Statistical models for biphasic dose-response relationships (hormesis) in toxicological studies

The dose-response phenomenon characterized by low dose stimulation and high dose toxicity has been reawakened after a long period of marginalization. This phenomenon termed hormesis is induced by biological, physical and chemical agents and occurs in all groups of living things including whole plants and animals, microorganisms, cells and tissues. Hormesis has attracted increased interest among toxicologists from diverse disciplines, resulting to emergence of new scientific tools for its study. Statistical models have been developed and used to characterize hormesis dose-response relationships. Some of these models include the classical Brain-Cousens model, the Cedergreen-Ritz-Streibig model and their reparameterizations. Other hormesis models are the bilogistic models, their modifications or extensions and the hormesis models used in allelopathy such as An-Johnson-Lovett model. These models are used to describe either U-shaped or inverted U-shaped dose-response relationships and to compute hormesis quantities. This review explored the applications of these models in toxicological studies with emphasis to their strengths and weaknesses.