). The MTD for rats has also been shown to be correlated with the MTD for mice, for carcinogens that are effective in both species, thereby implying a correlation between the TD_{50} values for these two species (Crouch and Wilson, 1979; Reith and Starr, 1989b).

These meta-analytic results have important implications for carcinogenic risk assessment. The correlation between the MTD and TD_{50} has led to suggestions that the latter measure of carcinogenic potency is simply an artifact of the experimental design specifying the highest dose to be used in the bioassay (Bernstein et al., 1985) and of the use of an essentially linear dose-response model to estimate the TD_{50} (Kodell et al., 1990). The existence of such a correlation has also led to suggestions that preliminary estimates of cancer risk may be derived from the MTD in the absence of carcinogen bioassay data (Gaylor, 1989).

In this paper, we examine these and other issues involved in the use of carcinogen bioassay data for risk assessment purposes. In section 2, we discuss measures of carcinogenic potency proposed in the literature. The reasons for the apparent correlation between the MDT and carcinogenic potency are explored in section 3. The prediction of the TD_{50} on the basis of indicators of subchronic toxicity and genotoxicity is discussed in section 4, along with the calculation of preliminary estimates of cancer risk based on the MTD. Evidence for interspecies correlation in carcinogenic potency is reviewed in section 5. Our conclusions regarding the implications of these results for carcinogenic risk assessment are presented in section 6.

**2.** **Carcinogenic Potency**

**2.1** **Measures of Carcinogenic Potency**

Barr (1985) has reviewed a number of proposed measures of carci-

**Suggested Citation:**"2.1 Measures of Carcinogenic Potency." National Research Council. 1993.

*Issues in Risk Assessment*. Washington, DC: The National Academies Press. doi: 10.17226/2078.

nogenic potency. Such indices provide a quantitative measure of carcinogenic potential, which may be used to rank the relative potency of different carcinogens. A widely used measure of potency is the TD_{50} proposed by Peto et al. (1984). Application of the TD_{50} in ranking chemical carcinogens has recently been discussed by Woodward et al. (1991); the TD_{50} also represents a primary component of the multifactor ranking scheme proposed by Nesnow (1990). Letting P(d) denote the probability of a tumor occurring in an individual exposed to dose d, the TD_{50} is defined as the dose d that satisfies the equation

where R(d) is the extra risk over background at dose d. Thus, the TD_{50} is the dose for which the extra risk is equal to 50% or, equivalently, the dose at which the proportion of tumor-free animals is reduced by one-half.

The TD_{50} may be estimated on the basis of tumor response rates observed in laboratory studies involving a series of increasing dose levels. Sawyer et al. (1984) employ an essentially linear one-stage dose-response model for this purpose, with

The slope parameter ß in this one-hit model is related to the TD_{50} by

and has been used as a measure of potency by Crouch and Wilson (1981). To accommodate curvature, however, a nonlinear model such as the multi-stage (Armitage, 1985)

(q_{i} = 0) or Weibull (Kodell et al., 1991)

(a, ß, k > 0) may be more appropriate. We note that the Weibull mod-

**Suggested Citation:**"2.1 Measures of Carcinogenic Potency." National Research Council. 1993.

*Issues in Risk Assessment*. Washington, DC: The National Academies Press. doi: 10.17226/2078.

el is not being proposed for purposes of low dose risk estimation; rather, it is a relatively simple yet flexible model that allows for curvature in the observable response range.

Another measure of potency, which has been used by the U.S. Environmental Protection Agency (1986), is the estimate of the linear term q_{1} in the multi-stage model. Since the extra risk is approximated by

at low doses, the value of q_{1} may be used to estimate the risk associated with environmental exposures to a dose d of a carcinogen. In practice, an upper confidence limit q_{1}* on the value of q_{1} (Crump, 1984a) is used due to the instability of the maximum likelihood estimate of the linear term in the multi-stage model. This application is commonly referred to as the linearized multistage (LMS) model.

Estimates of q_{1}* have been criticized on the grounds that they require extrapolation of data well below the experimentally observable tumor response range. The TD_{50}, on the other hand, does not require low dose extrapolation, but does not lead directly to estimates of risk at environmental exposure levels. Since an added risk of 50% will not always be achieved at the MTD, estimation of the TD_{50} may also require extrapolation outside the experimental dose range, albeit to a lesser degree than with q_{1}*. Of 217 bioassays considered by Krewski et al. (1990b), for example, 65 of the TD_{50} values exceeded the MDT (cf. Munro, 1990). The need to extrapolate above the experimental dose range can be reduced by the use of a lower quantile of the dose-response curve, such as the TD_{25} employed by Allen et al. (1988a). (Note that the TD_{25} will *not* generally be equal to one-half of the TD_{50} in the presence of curvilinear dose-response.)

Arguments in favor of the use of an even lower quantile of the dose-response curve can be made. Crump (1984b) introduced the notion of a benchmmark dose for toxicological risk assessment, which corresponds to a quantile such as the TD_{10}. This benchmark dose is not strongly dependent on the dose-response model used to describe the data (Krewski et al., 1990a), and will likely lead to rankings similar to the TD_{50} or TD _{25}. Cogliano (1986) has recently shown that the TD_{10} is highly correlated with q_{1}*; the TD_{10} could then be used as a starting point for linear extrapolation to lower doses, thereby providing a single index for