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Graphical Model

Let

be the collection of drug names, and

be the collection of medical terms for adverse reaction. A drug-adverse reaction relationship is formed as an edge of a bipartite graph

between

and

, and a pair

from $2^D \times 2^{R}$ is called a association candidate if

the induced bipartite subgraph on the pair share at least one edge with the original graph ;
any smaller pair with $A' \subset A$ and $B' \subset B$ has a fewer edge than .

Report count. The report count of an association candidate can be constructed from the frequency of event.

$m_{A,B} = \sum N_{A',B'}$

where the sum is over

which contains

as a maximal association candidate.

Marginal count and baseline.

$m_{A,\cdot} = \sum_B m_{A,B}$ (marginal count for the list of drugs)
$m_{\cdot,B} = \sum_A m_{A,B}$ (marginal count for the list of AE's)
$m_{\cdot\cdot} = \sum_A m_{A,\cdot} = \sum_B m_{\cdot,B} = \sum_{(A,B)} m_{A,B}$

where the summation $\sum_A$ indicates the sum over all the possible association candidate

and $\sum_B$ over all the possible association candidate

. 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 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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