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We recently had a customer that was interested in MasterPlex QT because his current analysis software for his Bio-Plex instrument was reporting a lot of "OOR <" or out of range concentration values (below the lower asymptote in this case) for points on the lower end of curve. This is what you would normally expect to see for values that fall below the minimum asymptote BUT the software did not have the capability to use weighting in calculating the lower asymptote which can greatly affect points on the lower part of the curve.

Weighting algorithms are used to offset heteroscedasticity and apply a nonconstant variance across your data. In the case of Luminex/Bio-Plex data where you have a curve fit of MFI vs concentration, let's say you have a sample A with 20 MFI on the lower end of the curve and another sample B on the higher end of the curve with 5000 MFI. Now let's say we wanted to do a background subtraction where our background sample is 10 MFI.

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.

 

The affect of variance on the lower part of the curve

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!

MiraiBio offers 3 powerful curve-fitting quantitative analysis solutions that utilizes our time-tested 4-PL and 5-PL nonlinear regression model with weighting as well as many others:

ReaderFit.com - Free online curve-fitting application
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ReaderFit Desktop - Robust curve-fitting, quality control and reporting desktop software
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MasterPlex QT - Robust curve-fitting, quality control and reporting desktop software for multiplex ELISA data (Luminex, Bio-Plex, Meso Scale Discovery and Applied BioCode platforms)
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