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Abstract:
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Sigmoid curve is prevalent in biological sciences: from bioassay, to dose-response or growth curve. We compare three typical models: (4P) logistic, (4P) Gompertz, and Richards (aka "5PL") models. We also propose a new, flexible, model which is a 5P extension of the Gompertz curve. Nonlinearity with respect to the parameters is not only the defining characteristic of a nonlinear model, but the degree of which is also central to the fidelity of the first order approximations that is the basis of standard statistical treatment. Close-to-linear nonlinear models are more conductive to typical statistical inference and numerical fitting. We develop several new measures to quantify the concept of close-to-linear. We demonstrate in a case study that logistic, Gompertz, and the new models are close-to-linear, while Richards model is not.
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