A Bayesian inference of P(λ<sub>1</sub>>λ<sub>2</sub>) for two Poisson parameters
The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in the medical literature. However, such discussions are usually based on the frequentist viewpoint rather than the Bayesian viewpoint. Here, we propose an index θ=P(λ<sub>1, post</sub>>λ<sub>2, post</sub>), where λ<sub>1, post</sub> and λ<sub>2, post</sub> denote Poisson parameters following posterior density. We provide an exact and an approximate expression for calculating θ using the conjugate gamma prior and compare the probabilities obtained using the approximate and the exact expressions. Moreover, we also show a relation between θ and the <italic>p</italic>-value. We also highlight the significance of θ by applying it to the result of actual clinical trials. Our findings suggest that θ may provide useful information in a clinical trial.
Year of publication: |
2012
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Authors: | Kawasaki, Youhei ; Miyaoka, Etsuo |
Published in: |
Journal of Applied Statistics. - Taylor & Francis Journals, ISSN 0266-4763. - Vol. 39.2012, 10, p. 2141-2152
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Publisher: |
Taylor & Francis Journals |
Saved in:
Online Resource
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