Applied statisticians are often confronted with statistical inference problems dealing with situations in which there appear to be no data, or data of only limited usefulness. For example, when attempting to find a confidence interval for a binomial proportion, the sample may contain no successes. Such a scenario could be encountered when attempting to estimate the incidence of an extremely rare side effect associated with the administration of a newly developed drug. In this article, we use

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... mples for our experiences working with scientific investigators and describe several scenarios in which there appeared to be no useful data, or data of only limited usefulness. We describe the methods we prefer for analyzing the data in these situations and illustrate their application using the actual data from the investigations we participated in.