Here are some curve-fitting tips for ELISA data analysis:

### 1. Use Weighting to Offset Heteroscedasticity

Heteroscedasticity is a situation that arises in almost all fields, including chemical- and immuno-assays, in which the variance of the dependent variable varies across the data. When dealing with RLU and concentration values, the concentrations usually increase as the RLU increases. When dealing with the high end of the standard curve, it is natural for the concentration values to have a greater variance when compared to the small concentration values on the low end of the standard curve. Many of the regression analyses used in analyzing Luminex data, such as the popular 5PL, **assume equal variance**.

For analyzing ELISA, the **1/Y^2** (preferred) and **1/Y** weighting algorithms are recommended in addition to using the 5-PL model equation.

**1/Y^2**– Minimizes residuals (errors) based on relative RLU values**1/Y**– This algorithm is useful if you know the errors follow a Poisson distribution

Here is an actual case where weighting was able to resurrect data that would otherwise have been useless. The platform and assay is slightly different than ELISA but the underlying concepts of data analysis are identical.

MasterPlex ReaderFit offers these weighting algorithms in addition to a couple of other options.

### 2. Use the 5 Parameter Logistic (5PL) Nonlinear Regression Model

The **5 Parameter Logistic** or **5PL** nonlinear regression model is an asymmetric function that is ideal for analyzing ELISA data. Learn more about the 5PL model equation.

MasterPlex ReaderFit offers the 5PL curve-fit regression model in addition to a number of other curve-fitting model equations.

### 3. Run your samples in replicates

Having replicate samples will bring good karma in addition to the following:

**Backups**– If one sample well is accidentally prepared, you will have backups that you can rely on.**Statistics**– Naturally, you will obtain more reliable results when dealing with a larger pool of data. You will also be able to obtain statistics such as %CV and standard deviation that will tell how much variation or dispersion you have amongst data points of the same replicate group.

MasterPlex ReaderFit allows you to group your replicate samples and automatically generates the **mean**, **%CV**, and **standard deviation** statistics for the **MFI **and **concentration** values.

### 4. Knock out those standard outliers

One of the simplest ways to identify outliers in your standards is by analyzing the **Residuals** and **% Recovery**.

**Residual**= Calculated Concentration – Expected Concentration**% Recovery**= ( Calculated Concentration / Expected Concentration ) * 100

% Recovery is a better metric to use because it is a relative metric. Obviously, the further the % Recovery deviates from 100%, the higher the probability that the data point is an outlier.

Although there is no strict rule or standard on what the limits are for considering outliers, I tend to mark any standard that has < 50% recovery or > 150% recovery as outliers and that has generated pretty good results.

MasterPlex ReaderFit has a user-friendly interface that allows one to view the Residuals, % Recovery, and the Standard Curve all at the same time while being able to mark outliers.

### 5. Use controls

This should go without saying but it is quite alarming for me to see that most of the analysis data files that I see are missing control groups. It should be as important as your background groups. Not only will they tell you if your assay worked but knowing this information is invaluable when it comes time to have to troubleshoot when something goes wrong. The workflow for setting up and running an Elisa assay can become quite complicated and there are many opportunities for things to go awry. Having control groups will keep you sane.

### 6. Use a sufficient standard curve range for your unknowns

Extrapolation is the process of inferring or estimating the concentrations for points that are within calculable limits but outside of the standard curve range. Extrapolations are often less meaningful especially when the values lie on the flatter parts of the curve. Please read this blog post for more on the dangers of extrapolating data.

There are several ways to avoid extrapolating data:

- If your unknown RLU is
**above the standard curve range**, you can dilute the unknown sample enough to bring it back within range and just take the dilution factor into account when calculating your concentrations. MasterPlex ReaderFitallows you to input the dilution factors of your unknown samples and it will automatically take them into account when calculating the concentrations. - If your response value is
**below the standard curve range**, you can create one or more standard groups on the lower end by extending your serial dilutions.

### 7. Individual Standard Points vs. Mean of each Standard Replicate Group

Generally speaking, the more standard points you have (using individual standard points for the curve fit), the better the curve fit because you will have a greater number of degrees of freedom. This method will be more sensitive to outliers though so it is recommended that you first knock out any outliers that you might have and proceed with the standard calculations.

Using the mean of each standard replicate group will lead to less data points and that in turn will lead to a worse curve fit. This method is less susceptible to outliers though if you do not intend to mark them.

MasterPlex ReaderFit let’s the user choose between both these methods.

### 8. Keep it in the Linear Range

In an ideal situation, you will want to be interpolating your unknown concentrations from the dynamic or linear portion of the standard curve. You definitely do not want to be interpolating or extrapolating any concentration values near the top of the curve where it is flat. Minute changes in RLU changes in this part of the curve can lead to huge differences in concentration so any errors that may have occurred will be multiplied by a very large factor.

### 9. Use the 4PL or 5PL for easy EC50/IC50 Determination

Dose response curves are best described using nonlinear regression models such as the 4PL and 5PL. Using these model equations, one can easily determine that the EC50/IC50 values.

**Do you have anything additional tips that you would like to share? If so, please comment below. **

If you are looking for curve-fitting software with the 4PL model equation that also does weighting we have a couple options:

**ReaderFit.com** – Free online curve-fitting application

**Sign Up for Free Account**

**ReaderFit Desktop** – Robust curve-fitting, quality control and reporting desktop software

**Download Free Trial**

You may also be interested in reading our blog post on:

Allen’s “Top Ten” certainly make sense for us when we have been running ELISAs on 4000 samples for an epidemiological study. We have gained some added insights that I offer for consideration: 1) calculate the %CV for each pair of unknown sample replicates (we run duplicates), then plot %CV vs concentration of the unknowns to see if variance is as you expect, 2) periodically run the same set (n=20-30) of ‘normal’ samples through your ELISA method (if doing a large study) to estimate presence of long term drift (calculate medians and distributions), and 3) graphically review the concentrations of controls over long term using a Levey-Jennings or Shuwart plots to look for shifts or drifts in results.

Thanks for the great insight Ted. I guess we are now at “Top 12 Tips” =)

Workshop/Conference Report — Quantitative Bioanalytical Methods

Validation and Implementation: Best Practices for Chromatographic and

Ligand Binding Assays. C. T. Viswanathan et al (The AAPS Journal 2007; 9 (1) Article 4)

Although a bit over the top for most users, this paper offers some very valuable tools and insights for preforming ligand binding assays

Thanks James for sharing this resource! Here is a direct link to the PDF of the article for those that are interested:

http://www.aapsj.org/articles/aapsj0901/aapsj0901004/aapsj0901004.pdf

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