A regression spline model for developmental toxicity data.

Observed dose-response patterns of data from several developmental toxicity experiments appear to be nonlinear and should be characterized by an appropriate model to adequately fit this observed pattern. Information from these animal studies of ambient substances that are noncarcinogenic, yet potentially toxic, to humans is used by federal protection agencies (Environmental Protection Agency, Occupational Safety and Health Administration, Food and Drug Administration) to determine safe exposure levels, such as no observed adverse effects level and benchmark dose. We have developed a flexible regression linear B-spline model for application to developmental toxicity dose-response data from animal studies of these noncarcinogens. We apply our model to data from two CD-1 mice studies of the National Toxicology Program; the observed dose-response pattern from both appears nonlinear: (1) experiment of 131 pregnant mice allocated over five exposure levels (0, 0.025, 0.05, 0.10, and 0.15% diet) of diethylhexyl phthalate and (2) experiment of 111 pregnant mice exposed to five levels (0, 62.5, 125, 250, and 500 mg/kg/day) of diethylene glycol dimethyl ether. In each study, we measure litter response as the proportion of adversely affected fetuses. Upon applying our B-spline model to the data from both studies, we predict nonlinear dose-response, with improvement over the more typical logistic dose-response model in each of the two studies.