The person-time ratio distribution for the exact monitoring of adverse events: Historical vs surveillance Poisson data.

In the postmarket drug and vaccine safety surveillance, when the number of adverse events follows a Poisson distribution, the ratio between the exposed and the unexposed person-time information is the random variable that governs the decision rule about the safety of the drug or vaccine. The probability distribution function of such a ratio is derived in this paper. Exact point and interval estimators for the relative risk are discussed as well as statistical hypothesis testing.