Exact and Mid-p Confidence Intervals for the Odds Ratio

Unconditional small-sample confidence intervals for the odds ratio.

The traditional approach to 'exact' small-sample interval estimation of the odds ratio for binomial, Poisson, or multinomial samples uses the conditional distribution to eliminate nuisance parameters. This approach can be very conservative. For two independent binomial samples, we study an unconditional approach with overall confidence level guaranteed to equal at least the nominal level. With ...

Comment: Randomized Confidence Intervals and the Mid-P Approach

We enjoyed reading the interesting, thought-provoking article by Geyer and Meeden. In our comments we will try to place their work in perspective relative to the original proposals for exact and randomized confidence intervals for the binomial parameter. We propose a fuzzy version of the original binomial randomized confidence interval, due to Stevens (1950). Our approach motivates an existing ...

An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions

An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne’s test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it pe...

Exact Confidence Intervals

On logit confidence intervals for the odds ratio with small samples.

Unless the true association is very strong, simple large-sample confidence intervals for the odds ratio based on the delta method perform well even for small samples. Such intervals include the Woolf logit interval and the related Gart interval based on adding .5 before computing the log odds ratio estimate and its standard error. The Gart interval smooths the observed counts toward the model o...