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C   0.10

The answer to this question is derived using the "rule of three" (as explained by Hanley and Hand, JAMA, 1983). When there are no events of interest observed in a particular group, the upper 95% confidence bound can be calculated by dividing 3 by the number of subjects in the group (i.e., n). In the question, 3/n is equivalent to 3/31 or 0.097. Rounding up produces the answer 0.10, and thus the largest rate that we would expect (with 95% confidence) would be 0.10 or approximately 3.0 events in this group of 31 study subjects. The 99% confidence bound can be obtained by using the "rule of 4.6" (i.e., 4.6/n), and the 99.9% confidence bound can be obtained using the "rule of 6.9" (i.e., 6.9/n). While this explanation will not go into the derivation of this rule, the calculations underpinning the convenient statistical device are sound and well-tested.

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