A Novel Approach for Modeling Biphasic Dose–Response Curves

AbstractAbstractEstimates of EC5011 Without loss of generality, an IC50, ED50, or LD50. from dose–response data play an important role in comparing drug potencies. When the sampling data of dose–response studies fail to follow a sigmoidal shaped curve, and the data display a biphasic property at higher dose levels where the response profile concaves and takes an inverted U-shape, this is known as the hook or prozone effect. To address this concern, some research investigators may pursue data removal. Others may choose to ignore the data shape and fit a model blindly. Unfortunately for both practices, the estimates of the fitting parameters, such as the EC50, will be of poor quality and result in misleading inference. The authors propose the use of an empirical and novel extension of a sigmoid model to properly and effectively capture the information from all of the dose–response data, including that of the inverted U-shaped tail. Methods for using 3- and 4-parameter logistic models with examples, are discussed.Keywords: Hook effectHormesisProzoneSigmoid curveSignal processingU-shape curve AcknowledgmentsThe authors gratefully acknowledge the referees and editor for their careful review of our manuscript and for providing many insightful comments and valuable suggestions, all leading to a much improved article. In particular we thank an anonymous referee for the references that the authors were unaware of.Supplementary MaterialsData analysis examples demonstrated in the paper.Disclosure StatementThe authors report there are no competing interests to declare.Additional informationFundingThe author(s) reported there is no funding associated with the work featured in this article.Notes1 Without loss of generality, an IC50, ED50, or LD50.2 In fact, the idea of using sigmoid function as a "switch" was inspired by signal processing image data successfully modeled by the author while a graduate student. Many signal curves of that image data are very similar to the one shown in Figure C.2 and the model fitting and estimation of S, D and R were all successful. Though, later more curve data from the same image study had even more complicated profiles, thus, the final model used became more complex than the switch point model.