A two-stage design for comparing binomial treatments with a standard

Abstract

We propose a two-stage selection and testing procedure for comparing success rates of several populations among each other and against a desired standard success rate to identify which treatment has the highest rate of success that is also higher than the standard. The design combines elements of both hypothesis testing and statistical selection. As a hybrid two-stage procedure, it allows for dropping the poorly performing treatments early on the basis of interim analysis results or for early termination if none of the experimental treatments seems promising. Because this procedure is not a pure hypothesis testing procedure, power and size are redefined to account for its hybrid nature. Using these definitions, we determine the design parameters for given size and power values. When multiple designs meet these requirements, we will recommend the set of design parameters that produces the lowest expected sample size.

Keywords:

• Binomial distribution
• probability of correct selection
• ranking and selection
• sample size
• two-stage design

SUBJECT CLASSIFICATIONS:

• 62F07
• 62L05

ACKNOWLEDGMENTS

The authors are grateful to the Editor-in-Chief, the Associate Editor, and anonymous referees for their valuable constructive comments and suggestions that improved the quality of this article.

DISCLOSURE

The authors have no conflicts of interest to report.