title: Modeling non-monotonic dose-response relationships: model evaluation and hormetic quantities exploration.
abstract: Non-monotonic (biphasic) dose-response relationships, known as hormetic relationships, have been observed across multiple experimental systems. Several models were proposed to describe non-monotonic relationships. However, few studies provided comprehensive description of hermetic quantities and their potential application. In this study, five biphasic models were used to fit five hormetic datasets from three different experimental systems of our lab. The bisection algorithm based on individual monotone functions was proposed to calculate arbitrary hormetic quantities instead of traditional methods (e.g., model reparameterization) which need complex mathematical manipulation. Results showed that all the five biphasic models could describe those datasets fairly well with coefficient of determination ( R(2) adj) greater than 0.95 and root mean square error (RMSE) smaller than 0.10. The best-fit model could be selected based on EC(R10), RMSE, and a supplemental criterion of Akaike information criterion (AIC). Hormetic quantities that trigger 10% stimulation at the left (EC(L10)) and right (EC(R10)) side of stimulatory peak were calculated and emphasized for their implication in hormesis exploration for the first time. Furthermore, the EC(L10), proposed as an alarm threshold for hormesis, was expected to be useful in risk assessment of environmental chemicals. This study lays a foundation in the quantitative description of the low dose hormetic effect and the investigation of hormesis in environmental risk assessment.
authors.affiliation: Key Laboratory of Yangtze River Water Environment, Ministry of Education, College of Environmental Science and Engineering, Tongji University, Shanghai 200092, PR China.
authors.forename: Xiang-Wei
authors.initials: XW
authors.lastname: Zhu
authors.forename: Shu-Shen
authors.initials: SS
authors.lastname: Liu
authors.forename: Li-Tang
authors.initials: LT
authors.lastname: Qin
authors.forename: Fu
authors.initials: F
authors.lastname: Chen
authors.forename: Hai-Ling
authors.initials: HL
authors.lastname: Liu
mesh_terms: D004305:Dose-Response Relationship, Drug; D059165:Hormesis; D006801:Humans; D008954:Models, Biological; D018570:Risk Assessment / Q000379:methods*