Dose-response models for developmental malformations.

An empirical dose-response model can generally be found for bioassay data, which provides a mathematical relationship between the incidence of a developmental malformation and dose of a toxicant in the experimental dose range. If biological principles and data can be used in the formulation of the dose-response model, the estimation of the incidence of malformations outside of the experimental dose range may be improved. In this paper, exponential growth of morphological structures in rodents during gestation is assumed. Further, it is assumed that some structural malformations are the result of reduced or delayed growth and the incidence of structurally normal fetuses is proportional to fetal weight raised to a power. When the exponential growth rate constant is reduced by dose raised to a power, a Weibull dose-response function is obtained. When the exponential growth rate constant is modeled by a polynomial function of dose, a polynomial-exponential dose-response model is obtained. The Weibull and the polynomial-exponential model, restricted to degrees from one up to the number of dosed groups, were fit to a database of bioassay data assembled from Teratology Vol. 1 (1968) to Vol. 42 (1990). In general the two models gave similar results and often gave exactly the same fit. The linear term appeared in the polynomial-exponential model in about one-fourth of the cases and was not related to the background incidence.