Re: RE : Statistics questions

Yes, the statistics on the MFI follow very closely that on the	
frequency.

The standard error of the mean of a population (SEM), which defines  
how precisely you know the "true" mean, is equal to the standard  
deviation divided by the square root of the number of events.  The SD  
(or CV) tells you how broad the distribution is, but will not change  
substantially as you collect more and more events.  But the SEM  
decreases with increased events,, in your example, if you count 10,000	
events vs. 1,000 events, the SEM will be about 30% as large on the  
first sample -- saying that you know the mean with 3x increased  
precision.

Note that while the use of the SD is most appropriate for gaussian  
(normal) distributions, the relationship between increased precision  
of the mean and increasing numbers of events is independent of the  
actual distribution.

By the way, I advocate use of the median fluorescence intensity rather	
than the mean, since the median is less subject to outliers  
(particularly when you are dealing with log-distributions).  I don't  
know (nor did a statistician I asked!) how the variance in the median  
will relate to the number of events used to calculate it.  However, I  
think the square-root relationship is probably a reasonable one to use	
as an estimator... i.e., you need 100x the number of events to	
increase your precision 10x.

Finally, note that once you have more than a few dozen events on which	
you are computing the MFI (or frequency), the statistical error in the	
MFI (or %) is probably much lower than experimental error, so it's  
kind of pointless to collect much more than this if your goal is only  
to increase precision of the measurement.

mr

On Feb 15, 2008, at 8:50 AM, Carl Simard wrote:

