Hierarchical multinomial model. By we denote the law of probability of a random variable conditionally given for another random variable , and by the binomial distribution with parameter . Then the hierarchical binomial model of report count is formed by a series of binomial distributions.
- for the list of adverse reactions.
- for the pair of valid association
Introducting Poisson distributions. The hierarchical model of binomial distribution is conditioned upon and , and related to the unconditional model via and where
Model parameters. Empirical Bayes approach can achieve the interpretability of the relative report model. Assume that each report count is a draw from a Poisson distribution with unknown mean . Here the values
Prior density. The prior distribution of relative report rate is assumed to be the mixture of two gamma distributions
Posterior density. If the prior density and the baseline are known then the posterior density given the report count is proportional to
Gamma-Poisson shrinker. The posterior probability of the first component can be derived as
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