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

## TL;DR

This paper introduces a new statistical method to improve the efficiency and accuracy of early-stage cancer trials by reducing sample sizes and controlling errors better than traditional approaches.

## Contribution

A novel convolution-based method combining binomial and normal distributions is proposed to enhance Type I error control and trial efficiency.

## Key findings

- The convolution-based method achieves more precise Type I error control compared to traditional binomial tests.
- The new two-stage design with early stopping for futility reduces sample sizes and trial costs.
- Simulations show the proposed approach improves efficiency without compromising statistical rigor.

## Abstract

Phase II oncology trials often use single-arm designs when randomized trials are too expensive or impractical, such as in rare diseases. These trials typically test whether a treatment’s success rate exceeds a specified benchmark. Standard statistical methods, like the exact binomial test or Simon’s two-stage design, are commonly used but tend to be conservative, often underestimating the actual probability of incorrectly rejecting a true null hypothesis (Type I error). To address this, a new method is proposed that blends the binomial distribution with simulated normal data to create an unbiased estimate of treatment success. This convolution-based method improves the precision of Type I error control and can lead to more efficient trial designs. It also introduces a new two-stage design that includes an early stopping point for futility, offering flexibility and reduced sample sizes without compromising statistical rigor. Compared to traditional methods, this approach can lower the cost and shorten the duration of trials, making it a promising tool for early-stage oncology research.

Background/Objectives: 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. Methods: 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. 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.