# statistics help

Mike Clark mrc7 at cam.ac.uk
Wed Nov 5 08:57:58 EST 1997

```In article <63m4km\$dnd\$1 at news.kersur.net>, Daniel E. Cox
<URL:mailto:decox at kersur.net> wrote:
> To all biostatistician and/or immunologists,
>
> We are developing a bacterial vaccine and are studying the use of an
> in vivo immunogenicity assay for potency and stability testing.  Our
> approach has been to simply immunize a group of mice (10-15) and
> determine the final titer of each animal against a purified antigen
> from the bacteria by EIA.  We generally see a very wide range in
> titers, often up to 5 logs.  We are presently optimizing our system
> and are in discussion regarding the best way to analyze these data.
> We are attempting to use this technique to compare one vaccine
> preparation against another to determine if a particular preparation
> is more or less active than a reference preparation, and need to know
> the best approach to determining significant differences.   I have
> several specific questions regarding the most appropriate way to
> proceed.
>
> - Is it more appropriate to perform the statistical calculations on
> unmodified titer data or to use a log of the individual titers?

The production of antibody follows on from the proliferation and
differentiation of responding B-cells and thus is likely to represent the
product of a logarithmic expansion of cells. Comparing log diferences of
antibody titres therefor seems reasonable. Also once made and if no
further plasma cells are produced, antibody titres will decline in an
exponential fashion over time dependent upon the half-life of the
particular isotypes being measured.

>
> - Similarly, is it more appropriate to compare groups by arithmetic means
> of titers or geometric means? and  why?

If you are going to look at systems which vary geometrically such as the
products of cell proliferation then geometric means should be used. Of
course if you log transform your data then the arithmetic mean of the
transformed data is related to  the  geometric mean of the untransformed
data.

>
> - When comparing groups of animals, what is the most appropriate
> statistical method for assessing significance?  I have used Student's
> t-test, dominance statistic and Wilcoxon-Mann-Whitney test.  It is not
> clear to me which, if any, of these techniques will yield the
> appropriate answer.  Is there another that may be more useful (and
> correct)?

Tricky question! Most biologists tend to present the results of tests which
show the significance they are after! If you can use non-parametric
statistics and get a clearly significant result then that is probably the
best. However often non-parametric tests are inconclusive for small
biological differences requiring larger experimental groups and so people
resort to parametric statistical tests. If you are going to use a
parametric test such as a student t-test you need to be sure that there
is good reason to expect that the samples conform to an expected
distribution eg a normal distribution. However for many biological systems
particularly using transformed data sets such as ratios or percentages, a
normal distribution would not be expected, particularly at the extremes of
the ranges.

>
> - Can anyone suggest either references or books in which statistical
> analysis of immune responses is discussed?  I would prefer information
> sources aimed at the non-statistician.
>
>
> If there is anyone out there with experience in developing
> immunogenicity assays such as these and would be willing to share
> their insights, it would be most appreciated.
>
>
> Daniel Cox,  Ph.D.
> Worcester, MA USA
>
> decox at kersur.net
>
>

Cheers,

Mike Clark,                        <URL:http://www.path.cam.ac.uk/~mrc7/>
--
o/ \\    //            ||  ,_ o   M.R. Clark, PhD. Division of Immunology
<\__,\\  //   __o       || /  /\,  Cambridge University, Dept. Pathology
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