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Testing the equality of two Poisson means using the rate ratio
Hon Keung Tony Ng1, Man-Lai Tang
1Department of Statistical Science, Southern Methodist University, Dallas, TX 75275-0332, USA.
Statistics in Medicine
|November 9, 2004
Summary
Comparing two Poisson rates with unequal sampling frames requires careful method selection. The constrained maximum likelihood estimation (CMLE) method is best for untransformed statistics (W(2)), while the sample-based method is better for log-transformed statistics (W(3)).
Area of Science:
- Biostatistics
- Statistical Inference
- Epidemiology
Background:
- Comparing independent Poisson variates is crucial in various scientific fields.
- Unequal sampling frames (time, population, area) complicate rate comparisons.
- Existing methods may lack robustness under these conditions.
Purpose of the Study:
- To evaluate statistical procedures for comparing two independent Poisson rates with unequal sampling frames.
- To assess the performance of different statistics and estimation methods.
- To provide guidance on selecting appropriate methods for rate comparison.
Main Methods:
- Investigated two statistics: one with and one without logarithmic transformation (W(2) and W(3)).
- Reviewed two implementation methods: sample-based and constrained maximum likelihood estimation (CMLE).
- Conducted an empirical study to compare method and statistic performance.
Main Results:
- CMLE method is satisfactory for W(2) (untransformed statistic).
- Sample-based method performs better for W(3) (log-transformed statistic).
- Both methods perform well for Poisson rates >= 10; W(2) can be liberal and W(3) conservative for rates < 10.
Conclusions:
- Method and statistic choice impacts the reliability of Poisson rate comparisons.
- Sample size formulas are provided and validated for practical application.
- Methodologies illustrated with a breast cancer study example.