Confidence interval estimation under inverse sampling

In comparative studies of rare events, fixing group sizes may result in groups with zero events. To overcome this difficulty, one may adopt an inverse sampling design which fixes the number of events, resulting in random variables following the negative binomial distribution. This article presents a new approach to setting confidence intervals for effect measures under inverse sampling, using the variance estimates recovered from exact confidence limits for single negative binomial proportions. Exact numerical evaluation results demonstrate that the proposed procedure performs well.