Let’s focus on MFI which stands for Median Fluoresence Intensity and NOT Mean Fluorescense Intensity.

Why do we use median and not mean?

Simply put, the median statistic is less sensitive to outliers where there is an inherent carryover of about 0.9% from these instruments. That is one of the reasons why Luminex recommends at least a minimum bead count of 35 to get statistically significant data but 50-100 is strongly suggested.

Here is an oversimplified example of why median is preferred over mean. Let’s say we are running a 1-plex with just 2 samples: A high control (well A1) and a low control (well A2). We have set a minimum bead count of 11. You will see in a second why I chose this odd number (no pun intended).

When we push the Acquisition button on our imaginary instrument, it begins reading well A1 with our high control and reads the following fluorescence intensities of 11 individual beads:

7833, 7609, 8335, 6900, 7354, 7234, 8120, 7777 (jackpot!), 7158, 7982, 7083

To figure out the median value, let’s place these readings in numerical order and the middle reading will be our median value.

6900, 7083, 7158, 7234, 7354, 7609, 7833, 7777 (jackpot!), 7982, 8120, 8335

Since we have an odd number of beads, the median value is simply the middle number which in this case is 7609. If this were an even count, we would have to take the average of the middle 2 readings after they are placed in order but that would just be too much work for me to do for this example. 7609 is the MFI value that this instrument would report for this particular analyte in well A1.

After the instrument reaches the minimum bead count for well A1, it moves on to well A2. (The probe actually goes back down in well A1 and spits out some of the leftover sample plus some additional sheath fluid but there is still a good chance there will be left over beads from A1.) Let’s say our imaginary instrument reports the following fluorescent intensities for A2 (our low control):

8001, 209, 7315, 199, 189, 217, 207, 186, 188, 208, 7917

Let’s place these readings in numerical order to figure out the MFI:

186, 188, 189, 199, 207, 208, 209, 217, 7315, 7917, 8001

The MFI value for the same analyte (we’re only doing a 1-plex) in well A2 is 208. Note though, that we had 3 pretty high readings (7315, 7917, 8001) that were most likely carried over from well A1. 3 out of 11 or 28% carryover is insanely high but I just wanted to illustrate this point that even though we had 28% carryover, we still have a respectable median (or MFI) value of 208 =)

If we used the mean fluorescence intensity, our value would be 2258 which is just bananas!

So in conclusion, the median statistic is preferred over the mean because the median is less sensitive to outliers or beads that are carried over from a previous well.

Thanks for tuning in!

If you have any questions or would like an explanation on other aspects of the Luminex technology feel free to comment below and we’ll try our best to address them!

Sample A = 20 MFI – 10 MFI (background) = 10 MFI (50% reduction)
Sample B = 5000 MFI – 10 MFI (background) = 4990 MFI (0.2% reduction)

As can clearly be seen, slight MFI changes on the lower end of the curve can dramatically affect MFI values on the lower end where it barely makes a dent with points on the higher end of the curve. To make things worse, if Sample A were on the really flat part of the curve, this issue will be magnified as really small changes in MFI greatly affect the concentration values.

An MFI change on the lower part of the curve has greater weight

A change in MFI has greater weight on the lower end of the curve because values here have smaller variance. This is a natural situation that arises in almost all fields, including chemical- and immuno-assays, in which the variance of a dependent variable varies across the data. Simply using the 4PL or 5PL model equations without weighting will assume equal variance across the entire curve which is certainly not optimal.

Heteroscedasticity - Nonconstant Variance in Immunoassay Data

Ok…back to my story on the true case. We first wanted to compare apples to apples so we imported the data into MasterPlex QT and used the 5PL model equation with no weighting. The results were very similar where both analysis software had calculated the minimum asymptote to roughly about 8. This means that any sample with an MFI lower than 8 is considered out of range (for the lower part of the curve). Both analysis software reported out of range results since most of the samples were on the lower part of the curve. Not good.

