A Free Gift: An Adaptive Strategy in a Single-Arm Trial Using an Exact Test Through the Binomial Distribution

Abstract

For medical product development within the same generation, single-arm trial designs are commonly implemented to test the performance of the new product against an objective performance criterion. When the primary endpoint is binary and the sample size is moderate, an exact test through the binomial distribution is usually used. This article shows that it is a free gift to add an adaptive component to a fixed-sample-size design so that when the interim result is marginal, the adaptive feature can be activated without any penalty. A hypothetical example is used to illustrate the application of this method.

Key Words:

• Adaptive design
• Binomial distribution
• Conditional error function
• Single-arm trial

ACKNOWLEDGMENTS

The author thanks Xiaolu Su and Andrew Mugglin for the motivating discussion and references. The author is also grateful to the editor, associate editor, and two referees for critical and constructive comments, which improved and enriched the paper.

Notes

Note. c ₁: Critical value at stage 1; α₁: type I error assigned to stage 1 (p ₁ ≤ α₁, where p ₁ is the p-value for the first stage); c*: futility boundary; p*: type I error associated with c*; α _c : conditional type I error.

Note. The entry numbers are the approximate required effective sample sizes for the second stage; due to the seesaw effect in the setting of a discrete outcome, the sample sizes in the entries may either slightly miss the targeted power or lead to a higher than expected targeted power.