Testing for familial aggregation of a dichotomous trait

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Abstract
Familial aggregation of a disease is usually tested using a chi square statistic on a sample of pairs of related individuals. Standard sampling designs often produce dependent observations (multiple pairs from the same family), possibly inflating the numerical value of the statistic over the value independent observations would produce. This article presents a derivation of the chi square statistic for familial aggregation, allowing for dependency because of the inclusion of the same and related persons in multiple pairs. For intraclass aggregation, the standard chi square statistic is appropriate. For interclass aggregation, an adjustment to the standard chi square statistic is needed; the adjustment depends on the disease frequency and the intraclass aggregation within each class.