The Frequency of Cancer Deaths in the Same House and in Neighbouring Houses

Abstract

The problem as to the frequency with which multiple cases of, or deaths from, a disease may be expected to occur in the same house has been attacked by Troup and Maynard (1911–12), Karl Pearson (1911–12, 1911–12 a, 1913), McKendrick (1911–12), Greenwood and Yule (1920), Greenwood (1910, 1931) and others. Troup and Maynard obtained a general expression for the frequency of occurrence, and the standard deviation of the frequency, of s casesin a house when n cases of a disease occur in a town with m houses, assumingeach house to contain the same number of persons, all equally liable to contract it. Karl Pearson (1911–12) considered the problem as analogous to throwing balls at random into equally accessible pigeon-holes, and showed that since the chance that any one case will fall into any one house is , and that it will not is , the numbers of houses having 0, 1, 2, 3, ... cases should be given by the successive terms of the binomial . In a later paper (1913) he showed that the correspondence between the observed andexpected frequencies could be measured by applying the ordinary X2 test to the frequencies, omitting the houses having no cases.