Statistical modeling of hormesis quantities in inverted U-shaped dose-response relationships by reparameterization of a bilogistic model.

Statistical procedures that allow quantitative determination of hormesis features are required for quantitative characterization of hormesis to provide information on the biphasic dose-response phenomenon and its variability. Only a direct estimate of individual effective doses in hormetic dose-response relationships is possible using prior extensions of the bilogistic model of Beckon and coworkers. This study presented further extensions of the model to determine the toxic potency and hormetic dose zone by estimating two effective doses simultaneously. In addition, the extended models allow for partitioning the hormetic dose zone through the dose of maximum stimulation. This study demonstrated a 4-step statistical modeling approach to quantify 20 hormesis quantities. The applicability and challenges of the mathematical procedures are discussed based on a few examples of hormetic dose-response relationships. The syntaxes for the analyses were provided as Appendix to demonstrate its implementation in SAS® statistical software. Given the variability of hormetic dose-responses generated from toxicological studies in many disciplines, the proposed approach cannot apply to all dose-response patterns. However, we hope the proposed extensions could provide versatile statistical tools for quantitatively exploring a variety of biphasic dose-response curves.