francogrex wrote:
Data from Fisher's paper: Confidence Limits for a Cross-Product Ratio.
y
col1 col2
[1,] 10 3
[2,] 2 15
fisher.test(y)
Fisher's Exact Test for Count Data
data: y
p-value = 0.0005367
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
2.753438 300.682787
sample estimates:
odds ratio
21.30533
The crude odds ratio in Fisher's paper is 25 and the lower 95%CI is 2.750.
How come this is different here? Why is the estimate 21.30533 and how is the
confidence limits calculated (is there a reference for a statistical paper
other than that of Fisher)?
(R is open source, you know. You _can_ read the code of fisher.test for
yourself.)
The estimated OR is the conditional MLE in the noncentral hypergeometric
distribution. This is not equal to the crude OR, a fact that can be
easily noted by the results being different(!), but it's also mentioned
in places like Breslow/Day's book on case-control studies.
The CI given is the intersection of the two exact one-sided 0.975
levels. (Exact in the sense that it looks for the parameter for which
the p-value is exactly 0.025).
Exact 2-sided intervals are awkward to do (insofar as they can even be
defined) because of probability mass switching between the tails of the
distribution.
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
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