Confidence limits based on the first occurrence of an event

Confidence limits for population prevalence based on the first occurrence of an item in a medical database, or for incidence based on time to first occurrence, should be based on the geometric or exponential distributions, respectively. These intervals are presented and compared with the corresponding intervals based on the binomial and Poisson distributions. The lower confidence limits are shown to be the same, but the upper limits are smaller, hence leading to shorter intervals. Applications of these intervals are also presented.