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Graphical Model

Let $ D$ be the collection of drug names, and $ R$ be the collection of medical terms for adverse reaction. A drug-adverse reaction relationship is formed as an edge of a bipartite graph $ G$ between $ D$ and $ R$, and a pair $ (A,B)$ from $ 2^D \times 2^{R}$ is called a association candidate if

Report count. The report count of an association candidate $ (A,B)$ can be constructed from the frequency of event.

$ m_{A,B} = \sum N_{A',B'}$
where the sum is over $ (A',B')$ which contains $ (A,B)$ as a maximal association candidate.

Marginal count and baseline.

where the summation $ \sum_A$ indicates the sum over all the possible association candidate $ (A,B)$ and $ \sum_B$ over all the possible association candidate $ (A,B)$. Then we can define the baseline by

$\displaystyle E_{A,B} = m_{A,\cdot} m_{\cdot,B} / m_{\cdot\cdot}

Contingency table. In a similar manner, the conventional contingency table can be obtained from the frequency $ N_{A,B}$ of event. Here for a pair $ (i,j)$ of individual drug ad AE we can define the cell count

$ C_{i,j} = \sum \{N_{A,B}: i\in A, j\in B\}$
Note that the total number of reporting events is substantially smaller than the sum of all the cell counts of the contingency table.

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