## 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 denote the count of reporting incidents involving the list of drugs and the list of AE's. Then the marginal counts are formulated listwise as follows:

- (marginal count for the list of drugs)
- (marginal count for the list of AE's)
- (total count)

Here the summation indicates the sum over all the possible lists 's of drugs, and is over all the possible lists 's of AE's. The reporting incident is also counted itemwise between drug and adverse reaction as follows:

- (cell count)

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

- (marginal count for the drug )
- (marginal count for the AE )

Here the sum of cell counts does not become the marginal count. That is, it does not necessarily satisfy and .

© TTU Mathematics