Our immunoassays are validated for over 200 analytes, from individual and sandwich-based ELISAs to flow cytometry-based multiplex panels. Our pre-defined panels quantify up to 14 analytes and are designed for your research area. Alternatively, our custom solutions team can build custom panels with your analytes of interest.

Linear and logistic regressions are the two most commonly used curve-fitting models for sandwich immunoassays. Although linear regression may be useful when analyzing samples that fall within the linear portion of the response curve, logistic regression is the preferred regression type for multiplex immunoassays.

Before samples can be analyzed, it is important to choose the best curve fit model to achieve the most accurate and reliable results. Thankfully, you can use our free LEGENDplex™ Data Analysis Software Suite, and the analysis will be done for you and you do not need to use all of the formulas discussed later in the blog. However, they are important for understanding what curve to choose for your analysis.

However, there is an underlying problem here that needs to be addressed. Take an over-simplified example where we are looking at residuals from just 2 data points, A & B. Now, imagine we fit 2 linear curves to the data. The first gives residuals of A = 1 and B = 9, and the second gives A = 5 and B = 5. If we sum the residuals, both curves give the same answer of 10. This is problematic since mathematically they are "equivalent", but clearly the second curve fits the data better as it passes closer to both data points. More simply put, 5 for each is a better fit than 1 and 9. 

The solution to this issue is to square the residual values first, and then add them together. By transforming the data like this, curves with poorer fits and larger residuals will be scored higher and become less desirable. To revisit the example from above, 5² + 5² = 50, and 1² + 9² = 82. Rather than being mathematically equivalent, now the better fit curve has the lower sum of squared residuals.

Using the appropriate curve fitting model is important for generating reliable, high quality data. The "goodness of the curve fit" refers to how well a curve fits the data that has been generated. Linear regression uses the R² value as a good representation of the "goodness of fit". A curve is considered to have a very good fit when the R² value is over 0.99.

We have discussed how linear regression analysis may not be the best for complex biological assays, and the need for more complex modeling is generally necessary. When using a 4PL or 5PL analysis, evaluating the "goodness of fit" is a little more complicated. Two methods of doing so are to measure the recovery of the standards and to perform a spike recovery. 

The closer the recovery is to 100%, the better the curve fit model being used. The general rule of thumb says for accurate quantification, the recovery should fall between 80-120%. Using logistic regression (4PL or 5PL), rather than linear regression, will allow for more accurate quantitation across a wider range.

Spike and recovery is used to test the accuracy of your assay. Spike and recovery experiments are generally used to assess if your sample matrix (plasma, serum, etc.) is causing interference with the ability of the capture and detection antibodies to bind to the target protein being assayed. By adding, or "spiking", a known concentration of the recombinant standard into your sample and comparing this to the same concentration of recombinant spiked into the standard diluent, or blank, you can assess whether anything in your sample matrix is causing interference. You should always include your sample with no spiked recombinant so you are able to measure any endogenous protein that may already be there. All three of these samples are measured and concentrations are determined relative to the standard curve. As with the standard recovery, your spike recovery should also fall between 80-120%.

Our featured LEGENDplex™ Human B Cell Panel is a bead-based multiplex assay panel that quantifies 13 key targets involved in B cell function, activation, proliferation, and survival. It allows simultaneous quantification of 13 human cytokines, which include: TNF-α, IL-2, IL-4, IL-6, IL-10, IL-12p70, IL-13, IL-17A, APRIL, BAFF, CD40L, IFN-γ, and TNF-β, and are collectively secreted by Be1, Be2, Breg, CD4⁺ T lymphocytes, dendritic cells and monocytes. This panel has been validated for use on cell culture supernatant, serum, and plasma samples.

The most common curve fitting models used for ELISAs and multiplexing immunoassays are linear regression and logistic regression. As discussed, the results for biological assays may not fall within the linear portion of the curve, so the need for logistic regression analysis such as 4PL or 5PL is almost always recommended. In our free LEGENDplex™ Data Analysis Software Suite, the default is 5PL. However, the user can opt to use a 4PL fit. In general, the 5PL algorithm provides the best fit regression line to assay data. In addition, the software evaluates the standard curve data using both the 5PL and 4PL algorithms, and then performs a statistical test comparing the goodness of fit for each of the regression lines (F-test comparing the residuals at each standard curve point for each algorithm). If the p-value derived is < 0.05, the 5PL algorithm should be used. If the p-value is non-significant, then either algorithm can be used.

Analyze your immunoassay data with confidence with our resources for ELISA and multiplex immunoassays. Learn how our complimentary LEGENDplex™ Data Analysis Software Suite analyzes flow cytometry data.