Two-tailed approximate confidence intervals for the ratio of proportions

Various approximate methods have been proposed for obtaining a two-tailed confidence interval for the ratio R of two proportions (independent samples). This paper evaluates 73 different methods (64 of which are new methods or modifications of older methods) and concludes that: (1) none of the classic methods (including the well-known score method) is acceptable since they are too liberal; (2), the best of the classic methods is the one based on logarithmic transformation (after increasing the data by 0.5), but it is only valid for large samples and moderate values of R; (3) the best methods among the 73 methods is based on an approximation to the score method (after adding 0.5 to all the data), with the added advantage of obtaining the interval by a simple method (i.e. solving a second degree equation); and (4) an option that is simpler than the previous one, and which is almost as effective for moderate values of R, consists of applying the classic Wald method (after adding a quantity to the data which is usually $z_{\alpha /2}^{2}/4$ ).