Sample Size for Testing Difference Between Two Proportions for the Bilateral-Sample Design

Abstract

In this article, we consider approximate sample size formulas for testing difference between two proportions for bilateral studies with binary outcomes. Sample size formulas are derived to achieve a prespecified power of a statistical test at a prechosen significance level. Four statistical tests are considered. Simulation studies are conducted to investigate the accuracy of various formulas. In general, the sample size formula for Rosner's statistic based on the dependence assumption is highly recommended in the sense that its actual power is satisfactorily close to the desired power level. An example from an otolaryngological study is used to demonstrate the proposed methodologies.

Key Words:

• Bilateral-sample design
• Comparative study
• Correlated binary data
• Sample sizes

ACKNOWLEDGMENTS

This research is fully supported by grants from the Research Grant Council of the Hong Kong Special Administration Region (project number HKBU261007), the National Nature Science Foundation of China (10561008, 10761011), the Ph.D. Special Scientific Research Foundation of the Chinese University (20060673002), and by the program New Century Excellent Talents in University (NCET-07-0737).