Statistical dose-response models with hormetic effects

Monotonically increasing or decreasing functions are often used to model th e relationship between the response of an experimental unit and the dose of a given substance. Of late, there has been an increased interest in dose-r esponse relationships that exhibit hormetic effects. These effects may be c haracterized by an increase in response at low doses instead of the expecte d decrease in response that is observed at higher doses. Herein, we study t he statistical implications of hormesis in several ways. First, we present a broad class of parametric mathematical-statistical models, constructed fr om standard dose-response models, that allow the incorporation of hormetic effects in such a way that the presence of hormesis can be tested statistic ally. Second, we consider the impact of model misspecification on effective dose estimation, such as the ED50 and the limiting dose for stimulation, w hen the hormetic effect is present but ignored in the dose-response model b y the researcher (model underspecification) and when an hormetic effect is not present but incorporated into the dose-response model (model overspecif ication). Our simulation study reveals that it is more damaging to the esti mation of effective dose to ignore the hormetic effect through model unders pecification than to include the hormetic effect in the model through model overspecification. Third, we develop a nonparametric regression technique useful as an exploratory procedure to indicate hormetic effects when presen t. Finally, both parametric and nonparametric methods are illustrated with an example.