Re: negative values for gMFI

Tina,

negative values are not a consequence of the biexponential scaling --  
that's only a visualization too.  Rather, negative values are a  
consequence of two different operations: (1) baseline restore -- a  
subtraction process that instruments do on a event-by-event basis  
before reporting the data to the computer; on the DiVa, this can  
result in a value less than zero for events that have essentially no  
fluorescence, because the error in the estimation of the background  
can exceed the absolute magnitude of the background itself; and (2)  
compensation, which subtracts values from the fluorescence signal  
based on the fluorescence in other channels -- and once again, the  
error in the estimation of the amount to subtract can exceed by a  
large amount the absolute magnitude of the value after subtraction.   
With both of these operations, you will end up with a distribution of  
events near zero, but with a standard deviation such that the tails of  
the distributions go negative or positive.

If you've over-compensated, or if you've gated on events to select  
primarily events that are below zero, then any estimate of the central  
tendency of this population (median, mean, geometric mean) will be  
negative.  If the value is substantially less than zero, then you have  
overcompensation problems.  If the value is near zero, then it's  
probably just random luck that it wasn't above zero...	In the former  
case, I would be cautious about any MFI values to begin with, since  
with improper compensation settings you cannot rely on the MFI.  In  
the latter case, whether you use the actual value or you use "zero"  
probably won't change your answer, so it becomes academic.

Finally, a purist may note that the geometric mean fluorescence should  
never be less than zero (because of how geometric mean is  
computationally defined).  Strictly speaking, this is correct -- a  
geometric mean can never be negative.  The software, however, is  
attempting to compute a central tendency that is weighted similarly to  
the geometric mean for these distributions, where negative values can  
exist.	Thus, it uses the same biexponential transformation to aid in  
defining a statistic that gives you this value -- the "geometric" mean  
has the same functionality in terms of providing an estimate of the  
center of the population as it is drawn in your graphs (after all,  
this is origin of the term "geometric") -- and thus, a population that  
is centered below zero would have an "undefined" geometric mean by the  
original algorithm, but a meaningful and applicable geometric mean in  
biexponential geometry.

mr

(Note: here's a trivial example of why the "standard" geometric mean  
is not a good estimate of central tendency when you have values near  
zero.  If you have a single cell with zero fluorescence, and a million  
cells with fluorescence of 10^5, then the geometric mean of this  
population of 1,000,001 cells is.... zero!  Not a very good estimate.   
However, software that uses the biexponential geometry to calculate  
the gMFI will give the much better value of 10^5, as it would for the  
mean and the median...)


On May 8, 2008, at 4:44 PM, <Tina.Powell@UCHSC.edu> <Tina.Powell@UCHSC.edu 
 > wrote:

> Hello,
>
> I’m looking at an FMO tube for PD-1 which has been stimulated with  
> SEB.	I was curious as to whether anyone has ever encountered a  
> negative gMFI.  I’m not sure as to how this makes sense.  When I  
> look at the histogram, there are defiantly peaks which show up to  
> the left of the zero.  If the value is negative for the FMO, is it  
> justifiable to add this to your sample values to get your specific  
> gMFI value?  Can someone please explain how a negative FMO is  
> obtainable?  Does it have something to do with a bivariate scale?
>
> Thanks,
>
> Tina Powell
> University of Colorado HSC