Re-parameterization of five-parameter logistic function

摘要

Recently, the five-parameter logistic (5PL) function has seen increased use as a model for bioassay dose-response curves. The 5PL function takes curve asymmetry into consideration to overcome some drawbacks of the four-parameter logistic (4PL) function. These drawbacks include biased estimates of important model parameters, poor characterization of pharmacological pathways and the mechanisms, and inaccurate inference of drug-receptor interactions. However, currently used 5PL functional form does not have the same practical useful parameter interpretation as the 4PL function. In this paper, we re-parameterize the 5PL function to preserve the practical useful parameter interpretation of the 4PL. Comparing to the currently used 5PL, the re-parameterized 5PL function preserves practical useful parameter interpretation of 4PL and has better statistical properties in terms of bias and mean squared error (MSE).