The five-parameter logistic: A characterization and comparison with the four-parameter logistic

Improvements in assay technology have reduced the amount of random variation in measured responses to the point where even slight asymmetry of the assay data can be more significant than random variation. Use of the five-parameter logistic (5PL) function to fit dose–response data easily accommodates such asymmetry. The 5PL can dramatically improve the accuracy of asymmetric assays over the use of symmetric models such as the four-parameter logistic (4PL) function. Until recently, however, the process of fitting the 5PL function has been difficult, with the result that the 4PL function has continued to be used even for highly asymmetric data. Various ad hoc modifications of the 4PL method have been developed in an attempt to address asymmetric data. However, recent advances in numerical methods and assay analysis software have rendered easier the fitting of the 5PL routine. This paper demonstrates how use of the 5PL function can improve assay performance over the 4PL and its variants. Specifically, the improvement in the accuracy of concentration estimates that can be obtained using the 5PL over the 4PL as a function of the asymmetry present in the data is studied. The behavior of the 5PL curve and how it differs from the 4PL curve are discussed. Common experimental designs, which can lead to ill-conditioned regression problems, are also examined.