Nonlinear Calibration Model Choice between the Four and Five Parameter Logistic Models

Both the four-parameter logistic (4PL) and the five-parameter logistic (5PL) models are widely used in nonlinear calibration. In this paper, we study the choice between 5PL and 4PL both by the accuracy and precision of the estimated concentrations and by the power to detect an association between a binary disease outcome and the estimated concentrations. Our results show that when the true curve is symmetric around its inflection point, the efficiency loss from using 5PL is negligible under the prevalent experimental design. When the true curve is asymmetric, 4PL may sometimes offer better performance due to bias-variance trade-off. We provide a practical guideline for choosing between 5PL and 4PL and illustrate its application with a real dataset from the HIV Vaccine Trials Network laboratory.