Optimizing One-Sample Tests for Proportions in Single- and Two-Stage Oncology Trials

Background/Objectives: Phase II oncology trials often rely on single-arm designs to test (Formula presented.) versus (Formula presented.), especially when randomized trials are infeasible due to cost or disease rarity. Traditional approaches, such as the exact binomial test and Simon’s two-stage design, tend to be conservative, with actual Type I error rates falling below the nominal (Formula presented.) due to the discreteness of the underlying binomial distribution. This study aims to develop a more efficient and flexible method that maintains accurate Type I error control in such settings. Methods: We propose a convolution-based method that combines the binomial distribution with a simulated normal variable to construct an unbiased estimator of (Formula presented.). This method is designed to precisely control the Type I error rate while enabling more efficient trial designs. We derive its theoretical properties and assess its performance against traditional exact tests in both one-stage and two-stage trial designs. Results: The proposed method results in more efficient designs with reduced sample sizes compared to standard approaches, without compromising the control of Type I error rates. We introduce a new two-stage design incorporating interim futility analysis and compare it with Simon’s design. Simulations and real-world examples demonstrate that the proposed approach can significantly lower trial cost and duration. Conclusions: This convolution-based approach offers a flexible and efficient alternative to traditional methods for early-phase oncology trial design. It addresses the conservativeness of existing designs and provides practical benefits in terms of resource use and study timelines.