Cancer Clusters

It is not inconsistent with randomness to have regions in the United States in which there is an unusually high incidence of some specific cancer. These cancer clusters occur in various parts of the nation and lead to a belief among some residents of these communities that there must be an unnatural source for the higher than usual rate of malignancies, such as toxic wastes secretly dumped into the water supply by local industries or government agencies who connive in a conspiracy of silence. It seems like just too much of a coincidence. Public health agencies are often cajoled into investigating what the residents of such a targeted township regards with suspicion, disregarding the fact that there are many such locales throughout the nation some of which may not even be aware that their cancer rate is above average. Once again it is a case of ignoring that the probability of such a cluster, somewhere, not just in your backyard, may not be all that small. As the Poisson approximation shows, a cluster is likely to happen somewhere by chance and will affect someone other than you and your community. When it happens to you it induces skepticism and distrust (see Gawande [18]). This is a common problem of misjudging coincidences, a topic that is taken up in more detail in a later vignette.