Modeling Hormesis Using a Non-Monotonic Copula Method

This paper presents a probabilistic method for capturing non-monotonic behavior under the biphasic dose-response regime observed in many biological systems experiencing different types of stress. The proposed method is based on the rolling-pin method introduced earlier to estimate highly nonlinear and non-monotonic joint probability distributions from continuous domain data. We show that the proposed method outperforms the conventional parametric methods in terms of the error (namely RMSE) and it needs fewer parameters to be estimated a priori, while offering high flexibility. The application and performance of the proposed method are shown through an example.