Asymptotic simultaneous confidence intervals for many-to-one comparisons of binary proportions in randomized clinical trials

The simultaneous comparison of proportions of success between many treatments and one control group is a common problem in randomized clinical trials or toxicity studies. In this article, three recently recommended asymptotic confidence interval approaches for the difference of proportions are adjusted for multiplicity, taking the correlation into account. The coverage probability of the resulting interval methods is compared in a simulation study using parameter settings relevant for clinical trials. For moderate to small sample sizes, a method adding two successes and two failures can be recommended. The usage of the proposed methods is illustrated by two examples; an R package is available.