Detecting and Estimating Hormesis Using a Model-Based Approach

Abstract

Hormesis is defined as a dose-response relationship that is stimulatory at low doses, but is inhibitory at higher doses. In a given experiment, it is not unusual to observe enhanced responses at low doses, however, such enhanced responses may not imply hormesis, but the random fluctuation of the data. Statistical tests can be developed to detect hormesis when enhanced responses at low concentrations are observed. We propose the use of a model-based approach to detect the presence of, and estimate the extent of, hormesis. This approach includes two steps: detection and estimation. In the detection step, we compare the full and the reduced models. The full model describes the dose-response relationship incorporating the hormetic effect; the reduced model describes the dose-response relationship without the hormetic effect. The full model is an extension of the reduced model and has an extra parameter that measures the amount of increase in response at low doses. A test of statistical significance of this extra parameter can essentially be a test for detecting hormesis. In the estimation step, we obtain the area under the best-fitted dose-response curve falling within the hormetic zone. Considering both the number of concentrations within the hormetic zone and the magnitude of the stimulatory response, we propose using the ratio of the area under the hormetic zone (AUC_H) and the area under the best-fitted curve from zero to zero equivalent point (AUC_ZEP) as an estimate of magnitude of the hormetic effect. Two numerical examples are used to illustrate the use of this model-based approach.

Keywords:

• hormesis
• model-based
• AUC
• Zero Equivalent Point (ZEP)
• Whole Effluent Toxicity.