We then applied 1/Y weighting to our 5PL model equation and the minimum asymptote was lowered to about -4. I know what you are thinking right about now; how it is possible to have a negative MFI value for the minimum asymptote? This is something that is certainly possible with background subtraction on background wells with higher MFI values than the actual samples. Anyway, with weighting applied, we were able to recover 95% of the out of range values =) It is also worthy to note that the majority of these points were interpolated rather than extrapolated so they were in fact within standard range. This is not to say to adding weighting will always push the minimum asymptote lower. What can be said with confidence is that the lower asymptote is more accurate with weighting than without weighting because it takes into account the natural heteroscedastic nature of bioassay data. In this particular case, having weighting was able to bring a large majority of the unknown samples into calculable range.

For more details regarding heteroscedasticity, please review point #2 of our 10 Tips for Luminex/Bio-Plex Data Analysis post.

You may also be interesting in reading our previous blog post on the 5PL nonlinear regression model equation.

This is sort of non-related but I just wanted to add that according to our most recent survey results, users who switch to MasterPlex QT from their old analysis software, save (on average) 83 minutes per analysis!

• MasterPlex QT v4.0 – Curve-fitting quantitative analysis software
• MasterPlex EX – miRNA and Gene Expression analysis software

Many Bio-Plex owners may not be aware of this but the new MasterPlex platform is fully compatible with the raw data files that can be exported with the Bio-Plex Manager software.

To obtain the raw data file from the BioPlex Manager software:

1. Locate the original RBX file and open it with BioPlex Manager
2. Make sure you are viewing the Raw Data table
3. In the top row of icons, there is an Export to Excel icon. This icon may be in a different position depending on the version of the software. This function will export the raw data into an Excel .xls file that is compatible with MasterPlex.
4. Simply use the Open file function in the MasterPlex software and browse to the .xls file and that is it!

Bio-Plex® is a registered trademark of Bio-Rad Laboratories, Inc.

1. Use Data Points with at least 35 Bead or Microsphere Counts

35 is the minimum bead count needed for statistically significant analyses.  MasterPlex QT Quantitative Analysis software for Luminex/Bio-Plex has a built-in feature for setting thresholds and marking outliers automatically for you based on many parameters including MFI, bead count, concentration, and standard deviation.

Automatic Outlier Detection in MasterPlex QT

2. 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 MFI and concentration values, the concentrations usually increase as the MFI 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.

Heteroscedasticity - Nonconstant Variance in Immunoassay Data

For analyzing Luminex/Bio-Plex data, 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 MFI values
• 1/Y – This algorithm is useful if you know the errors follow a Poisson distribution

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

Weighting Algoritms available in MasterPlex QT

3. 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 Luminex immunoassay data. Learn more about the 5PL model equation.

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

Model Equations available in MasterPlex QT

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

MasterPlex QT's Powerful Reporting Engine

5. 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 QT 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.

Viewing Standard Data and Marking Outliers in MasterPlex QT

6. 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. As you may already know, the workflow for the Luminex/Bio-Plex technology can become quite complicated and there are many opportunities for things to go awry. Having control groups will keep you sane.

7. 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:

1. If your unknown MFI 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 QT allows you to input the dilution factors of your unknown samples and it will automatically take them into account when calculating the concentrations.
   

   Setting the dilution factors in MasterPlex QT

2. If your unknown MFI is below the standard curve range, you can create one or more standard groups on the lower end by extending your serial dilutions.

8. 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.

Unlike some of the Luminex data analysis packages that are out there, MasterPlex QT let’s the user choose between both these methods.

Individual and Average Standard Point Options in MasterPlex QT

9. Use the R-PE Reporter Dye for Best Signal

R-phycoerythrin (R-PE) is the primary reporter molecule used in Luminex/Bio-Plex assays. Out of all the reporter dyes tested with the Luminex xMAP platform, R-PE will output the highest signals. Alexa 532 is second to R-PE but it’s relative fluorescence intensity is only 28% that of R-PE.

Reporter Dyes and their Intensities on the Luminex xMAP Platform

10. Keep it in the Linear Range

Depending on what is coupled to your beads, the maximum MFI values that can be reported will generally top out between 20000-30000 MFI.  You definitely do not want to be interpolating or extrapolating any concentration values near the top of this curve where it is flat.  In general, it is best to keep all your MFI values between 0-10000 MFI where it is more linear.

If you found this post useful, you may also be interested in the 10 Tips for MasterPlex QT v4.0 Power Users blog post.

Bio-Plex® is a registered trademark of Bio-Rad Laboratories, Inc.