The probability of a cancer cluster due to chance alone

We propose to use a very simple model to test whether a cancer cluster is due to chance alone. We focus on the acute childhood leukaemia cluster in Columbus, Ohio. In 1975, 12 leukaemia cases were observed in Columbus while the expected number is 6 cases per year. According to our simple model, the probability of such an occurrence, due to chance alone, is less than 1 per cent. However, if we divide the child population of the U.S.A. into 200 regions (each region having 200 000 children) then the probability that at least one region will see, in a given year, 12 or more cases is higher than 80 per cent. So in this sense the Columbus cluster could be attributed to chance alone. However, the probability that any of the 200 regions see 18 cases or more in a given year is almost 0. Thus, a cluster of 18 or more cases in a region of 200 000 children should be regarded as highly suspicious and should be investigated.