Modeling non-monotonic dose-response relationships: model evaluation and hormetic quantities exploration.

Area of Science:

• Toxicology
• Environmental Science
• Biostatistics

Background:

• Non-monotonic (biphasic) dose-response relationships, known as hormetic relationships, are observed across various experimental systems.
• Existing models for non-monotonic relationships often lack comprehensive descriptions of hormetic quantities and their applications.
• Quantitative analysis of hormesis is crucial for understanding low-dose effects and environmental risk assessment.

Purpose of the Study:

• To evaluate five biphasic models for fitting hormetic datasets from different experimental systems.
• To propose and validate a novel bisection algorithm for calculating hormetic quantities, simplifying traditional complex methods.
• To introduce and emphasize the significance of specific hormetic quantities (EC(L10) and EC(R10)) for exploring hormesis and risk assessment.

Main Methods:

• Fitting five distinct biphasic models to five hormetic datasets originating from three laboratory experimental systems.
• Development and application of a bisection algorithm, based on individual monotone functions, for calculating hormetic quantities.
• Selection of the best-fit model using adjusted coefficient of determination (R(2) adj), root mean square error (RMSE), and Akaike information criterion (AIC).

Main Results:

• All five biphasic models demonstrated good data fitting capabilities, with R(2) adj > 0.95 and RMSE < 0.10.
• The bisection algorithm effectively calculated hormetic quantities, offering an alternative to complex model reparameterization.
• Hormetic quantities EC(L10) (left side, 10% stimulation) and EC(R10) (right side, 10% stimulation) were calculated and highlighted for their implications.

Conclusions:

• The study validates the utility of five biphasic models for describing hormetic dose-response data.
• The proposed bisection algorithm provides a robust and simplified method for quantifying hormetic effects.
• EC(L10) is proposed as a valuable alarm threshold for hormesis in environmental chemical risk assessment, laying groundwork for quantitative hormesis investigation.