Exact tests for epidemiological risks under independent negative binomial sampling for rare events in clinical trials

2 × 2 contingency tables are frequently obtained from independent binomial sampling. However, when the probabilities of the outcome of interest are small, we may use independent negative binomial sampling in which sampling stops after a predetermined number of the outcome of interest occurs. The obtained 2 × 2 contingency tables are likely to be unbalanced, and the asymptotic tests could be unreliable. In this article, we develop exact conditional tests for the risk difference, the risk ratio, and the odds ratio in 2 × 2 contingency tables obtained from independent negative binomial sampling. We investigate the exact unconditional powers of the exact tests. The main advantage of exact test is that it is guaranteed to control type I errors under the nominal level unconditionally.