StatLIA’s 5 Parameter Logistic

The Five Parameter Logistic:  A Characterization and Comparison with the Four-Parameter Logistic, Gottschalk PG, Dunn JR, Analytical Biochemistry, 2005; 343:54-65.  (Free Reprint Available)

StatLIA’s weighted 5 Parameter Logistic curve fitting model has been used for years by many of the most regulated, demanding biopharmaceutical laboratories in the world to compute their validated assays.  Brendan’s scientists and mathematicians have perfected the mathematical techniques over the years to develop a robust, highly accurate 5PL model that consistently defines the best possible curve (global minimum) every assay – even with ill-behaved data.

The 4 parameter logistic model has several advantages over other curve fitting routines, but it has an inherent weakness: it is a symmetrical function and most immunoassay and bioassay data are not symmetrical.  The 5 Parameter Logistic model has the flexibility to fit asymmetrical data. The 4PL, by design, makes one half of the curve exactly symmetrical to the other half.  The 5PL allows each half of the curve to be different.

A common problem for many 5 parameter models is that data sets often have more than one local minimum (a valley in the model’s values that is a local low point).  Many models will get stuck in a sub-optimal local minimum which leads to a correspondingly worse fit. The fit can be negligibly affected or significantly worse, depending on the data.   StatLIA uses sophisticated techniques to determine when it is truly at the minimum of the fitting function, thereby avoiding the problem of stopping too soon with a sub-optimal fit.  Other 5 parameter models can also be trapped by a flat region of data that causes the algorithm to remain in an infinite loop or terminate due to lack of progress in improving the fit.  StatLIA uses sophisticated techniques to avoid these problems as well.