The following paper describes a method for contrasts between proportions that can be used with just the individual point estimates and their confidence intervals. The resulting coverage of limits produced by this method are quite good.
Donner, A., & Zou, G. Y. (2011). Estimating Simultaneous Confidence Intervals for Multiple Contrasts of Proportions by the Method of Variance Estimates Recovery. Statistics in Biopharmaceutical Research, 3(2), 320–335. https://doi.org/10.1198/sbr.2010.09050
Donner, A., & Zou, G. Y. (2011). Estimating Simultaneous Confidence Intervals for Multiple Contrasts of Proportions by the Method of Variance Estimates Recovery. Statistics in Biopharmaceutical Research, 3(2), 320–335. https://doi.org/10.1198/sbr.2010.09050
Comment