Adaptive Group Sequential Confidence Intervals for the Ratio of Normal Means

In controlled group sequential trials, we consider the ratio of normal means as the effect measure of interest and derive group sequential nested confidence intervals on this parameter. In an interim analysis, the sample sizes of the following stages can be determined in a completely adaptive way using the unblinded data from all previously performed stages. Despite the data-dependent adaptation, the nested confidence intervals always keep the predefined confidence coefficient. Using nested confidence intervals, we make test decisions either in noninferiority or in superiority trials. However, in an interim analysis, we can change the planning from showing noninferiority to showing superiority or vice versa without affecting the predefined confidence coefficient of the nested intervals. A real data example is worked out in detail and the change in the planning from showing superiority to showing noninferiority is shown during the ongoing trial.