A Bayesian non-inferiority index for two Poisson parameters

The efficiency and safety of a new treatment is occasionally evaluated using Poisson distributed count data as the criteria in clinical studies. In such scenarios, non-inferiority tests using Poisson distributed count data are often employed and evaluated in frequentist frameworks. However, in our previous work, we proposed and presented an index that demonstrated that the Poisson parameter obtained in the Bayesian statistic framework is superior to that obtained in inference frameworks, and we also proposed a non-inferiority index of the Poisson parameters. In this paper, we expand upon these methods and propose a new index that utilizes the empirical Bayes method. The results of comparisons to approximate values in terms of accuracy as well as application to examples obtained from actual clinical studies indicate that our proposed new index is both effective and easy to understand intuitively, as it delivers probability directly. Subjects: Mathematics & Statistics; Medical Statistics; Medical Statistics & Computing; Medicine; Medicine, Dentistry, Nursing & Allied Health; Science; Statistics; Statistics & Probability