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

Phase II oncology trials often rely on single-arm designs to test H₀: π = π₀ versus Hₐ: π > π₀, 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 α 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 π 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.