Evaluating the Performance of Simultaneous Stepwise Confidence Intervals for the Difference between two Poisson Rates

Abstract

We consider the problem of simultaneously estimating Poisson rate differences via applications of the Hsu and Berger stepwise confidence interval method (termed HBM), where comparisons to a common reference group are performed. We discuss continuity-corrected confidence intervals (CIs) and investigate the HBM performance with a moment-based CI, and uncorrected and corrected for continuity Wald and Pooled confidence intervals (CIs). Using simulations, we compare nine individual CIs in terms of coverage probability and the HBM with nine intervals in terms of family-wise error rate (FWER) and overall and local power. The simulations show that these statistical properties depend highly on parameter settings.

Keywords:

• Multiple testing
• Poisson distribution
• Simultaneous confidence intervals

Mathematics Subject Classification:

• 62F10

Acknowledgments

The authors are also thankful to Nancy Brener (Survey Operations and Dissemination Team Leader, Division of Adolescent and School Health Centers for Disease Control and Prevention) for providing us with the 1999 Youth Risk Behavior Survey data.