RE: RE : Statistics questions

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)