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Summary

General expressions for the distribution of identity by descent (IBD) scores at a marker locus have been derived given neither, one or both sibs affected with a disorder determined by a linked trait locus with arbitrary gene frequency and penetrance vector. It is shown that the distribution of IBD scores depends only on the additive and dominance variances and the population prevalence of the disorder.

A one-sided test is suggested as an appropriate means of statistically testing the hypothesis that the recombination fraction is significantly less than. This sib pair approach is designed primarily to detect the presence of a critical disease susceptibility locus but when the assumptions of the incompletely penetrant single locus model are correct the methodology proposed here results in consistent estimates of the recombination fraction. The affected sib pair methodology seems especially suited to traits determined by single loci with non-Mendelian transmission.

We wish to express our gratitude to Mr P. Van Eerdewegh and to Drs P. Fishman and S. Hodge for their many helpful comments and criticisms.

This work has been supported by HEW grants MH 25430, MH 22521, MH 14677, MH 13002 and AA 00209.