I conducted an odds ratio test with a certain software, and I'm not sure about the right confidence interval (CI) to use. The 2x2 table consists the distribution of counts as follows, by each cell: a=26, b=21, c=12, d=2. The output of the results included the calculated OR, with the following four types of CIs: Mid-p exact, Fisher's exact, Cornfield, Wald. The question is: based on the distribution of the observations, particularly considering that cell d includes 2 observations (<5), which of the four abovementioned CIs is the most appropriate to use?
I'd be reading published evaluations of methods for computing odds ratio intervals. Ruxton and Neuhauser 2013 (Methods Ecol Evol 4) recommended the unconditional score interval method from Agresti and Min 2002 (Biostatistics 3). The score interval can be computed using the orscoreci function in the PropCIs R package.
The mid-p could be the best of the four estimates you have.
Thanks for raising this question because it prompted me to find a solution for computing risk ratios for 2 x 2 contingency tables.