Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model
In categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk relative, etc. In a Bayesian approach, the risk rat...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.469/ |
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| Summary: | In categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk relative, etc. In a Bayesian approach, the risk ratio is modeled according to a Beta-Binomial model, which has exact posterior distribution, due to the conjugacy property of the model. In this work, we provide the exact posterior distribution of the relative risk for the non-conjugate Kumaraswamy–Binomial model. The results are based on special functions and we give exact expressions for the posterior density, moments, and cumulative distribution. An example illustrates the theory. |
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| ISSN: | 1778-3569 |