Review of alternative approaches to calculation of a confidence interval for the odds ratio of a 2×2 contingency table
A common situation in biology is where we have count data and wish to explore whether there is an association between two categorical variables, each with two levels (a 2 × 2 contingency table). The size of the association can be measured using the odds ratio, with a confidence interval for this measure enclosing unity suggesting no evidence of an association. However, there is no universally agreed method for calculating such a confidence interval. Here, we provide a review of some commonly used and recently suggested methods. Of all of the methods currently available, the unconditional approach based on the score statistic was consistently closest to the nominal type I error level in our investigations, and this is the method we generally recommend. This method also offers good agreement with P-values from null hypothesis testing using the method of Fisher-Boschloo. However, some scientists may prefer the recently developed minlike or Blaker methods, which offered better agreement with P-values calculated using Fisher's Exact test or Blaker's Exact test, respectively. Lastly, where calculation without use of a computer is required, we recommend the Woolf method with Haldane-Anscombe correction.