A New Testing Procedure for the Probability of Rare Events

Abstract

We consider a testing procedure for the occurrence probability of rare events such as a severe adverse drug reaction observed after the release of a drug to market. Occurrence probabilities in two periods or populations Ω_0 and Ω_1 are compared. Under the condition that k events were observed among n patients for one population Ω_0, we test whether the occurrence probability for the second period or population Ω_1 is the same as that in Ω_0. We derive the null distribution and the non-null distribution of the test statistic both in exact and approximate forms, and make numerical assessment of the accuracy of the approximation. Further, the power function is also derived and the power of the test will be evaluated using the power function.