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 and investigate the HBM performance with a moment-based confidence interval, and uncorrected and corrected for continuity Wald and Pooled confidence intervals. Using simulations, we compare nine individual confidence intervals in terms of coverage probability and the HBM with nine intervals in terms of family-wise error rate and overall and local power. The simulations show that these statistical properties depend highly on parameter settings.
Keywords: Poisson distribution; multiple testing; simultaneous confidence intervals.