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, 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 α 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.

We propose a convolution-based method that combines the binomial distribution with a simulated normal variable to construct an unbiased estimator of π. 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.

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.

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.