Inference for the existence of hormetic dose–response relationships in toxicology studies

In toxicology studies hormesis refers to a dose–response relationship with a stimulatory response at low doses and an inhibitory response at high doses. In this manuscript, we particularly focus on a J-shaped dose–response relationship for binary cancer responses. We propose and examine two new flexible models for testing the hypothesis of hormesis in a Bayesian framework. The first model is parametric and enhances the flexibility of modeling a hormetic zone by using a non-linear predictor in a multistage model. The second model is non-parametric and allows multiple model specifications, weighting the contribution of each model via Bayesian model averaging (BMA). Simulation studies show that the non-parametric modeling approach with BMA provides robust sensitivity and specificity for detecting hormesis relative to the parametric approach, regardless of the shape of a hormetic zone.