**Suggested Citation:**"6.1 Extrapolation from Rats to Mice." National Research Council. 1993.

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

may be used to relate carcinogenic potency (P) to body weight (BW). A value of b = 1 corresponds to interspecies extrapolation on the basis of body weight, whereas b = 2/3 corresponds to extrapolation roughly on the basis of body surface area. Travis & White (1988) suggest an intermediate value of b = 3/4 (cf. Watanabe et al., 1992), which corresponds roughly to extrapolation on the basis of metabolic rate (Schmidt-Nielsen, 1984).

**6.1** **Extrapolation from Rats to Mice**

Quantitative interspecies extrapolation of measures of carcinogenic potency such as the TD_{50} may also be based on empirical observations of potency in the two target species, provided that the agents of interest are effective in both species. Crouch & Wilson (1979) demonstrated a positive correlation between rats and mice in carcinogenic potency expressed in terms of the slope coefficient ß in the one-hit model in (2.2). Subsequently, Crouch (1983) suggested that interspecies extrapolation of carcinogenic potency would generally be accurate to within a factor of about 4.5.

Gaylor & Chen (1986) compared the relative carcinogenic potency of chemicals in rats, mice, and hamsters based upon the TD_{50}s given by Gold et al. (1984). Since current practice generally is to base risk estimates upon the data set producing the highest cancer risk, the minimum TD_{50} was selected for each chemical in each species for each route of administration. The largest subset of relative potencies was obtained for rats and mice for 190 chemicals administered in the diet. With dose expressed in terms of mg/kg body weight/day, the geometric mean of the ratio of the minimum TD_{50} value for rats relative to that for mice was 0.45. For dose expressed in terms of concentration (ppm) in the diet, however, the mean ratio was 1.3. Using either dose metric, the mean carcinogenic potency of these chemicals in rats and mice agree to within a factor of about two-fold. The ratio R of the TD_{50} values for rats and mice were approximately lognormally distributed, with log_{10}R exhibiting a standard deviation of 0.82; this corresponds to a multiplicative factor of 10^{0.82} ˜ 7-fold. For 4 of the 190 chemicals, the ratios of

**Suggested Citation:**"6.1 Extrapolation from Rats to Mice." National Research Council. 1993.

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

the TD_{50}s for rats and mice differed by more than a factor of 100.

Chen & Gaylor (1987) used results from the NCI/NTP Carcinogenesis Bioassay Program to compare cancer risk estimates for rats relative to those for mice for chemicals administered orally. The 10^{-6} RSD was calculated for rats and mice for those chemicals that showed a dose-response trend in the same sex at the same tissue/organ site in both species. In all, 69 comparisons of RSDs between rats and mice for 38 rodent carcinogens were made. The overall geometric mean of the RSD ratios for rats to mice was 1.27, with dose was measured in terms of concentration (ppm) in the diet. The logarithms of the ratios of RSDs were approximately normally distributed with a standard deviation of 0.79, corresponding to a multiplicative factor of approximately 6-fold. The RSD ratios varied from 1:51 to 49:1 for the 69 cases. Without the restriction of tumors at the same sex and site in both species, the geometric mean of the ratio of the minimum RSDs of rats to mice was 1.38 with a standard deviation of log_{e} ratios of 0.78. It appears that relative potencies for rats and mice are generally within a multiplicative factor of 100-fold for rodent carcinogens. However, McGregor (1992) recently noted that amides and halides tended to exhibit disparate TD_{50}s in rats and mice.

Bernstein et al. (1985) suggested that this apparent interspecies correlation in carcinogenic potency simply reflects the corresponding high correlation in MTDs for rats and mice. This provoked a debate as to the interpretation of these results on interspecies potency correlation (Crouch et al., 1987; Reith & Starr, 1989b).

Reith & Starr (1989b) obtained a correlation of r = 0.83 on a logarithmic scale between potency estimates for n = 83 chemicals selected from the CPDB identified as carcinogens in both rats and mice. (In this analysis, potency was defined as the slope ß in (2.3), calculated using the TD_{50} values given in the CPDB.) They argued that the correlations arise from (i) the strong interspecies correlation between MTDs in chronic bioassays, (ii) the small numbers of animals used per dose group, and (iii) the narrow range of doses typically tested. Reith & Starr (1989b) further noted a high correlation for chemicals testing negative in both species (r = 0.85, n = 51), for chemicals testing positive in rats but negative in mice (r = 0.55, n = 15), and for chemicals testing negative in rats but positive in mice (r = 0.68, n = 25). Reith & Starr (1989b) recomputed these correlations after dividing each poten-

**Suggested Citation:**"6.1 Extrapolation from Rats to Mice." National Research Council. 1993.

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

cy estimate by the MDT. The largest correlation (r = 0.27) was obtained for chemicals testing negative in both rats and mice; none of the four recomputed correlations was significantly greater than zero (p > 0.05).

To further illustrate the correlation in TD_{50} values for rats and mice, consider the data on 127 of the 492 rodent carcinogens discussed by Gold et al. (1989) which are carcinogenic in both species. These data demonstrate a high correlation between TD_{50} values for rats and mice (Figure 5), with a Pearson correlation of 0.808.

This observation may also be derived analytically (annex E). Let us assume that the MDTs for the rat and mouse carcinogens are both lognormally distributed, with MTD_{rats} = cMTD_{mice}. (Although Bernstein et al., 1985, estimate c to be 0.357, the correlation coefficient is independent of c.) Suppose further that the TD_{50}s for each species are uniformly distributed about the MTD within the 32-fold range considered by Bernstein et al. (1985), and that, given the MTDs for each species, the TD_{50}s for rats and mice are statistically independent. These assumptions lead to a correlation based on equation (E.5) in annex E of 0.943 for the TD_{50} values for rats and mice. The assumption of strict proportionality between MTD rats and MTD mice may be relaxed as discussed in annex E, leading to a reduced correlation of 0.763.

Shlyakhter et al. (1992) studied the correlation between carcinogenic potency and the MTD and the correlation between carcinogenic potencies in rats and mice by computer simulation based upon characteristics of NCI/NTP carcinogenicity tests. This investigation demonstrated that the observed correlation between carcinogenic potency and the MTD could, under certain conditions, produce a correlation which is purely artifactual. However, by comparison with actual bioassay data it was concluded that the observed correlation cannot be an artifact of constraints on the data and therefore must have some biological basis. This suggests that the observed correlation in carcinogenic potency between rats and mice cannot be attributed solely to bioassay design (particularly the MTD), so that the correlation is at least partly attributable to the biological similarity of rodent species.

Freedman et al. (1992) also argue that the correlation in carcinogenic potency between rats and mice is not entirely tautological. This analysis is based on a comparison of models for interspecies correlation that are either entirely artifactual (due to constraints imposed by the MTD) or