i u du br According
i ( u )du
According to the multiplicative risk model, that is the excess relative risk model, animals exposed to a daily dose D have the cumulative hazard function:
and the cumulative risk among animals exposed to a daily dose D, Pi(D), will thus be:
The observed number of glycidol-responding neoplasms, assumed to be binomially distributed, was fitted to the proposed model by non-linear regression model, by the maximum likelihood method using PROC NLIN in SAS 9.4 (SAS Institute Inc., Cary, NC, USA). A common relative risk coefficient per dose unit, β, was estimated for males and females, and separately for rats and mice. The relative risk is expressed as the doubling dose (1/β), which is the dose that leads to a cumulative
hazard of 2αi. The evaluation was performed based both on adminis-tered dose (mg/kg) and on AUC (mMh), derived from Hb adducts in blood, acting as a surrogate measurement for target dose of glycidol (assuming an even distribution of glycidol throughout the body that would mean approximately the same dose in blood as in the target tissues). The predicted number of animals with neoplasms was esti-mated as Ni(D) × Pi(D), where Ni(D) is the number animals examined for site i and dose D and was compared to the corresponding observed neoplasms.
3.1. In vivo dosimetry of glycidol in short-term exposure studies
The measured Hb adduct levels (and AUC) increased with increasing exposure dose for both mice and rats with large individual variations at each dose level (Fig. 1). This variation is independent of the analytical precision (cf. Supplementary Figs. S1 and S2) and is most probably due to inter-individual differences in dosing and toxicokinetics. Higher le-vels of Hb adducts per administered dose were observed in rats com-pared to mice (p < 0.001). The data do not contradict an assumption of linearity, which would imply no saturation of the E 64d of glycidol at the administered doses. The internal doses (AUC) of glycidol in the exposed animals were calculated from the measured Hb adduct levels and the second-order reaction rate constant, kval (Equations (1) and (2)), for respective species. The second-order rate constant, kval, for formation of the adducts from glycidol to Hb was determined in vitro to be 19.3 (18.3–20.2, 95% CI) pmol/g per μMh and 23.7 (20.8–26.6, 95% CI) pmol/g per μMh for mice and rats, respectively (see Supplementary Fig. S2). In the in vivo short-term exposure experiments, no statistically significant differences in the adduct levels (or AUC) were observed between the sexes of either species exposed to glycidol (Table 1, Fig. 1). Therefore, the mean AUCday per administered dose (of both sexes) was calculated and used in the further evaluation of the risk model. The mean AUCday per administered dose observed in rats, 2.9 ± 1.6 μMh/ day per mg/kg, was about twice prostaglandins observed in mice, 1.6 ± 0.6 μMh/ day per mg/kg (p < 0.01).
3.2. Evaluation of the multiplicative risk model
The evaluation of the applicability of the relative (multiplicative) risk model (Equation (5)) to the tumor data from published carcino-genicity studies (Irwin et al., 1996; NTP, 1990) was performed by using the cumulative dose over a lifetime (D) expressed both as administered dose (mg/kg) and internal dose (mMh). The internal dose estimates were derived from Hb adduct levels obtained from the performed short-term exposure studies with glycidol in mice and rats. The risk
Measured Hb adduct levels and corresponding daily internal doses (AUC) in mice and rats treated with glycidol by gavage for five consecutive days. The mean values were calculated from three animals per dose level.
Daily dose Hb adduct level
a Measured Hb adduct levels adjusted for elimination due to erythrocyte lifetime ( × 1.1 for mice and × 1.07 for rats) for calculation of the internal dose according to Equations (1) and (2), n.a.: not applicable.
Comparison of the relative cancer risk of glycidol, expressed as β per dose (per mg/kg/day or per mMh, corresponding to the lifetime dose) or expressed as doubling dose, 1/β (mMh). The parameters were calculated from data from carcinogenicity studies in mice and rats and measurements of the internal dose of glycidol (per administered dose) in short-term exposure studies.
Mean relative risk coefficient (β) [95% CI] Mean doubling dose (1/
Relative risk increase Relative risk increase mMh
a The AUC per lifetime administered dose (mg/kg/day), calculated from the short-term in vivo studies, was used to transfer to the % risk increase per mMh, 1.6 μMh per mg/kg/day (mean for female and male mice) and 2.9 μMh per mg/ kg/day (mean from female and male rats).
Fig. 2. Predicted versus observed incidence of tumors in mice and rats applying the relative risk model (section 2.5), using the observed tumor incidence in treatment-responding sites reported in the 2-year carcinogenicity studies of glycidol (Irwin et al., 1996; NTP, 1990). Analysis of the residuals reveals no serious lack of fit for the suggested model. The scaled deviance for both mice and rats was 1.22, compared to the expected value of unity. The scaled de-viances for mice and rats separately were 1.12 and 1.32, respectively.