Confidence intervals for odds ratio from multistage randomized phase II trials

A multi-stage randomized trial design can significantly improve efficiency by allowing early termination of the trial when the experimental arm exhibits either low or high efficacy compared to the control arm during the study. However, proper inference methods are necessary because the underlying distribution of the target statistic changes due to the multi-stage structure. This article focuses on multi-stage randomized phase II trials with a dichotomous outcome, such as treatment response, and proposes exact conditional confidence intervals for the odds ratio. The usual single-stage confidence intervals are invalid when used in multi-stage trials. To address this issue, we propose a linear ordering of all possible outcomes. This ordering is conditioned on the total number of responders in each stage and utilizes the exact conditional distribution function of the outcomes. This approach enables the estimation of an exact confidence interval accounting for the multi-stage designs.