Testing the Equality of Two Poisson Means Using the Rate Ratio

• Activity Number: 311
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Hon Keung Ng*+ and Man Lai Tang
• Companies: Southern Methodist University and Harvard Medical School
• Keywords: Poisson rate ratio ; level of significance ; constrained maximum likelihood estimation ; sample size

Abstract

We investigate procedures for comparing two independent Poisson variates that are observed over unequal sampling frames (i.e., time intervals, populations, areas or any combination thereof). We consider two statistics (with and without the logarithmic transformation) for testing the equality of two Poisson rates. Two methods for implementing these statistics are reviewed: (1) the sample-based method, and (2) the constrained maximum likelihood estimation (CMLE) method. We conduct an empirical study to evaluate the performance of these two methods with and without logarithmic transformation. In general, all tests perform well for large Poisson rates and equal time/space. In particular we find that the CMLE method works satisfactorily only for the statistic without the logarithmic transformation, while sample-based method performs better for the statistic using logarithmic transformation. The corresponding sample size formulae are provided and valid in the sense that the simulated powers associated with the approximate sample size formulae are generally close to the pre-chosen power level. We illustrate our methodologies with a real example from a breast cancer study.