ALBERT

Notes: A new mathematical dose-response model for reproductive and developmental risk assessment is proposed. The model includes the possibility of an exposure threshold as well as a litter-size effect. Correlation of responses of offspring from the same litter is taken into account through the use of the beta-binomial distribution. Confidence limits for low-dose extrapolation are based on the asymptotic distribution of the likelihood ratio. An empirical comparison of the proposed procedure to that of Rai and Van Ryzin(1) demonstrates the improvement that can be achieved with the new procedure.

Notes: In the absence of data from multiple-compound exposure experiments, the health risk from exposure to a mixture of chemical carcinogens is generally based on the results of the individual single-compound experiments. A procedure to obtain an upper confidence limit on the total risk is proposed under the assumption that total risk for the mixture is additive. It is shown that the current practice of simply summing the individual upper-confidence-limit risk estimates as the upper-confidence-limit estimate on the total excess risk of the mixture may overestimate the true upper bound. In general, if the individual upper-confidence-limit risk estimates are on the same order of magnitude, the proposed method gives a smaller upper-confidence-limit risk estimate than the estimate based on summing the individual upper-confidence-limit estimates; the difference increases as the number of carcinogenic components increases.

Notes: There has been considerable discussion regarding the conservativeness of low-dose cancer risk estimates based upon linear extrapolation from upper confidence limits. Various groups have expressed a need for best (point) estimates of cancer risk in order to improve risk/benefit decisions. Point estimates of carcinogenic potency obtained from maximum likelihood estimates of low-dose slope may be highly unstable, being sensitive both to the choice of the dose–response model and possibly to minimal perturbations of the data. For carcinogens that augment background carcinogenic processes and/or for mutagenic carcinogens, at low doses the tumor incidence versus target tissue dose is expected to be linear. Pharmacokinetic data may be needed to identify and adjust for exposure-dose nonlinearities. Based on the assumption that the dose response is linear over low doses, a stable point estimate for low-dose cancer risk is proposed. Since various models give similar estimates of risk down to levels of 1%, a stable estimate of the low-dose cancer slope is provided by ŝ= 0.01/ED01, where ED01 is the dose corresponding to an excess cancer risk of 1%. Thus, low-dose estimates of cancer risk are obtained by, risk =ŝ× dose. The proposed procedure is similar to one which has been utilized in the past by the Center for Food Safety and Applied Nutrition, Food and Drug Administration. The upper confidence limit, s, corresponding to this point estimate of low-dose slope is similar to the upper limit, q1 obtained from the generalized multistage model. The advantage of the proposed procedure is that ŝ provides stable estimates of low-dose carcinogenic potency, which are not unduly influenced by small perturbations of the tumor incidence rates, unlike q̂1.

Notes: Several existing databases compiled by Gold et al.(1–3) for carcinogenesis bioassays are examined to obtain estimates of the reproducibility of cancer rates across experiments, strains, and rodent species. A measure of carcinogenic potency is given by the TD50 (daily dose that causes a tumor type in 50% of the exposed animals that otherwise would not develop the tumor in a standard lifetime). The lognormal distribution can be used to model the uncertainty of the estimates of potency (TD50) and the ratio of TD50's between two species. For near-replicate bioassays, approximately 95% of the TD50's are estimated to be within a factor of 4 of the mean. Between strains, about 95% of the TD50's are estimated to be within a factor of 11 of their mean, and the pure genetic component of variability is accounted for by a factor of 6.8. Between rats and mice, about 95% of the TD50's are estimated to be within a factor of 32 of the mean, while between humans and experimental animals the factor is 110 for 20 chemicals reported by Allen et al.(4) The common practice of basing cancer risk estimates on the most sensitive rodent species-strain-sex and using interspecies dose scaling based on body surface area appears to overestimate cancer rates for these 20 human carcinogens by about one order of magnitude on the average. Hence, for chemicals where the dose-response is nearly linear below experimental doses, cancer risk estimates based on animal data are not necessarily conservative and may range from a factor of 10 too low for human carcinogens up to a factor of 1000 too high for approximately 95% of the chemicals tested to date. These limits may need to be modified for specific chemicals where additional mechanistic or pharmacokinetic information may suggest alterations or where particularly sensitive subpopu-lations may be exposed. Supralinearity could lead to anticonservative estimates of cancer risk. Underestimating cancer risk by a specific factor has a much larger impact on the actual number of cancer cases than overestimates of smaller risks by the same factor. This paper does not address the uncertainties in high to low dose extrapolation. If the dose-response is sufficiently nonlinear at low doses to produce cancer risks near zero, then low-dose risk estimates based on linear extrapolation are likely to overestimate risk and the limits of uncertainty cannot be established.

Notes: The excess cancer risk that might result from exposure to a mixture of chemical carcinogens usually must be estimated using data from experiments conducted with individual chemicals. In estimating such risk, it is commonly assumed that the total risk due to the mixture is the sum of the risks of the individual components, provided that the risks associated with individual chemicals at levels present in the mixture are low. This assumption, while itself not necessarily conservative, has led to the conservative practice of summing individual upper-bound risk estimates in order to obtain an upper bound on the total excess cancer risk for a mixture. Less conservative procedures are described here and are illustrated for the case of a mixture of four carcinogens.

Notes: A dose-response model is often fit to bioassay data to provide a mathematical relationship between the incidence of a developmental malformation and dose of a toxicant. To utilize the interrelations among the fetal weight, incidence of malformation and number of the live fetuses, a conditional Gaussian regression chain model is proposed to model the dose-response function for developmental malformation incidence using the litter size and/or the fetal weight as covariates. The litter size is modeled as a function of dose, the fetal weight is modeled as a function of dose conditional on the litter size, and the malformation incidence is modeled as a function of dose conditional on both the litter size and the fetal weight, which itself is also conditional on the litter size. Data from a developmental experiment conducted at the National Center for Toxicological Research to investigate the growth stunting and increased incidence of cleft palate induced by Dexamethasone (DEX) exposure in rats was used as an illustration.