Robust methods for the detection of genetic linkage for quantitative data from pedigrees

The robust method for detecting linkage developed by Haseman and Elston [The investigation of linkage between a quantitative trait and a marker locus. Behav Genet 2:3-19, 1972] for data from sib pairs is extended to any type of noninbred relative pair. The regression of the squared relative-pair trait difference on the estimated proportion of genes identical by descent (i.b.d.) at a marker locus is shown to depend upon the recombination fraction between the two loci; the regression coefficient is negative if the trait and marker loci are linked. A test for linkage based on data from any informative type of relative pair can thus be obtained by testing that this regression coefficient is less than zero. Formulae for the asymptotic power of such tests for linkage based upon independent relative pairs are developed. Results are also given for the special case in which the proportion of genes shared i.b.d. for relative pairs is known. Finally, a general algorithm is described that will incorporate all available pedigree data to calculate an estimate of the proportion of genes that a relative pair shares i.b.d. at a marker locus.