Limited usefulness of mathematical models for assessing the carcinogenic risk of minute doses

No mathematical model for carcinogenesis can cover all the exigencies of life. The usefulness of any model is consequently limited. A model may provide a basis for graduating data, though it need not be altogether valid to give reasonable graduations in the observable range and competing models could do as well. Or for providing useful insights into situations, a model need not be completely valid. But for the problematic issue of extrapolating to minute doses, the question of validity is crucial. A variety of related issues and approaches are discussed, beginning with a kinetic model proposed by Cornfield. Other discussions relate to the empirical relationship described by Druckrey, the linear model approach espoused by Crump and Guess and their associates, the safe dose estimation procedure of Hartley and Sielken and the relation of these approaches to the Mantel-Bryan approach. Issues like between-species extrapolation, limiting concern to near lifetime risks, occupational exposures vs. general population exposures are also considered.