Non-linear transformation of enzyme-linked immunosorbent assay (ELISA) measurements allows usage of linear models for data analysis

Abstract

Background: In research questions such as in resistance breeding against the Beet necrotic yellow vein virus it is of interest to compare the virus concentrations of samples from different groups. The enzyme-linked immunosorbent assay (ELISA) counts as the standard tool to measure virus concentrations. Simple methods for data analysis such as analysis of variance (ANOVA), however, are impaired due to non-normality of the resulting optical density (OD) values as well as unequal variances in different groups.

Methods: To understand the relationship between the OD values from an ELISA test and the virus concentration per sample, we used a large serial dilution and modelled its non-linear form using a five parameter logistic regression model. Furthermore, we examined if the quality of the model can be increased if one or several of the model parameters are defined beforehand. Subsequently, we used the inverse of the best model to estimate the virus concentration for every measured OD value.

Results: We show that the transformed data are essentially normally distributed but provide unequal variances per group. Thus, we propose a generalised least squares model which allows for unequal variances of the groups to analyse the transformed data.

Conclusions: ANOVA requires normally distributed data as well as equal variances. Both requirements are not met with raw OD values from an ELISA test. A transformation with an inverse logistic function, however, gives the possibility to use linear models for data analysis of virus concentrations. We conclude that this method can be applied in every trial where virus concentrations of samples from different groups are to be compared via OD values from an ELISA test. To encourage researchers to use this method in their studies, we provide an R script for data transformation as well as the data from our trial.

Keywords: BNYVV; Beet necrotic yellow vein virus; Data analysis; Generalised least squares model; Logistic regression; Serial dilution; Virus concentration.

Fig. 1

The eleven serial dilutions used in this trial and the fitted curves. The dual logarithm of the relative concentration is displayed on the X axis, the corresponding OD value is displayed on the Y axis. Blue line: 5PL model, red line: 5PL model with predefined values for top and bottom asymptote, black dots: observed values