Optimizing One-Sample Tests for Proportions in Single- and Two-Stage Oncology Trials
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Phase II oncology trials often rely on single-arm designs to test $H_0: \pi = \pi_0$ versus $H_a: \pi > \pi_0$, especially when randomized trials are infeasible due to cost or disease rarity. Traditional approaches like the exact binomial test and Simon’s two-stage design tend to be conservative, with actual Type I error rates falling below the nominal $\alpha$ due to discreteness of the underlying binomial processes. We propose a convolution-based method that combines the binomial distribution with a simulated normal variable to construct an unbiased estimator of $\pi$ and ensure precise Type I error control. We derive its theoretical properties and compare its performance to exact tests in both one-stage and two-stage settings. The approach yields more efficient designs with reduced sample sizes while maintaining error rate constraints. A new two-stage design with interim futility analysis is introduced and compared to Simon’s design. Real-world examples show the method’s potential to reduce trial cost and duration. This work offers a flexible, efficient alternative for early-phase oncology trial design.