The correlation between estimates of familial frequencies.

For the determination of the mode of inheritance of a disease or disorder familial data is often used and is usually presented in frequency form. This data has usually been obtained from a single set of nuclear families and so the estimates of the frequencies in relatives of those affected are not independent of one another and this makes inference concerning the mode of inheritance difficult. The exact degree of the correlation between estimates is not easy to determine. In this paper expressions are derived for the asymptotic variances of estimates and for the covariances and correlations between the basic pairs of intrafamilial frequency estimates for families of a given structure, and the extension to families of different sizes and structures is outlined. It is shown that these correlations are not necessarily negligible and should be taken into consideration when testing hypotheses concerning the mode of inheritance.