Dear Ronald,
as far as I understand, the preference (dominance) of Fisher's test
has a historical/computational background. It was quite cumbersome to
calculate the probabilities for different margins by hand (huge number of
tables)
and, therefore, as long as the computers were not able to do this within
a feasible time Fisher's test was the best what one could do.
In the meanwhile it is no more necessary, but people get accustomed with this
test.
However, it is especially problematic if you are interested in shifted
hypothesis (e.g.
so called non-inferiority problems, where H_0: p_1>=p_2+delta should be
tested).
You can perorm the tests (and you get some p-values, which are, however not
really
informative, as it was stressed several times on this list), but as far as I
know, there is
no way to calculate "exact" confidence intervals.
There is a paper from Yates (J. Royal. Statist. Soc. vol. A147 p.426 + comments)
one of Habermann (JASA, vol. 53 p.555) commenting on conditioning. This topic is
also shortly discussed by Agresti (categorical data analysis, wiley).
Concerning the likelihood, your estimate of the odds ratio is NOT the usual
n_11*n_22/n_12*n_21, which belongs to the unconditional estimate. The
differences
are thought not to be large...
I hope it helps
kind regards
Robert
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Focus Clinical Drug Development GmbH, Neuss
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