Practical and robust test for comparing binomial proportions in the randomized phase II setting

The one-arm, non-randomized, one/two-stage phase II designs have been a mainstay in oncology trials for evaluating response rates or similar variants (i.e., tests about single proportions). With the goal of screening new therapies that have the potential to move into a randomized phase III trial or a subsequent randomized phase II trial, all while maintaining a logistically feasible sample size. However, since the implementation of the Food and Drug Administration's Fast Track Designation, there has been a trend toward randomized phase II clinical trials as a source of stronger evidence for those seeking fast-track approvals. While there are many single- and multi-stage randomized designs for evaluating proportions in this phase II setting, there still exist limitations in terms of sample size (which directly impacts cost and study duration) or operating characteristics (ex. maintained type I error). In this article, we propose a new test for comparing two binomial proportions, which is a modification across existing methods (the standard z-test and Jung's test). This approach is contrasted with existing methods via numeric evaluation and further contrasted using a real-world oncology trial. The proposed method demonstrates improvements in efficiency and robustness against deviations from design assumptions. When applied to the existing trial, significant savings with respect to cost and time are illustrated. Our proposed test for comparing binomial proportions provides an efficient and robust alternative in the randomized phase II oncology setting, especially when the control arm has a high rate.