Modeling Effective Dosages in Hormetic Dose-Response Studies

Background: Two hormetic modifications of a monotonically decreasing log-logistic dose-response function are most often used to model stimulatory effects of low dosages of a toxicant in plant biology. As just one of these empirical models is yet properly parameterized to allow inference about quantities of interest, this study contributes the parameterized functions for the second hormetic model and compares the estimates of effective dosages between both models based on 23 hormetic data sets. Based on this, the impact on effective dosage estimations was evaluated, especially in case of a substantially inferior fit by one of the two models. Methodology/Principal Findings: The data sets evaluated described the hormetic responses of four different test plant species exposed to 15 different chemical stressors in two different experimental dose-response test designs. Out of the 23 data sets, one could not be described by any of the two models, 14 could be better described by one of the two models, and eight could be equally described by both models. In cases of misspecification by any of the two models, the differences between effective dosages estimates (0–1768%) greatly exceeded the differences observed when both models provided a satisfactory fit (0–26%). This suggests that the conclusions drawn depending on the model used may diverge considerably when using an improper hormetic model especially regarding effective dosages quantifying hormesis. Conclusions/Significance: The study showed that hormetic dose responses can take on many shapes and that this diversity can not be captured by a single model without risking considerable misinterpretation. However, the two empirical models considered in this paper together provide a powerful means to model, prove, and now also to quantify a wide range of hormetic responses by reparameterization. Despite this, they should not be applied uncritically, but after statistical and graphical assessment of their adequacy.