Comparison of the proportions of affected relatives of cases and controls: analysis and minimum sample size formula

The problem of familial aggregation has frequently been approached by comparing the proportion of affected relatives of index cases with the proportion of affected relatives of index controls. This type of study has an analogy with the case-control design and is frequently analysed as if it was one. It is however an essentially different design which may involve dependent observations. We show that conventional tests for comparing proportions of affected subjects are still valid with this design; we give a formula for computing the minimum sample size required to detect a given degree of aggregation measured by the intracluster correlation coefficient, which can be estimated very simply by the difference in proportions of affected relatives in the two groups.