Exact and mid-p confidence intervals for the odds ratio
Morten W. Fagerland
Unit of Biostatistics and Epidemiology
Oslo University Hospital
Oslo, Norway
[email protected]
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Abstract. The odds ratio is a frequently used effect measure for two independent
binomial proportions. Unfortunately, the confidence intervals that are
available for it in Stata and other standard software packages are generally
wider than necessary, particularly for small-sample and exact estimation. The
performance of the Cornfield exact interval—the only widely available
exact interval for the odds ratio—may be improved by incorporating a
small modification attributed to Baptista and Pike (1977, Journal of the
Royal Statistical Society, Series C 26: 214–220). A further
improvement is achieved when the Baptista Pike method is combined with the
mid-p approach. In this article, I present the command merci
(mid-p and exact odds-ratio confidence intervals) and its immediate version
mercii, which calculate the Cornfield exact, Cornfield mid-p,
Baptista–Pike exact, and Baptista Pike mid-p confidence intervals
for the odds ratio. I compare these intervals with three well-known logit
intervals. I strongly recommend the Baptista–Pike mid-p interval.
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Morten W. Fagerland
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merci, mercii, confidence intervals, odds ratio, mid-p, exact, quasi-exact, Cornfield, Baptista–Pike
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