Summary.-Breast-cancer incidence and mortality rates in different countries were found to be correlated with height, weight and age at menarche, all of which have been identified as risk factors in cohort or case-control studies of breast cancer. There were, however, correlations with total fat and animal protein consumption per capita even after controlling for the 3 anthropometric variables. This suggests that, while some of the effects of diet on breast-cancer rates may be mediated through effects on these known risk factors, there may be more direct effects as well.
Two statistical tests have been suggested to detect household aggregation of disease. Mathen and Chakraborty [1950] proposed counting the number of households, Z, in which there were no cases of the disease, and Walter [1974] proposed counting the number of pairs, N, of cases within households. As originally formulated, both of these methods suffer from the limitation that it is assumed, in the null case, that all members of the population, who are assumed to be susceptible, are at equal risk to disease. In this paper we generalise these tests to the situation in which different population strata are at different risks to disease. Formulae are given for the first four moments of Z. The revised Walter's test is shown to be a special case of a test of Pike and Smith [1974] which enables the expectation and variance of N to be directly evaluated. A similar relationship is noted between Walter's test and Knox's [1964] test for space-time clustering. A further test statistic is suggested: the number of cases, T, in households containing two or more cases.
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