e-Statistics > Explore hidden confounding

Counting formulas

When each list is treated as category, the ``listwise'' contingency table is formulated for the reported lists of drugs versus the lists of AE's. Accordingly the respective marginal counts are calculated. Let $ N_{A,B}$ denote the count of reporting incidents involving the list $ A$ of drugs and the list $ B$ of AE's. Then the marginal counts are formulated listwise as follows:

Here the summation $ \sum_A$ indicates the sum over all the possible lists $ A$'s of drugs, and $ \sum_B$ is over all the possible lists $ B$'s of AE's. The reporting incident is also counted itemwise between drug $ i$ and adverse reaction $ j$ as follows:

The cell count is made over all the combinations of $ A$ and $ B$ which respectively contains drug $ i$ and adverse event $ j$ (that is, $ i\in A$ and $ j\in B$). The itemwise marginal counts are formulated as follows:

Here the sum of cell counts does not become the marginal count. That is, it does not necessarily satisfy $ D_i = \sum_j C_{i,j}$ and $ AE_j = \sum_i C_{i,j}$.

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