> Since we're on the subject of Poisson statistics, number of events  
> and CV, there's a
> question that I'm asking myself since some time. Does all these  
> statistics limitations
> also applied with MFI ?
>
> Just to give a practical example, let say I'm not interested in the  
> proportion of cells
> being positive or negative for a given marker (the experiement is  
> done on a cultured cell
> line and thus all cells behave pratically homogenously to a given  
> treatment). Instead, I
> just want to look at change in the relative expression of this  
> marker based on change on
> MFI readings. In this case, will the MFI be more significative if  
> you count, let say, 10
> 000 cells versus 1000 ?
>
> Carl
>
> -----Message d'origine-----
> De : Howard Shapiro [mailto:hms@shapirolab.com]
> Envoyé : 13 février 2008 21:40
> À : Cytometry Mailing List
> Objet : Re: Statistics questions
>
>
>
> Maciej Simm wrote (in response to Petra Disterer)
>
>>
>>> 2. I've read about coefficient of variation and that one should have
>>> more than 400
>>> positive events to have a CV of less than 5%. In my understanding
>>> that means that if I have 400 positive events the probability that
>>> these positive events are due to chance is
>>> less than 5%. I'm not sure that I have understood this correctly.
>>
>> CV=100/sqrt(400) or 5%, so "yes". This was elegantly described on  
>> this
>> list before - http://www.cyto.purdue.edu/hmarchiv/2001/0261.htm
>>
> I'm glad Maciej dug up the pointer to my 2001 posting, which saves  
> me some writing this
> time around, but Petra seems to be laboring under a misconception  
> about Poisson
> statistics. If you count n events, and there are no other sources of	
> variance in the
> measurement, the "mean" of your measurement is n, i.e., the number  
> of events you count,
> and the expected standard deviation of a series of counts of events  
> from the same sample
> is the square root of n. Since the coefficient of variation, in per  
> cent, is 100 times
> the mean divided by the standard deviation, i.e., 100 divided by the	
> square root of n,
> you get 5 per cent as the minimum possible CV for a count of 400  
> objects, 10 per cent for
> a count of 100 objects, 1 per cent for a count of 10,000 objects,  
> etc. Poisson statistics
> therefore tell you how many objects you actually need to count to  
> get the result to a
> desired level of precision. They tell you
> *nothing* about the probability that the events you count are or are	
> not due to chance!!!
>
> A major reason those of us who can afford it use cytometry is that  
> it is usually
> difficult for even the keenest-eyed and best-trained human observer  
> to sit at a
> microscope and count several hundred of anything. When I was a  
> medical student, one of
> the hardest tests my classmates and I had to do in our role as the  
> de facto "clinical
> laboratory" in the emergency department of a busy city hospital was  
> the blood
> reticulocyte count. Reticulocytes are immature red cells that have  
> not completely shed
> what's left of their protein synthetic apparatus (ribosomes and  
> endoplasmic reticulum).
> They take between one and two days to do this, and, since red cells  
> normally last about
> 120 days in circulation, we expect that about one per cent of red  
> cells in blood will be
> reticulocytes. Reticulocytes can be demonstrated on a blood smear by	
> staining them with a
> dye such as new methylene blue, which will precipitate the ribosomes	
> into a "network"
> (whence comes the term reticulocyte), which, if you are sharp-eyed,  
> persistent, and
> lucky, you will see as one or a few blue dots within the red cell.  
> The reticulocyte count
> goes up if someone has lost blood and is replacing it, and down if  
> he or she has a
> condition such as vitamin B12 deficiency, in which the marrow isn't  
> generating new red
> cells. To do a reticulocyte count on a blood smear, you look at and  
> count 1,000 red
> cells, noting the number of reticulocytes you see while you do this.	
> If a normal person
> has about 1 per cent reticulocytes, you can expect to count 10 of  
> them while you cruise
> (or bruise) through 1,000 red cells, meaning the CV of your  
> measurement will be over 30
> per cent. If you do the count the next day and only count 7, or  
> count a whopping 13, it
> is not at all unlikely that there has been no real change in the  
> patient's hematologic
> status. That's what we learn from Poisson statistics.
>
> These days, the Clinical Laboratory Improvement Act (CLIA) has made  
> it illegal for
> medical students to be used as lab slaves, at least in the United  
> States, and
> reticulocytes are typically counted in a properly certified lab in a	
> flow cytometer,
> using a dye such as thiazole orange, which binds to nucleic acid,  
> and analyzing at least
> a few tens of thousands of red cells in toto, which yields a	
> measurement with a
> respectable CV. Since red cells spit out their nuclei on the way to  
> becoming
> reticulocytes, they don't (except in pathologic situations) contain  
> DNA, so dyes that
> bind to both DNA and RNA are usually OK for reticulocyte counting.  
> It only took about
> five years for the hematologists to get comfortable with this.
>
> Reflecting on my career in cytometry, most of it seems to have been  
> spent automating
> various parts of the "scut" lab work I was forced to do as a medical	
> student; as many of
> you may know, I am now looking at cytometric diagnosis of TB (which  
> I did do in medical
> school) and malaria (which I don't recall ever doing, but might have	
> once or twice).
> These diseases were, and are, much bigger problems in resource-poor  
> countries than in
> places where laboratories can afford both flow cytometers and the  
> infrastructure needed
> to run them. TB is typically diagnosed by transmitted light  
> microscopy of sputum smears
> using the Ziehl-Neelsen stain developed in 1883; malaria is  
> diagnosed by transmitted
> light microscopy of blood smears using the Giemsa stain developed in	
> 1904.
>
> The vast majority of the people who use these stains don't know how  
> or why they work;
> when they try to evaluate modifications of the staining method, they	
> typically compare
> slides from clinical samples on which examination of several hundred	
> high-power
> microscope fields on a blood or sputum slide will often turn up  
> fewer than ten pathogens.
> Since Poisson statistics have, for the most part, not impinged on  
> the consciousness of TB
> and malaria diagnosticians, it is not generally appreciated that  
> many such comparisons
> are meaningless.
>
> Now that LEDs have become cheap, there is a big push toward  
> equipping TB labs in
> resource-poor countries with (relatively) inexpensive fluorescence  
> microscopes, so they
> can use stains based on auramine O, which is a blue-excited, green  
> fluorescent dye that
> stains nucleic acids (although the texts on TB erroneously describe  
> it as staining the
> mycolic acid in the cell wall) instead of the Ziehl-Neelsen stain.  
> That's going to be a
> waste of money; true, you can look at a slide at somewhat lower  
> magnification using
> fluorescence, but you're still up against Poisson statistics, and  
> you really need to look
> at much more of the slide than is practical even with a fluorescence	
> microscope. That's
> what cytometry is for. If it takes the TB diagnosticians as long to  
> catch on as it took
> the hematologists, we can chalk up a million or so preventable  
> deaths to the steep
> learning curve. And the same problem, and the same grim numbers,  
> turn up for malaria.
>
> The foundations of our science were laid by people very much focused	
> on human disease
> (OK, so the original paper on Poisson statistics and cell counting  
> was written by
> somebody at the Guinness brewery). The synthetic dyes that got us  
> from empirical
> microscopy to cytometry originated from an attempted synthesis of  
> quinine - for malaria
> treatment - that went wrong. Paul Ehrlich, who mastered the use of  
> those dyes (and caught
> TB in the process), made the inductive leap from selective staining  
> of different cell
> types to selective chemotherapy; many of the compounds he worked  
> with came from Hoechst,
> still a manufacturer of both dyes and drugs.
>
> Whatever else we do with cytometry, we are all ambassadors to our  
> colleagues. There are
> undoubtedly people coming through flow labs who want little more  
> than to run their
> samples and get back to their patients or labs. These folks may not  
> realize, as I hope
> you do, that cytometry does more than merely save time and labor.  
> Try to see that they
> learn something useful while you have their attention.
>
> -Howard
>
> (P.S. A lot of this stuff will be in the new book)
>
>
>