2. Introduction

Logit regression can be used to fit sigmoidal (S-shaped) curves to almost straight lines.

Calibration lines with a sigmoidal shape are dose-response curves that approach asymptotically to a maximum response. With the formulae calculated for the logit regression line and the measured response of the unknown sample, the dose or concentration in a sample is calculated and multiplied with the dilution made.

The average concentration is calculated from the multiple measurements of the same sample.

Parameters in the worksheet can be set to signal poor reproducibility of the averaged concentration, extrapolation of the measurement area, significant digits of the result and the name of an import and export file.

Logit regression has its origins in research of population growth.

On behalf of King Willem I, mathematician Verhulst was commissioned in 1838 to calculate the maximum population for Belgium on the basis of the population size established in 1815, 1830 and 1845. He calculated 9.5 million inhabitants (now 11 million). His calculation method was rediscovered around 1920.

The logit variant described in this document was described by Finney in 1971 in the third edition of the book "Statistical Method in biological assay".

For decades there were many discussions about the use of regression techniques in sigmoidal dose-response curves. The mathematical variations are known under the names: Logit, Probit, Rodbard, 4-parameter fit, logistic function, sigmoid function.

They all fit sigmoidal curves.

This logit variant uses and needs a response of the blank. This is especially useful when measuring low concentrations as are often done with ELISA’s and RIA’s

The logit algorithm was programmed on an HP9815 RPN calculator around 1976.

The Microsoft Excel version is a further development of versions written in Lotus, GW-Basic, Quick-Basic and C. The program was first written on January 17, 1998 in Excel in the password-protected Visual Basic for Application (VBA).

The programming languages and environments quickly became outdated at that time, Microsoft Excel was chosen. It was expected to remain unchanged and "backwards compatible" for a longer period of time.

This version V01Jul2018 has a few changes compared to the last validated and described version. V03Feb2013'_1.V24May2017 -> Bug fix in matrices in Logit and Datasheet. They will not be sorted after sorting. Some textual changes. GAMP-5 validated releaseV01Jan2018 -> Added Spline curve fit, date format under export button (O9)V01Feb2018 -> Changed> and <limits, ie LLOQ and ULOQ, now based on concentration instead of min and max response.

V01Mrt2018 -> Added non-linearity calculation from "Introduction to medical statistics, 2nd edition 1964, Preventive Medicine, Leiden", chapter 19 Made iteration steps smaller resulting is a slightly better fit (correlation)V01Jul2018 -> Final validated release. Disabled p non-linearity calculation.

A visible change in the results is that the lower and upper limits are now not based on the average response and the associated concentration, but on the concentration of the lowest or highest point of the calibration line. In addition, the spline function has been added.