Estimating the probability of occurrence of tumor for a rare cancer with zero occurrence in a sample.

In many physical situations one needs to estimate the probability of occurrence of a rare event based on a random sample when the event has not occurred at all. For example, if the true lifetime incidence of a tumor at a particular tissue site is less than 1%, it is not uncommon to observe no tumors in a typical sample size of 50 animals. This paper explores the suitability of nonzero Bayesian estimation procedures to replace zero maximum likelihood estimates for tissue sites with nonzero background tumor incidences.