Generalisations of Two Tests for the Detection of Household Aggregation of Disease

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Abstract
Two statistical tests were 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 methods are limited by assuming that in the null case all members of the population, who are assumed to be susceptible, are at equal risk to disease. In this paper these tests are generalized to the situation in which different population strata are at different risks to disease. Formulae are given for the first 4 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 .gtoreq. 2 cases.

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