Uncertainty distributions for cancer potency factors: Laboratory animal carcinogenicity bioassays and interspecies extrapolation

Current methodology uses a multistage dose-response formula to represent the dose-response curve of laboratory bioassays adequately at high doses, and to extrapolate to low doses. Standard likelihood methods are described to evaluate an uncertainty distribution for the linear term of the multistage formula, exactly analogous to the current method of obtaining a ''95% confidence limit.'' In the standard methodology, the number of terms in the dose-response formula and the assumed form for the distribution used to obtain the ''95% confidence limit'' are somewhat arbitrarily chosen. Modifications are described that allow consistent (although still arbitrary) treatment of all experiments, and potentially allow incorporation of mechanistic ideas about the correctness of the low-dose extrapolation. Also described are extensions that allow incorporation of results from multiple experiments into the uncertainty distribution. The result is a probability distribution for cancer potency factor in laboratory animals. Empirical results describing the extrapolation between species of the linear term of multistage dose-response formulas are presented, and a method is given for analysis of any dose-response model. It is shown that the interspecies extrapolation as currently performed is well represented by a lognormal distribution with well defined standard deviation but a median that depends on the species, and that is not representable by any simple allometric scaling law. The best available animal/human comparisons are analyzed in similar fashion to show consistency with the ideas presented, and obtain the best estimates for animal to human extrapolation.