Linkage between quantitative trait and marker loci: methods using all relative pairs

Relative-pair methods for detection of linkage between a quantitative trait and a marker locus have been proposed by a number of authors [e.g., Haseman and Elston, Behav Genet 3-19, 1972; Amos and Elston, Genet Epidemiol 349-360, 1989]. However, development of tests of significance that combine information from different types of relative pairs has been hampered by the presence of correlations between relative pairs from the same pedigree. In this paper, the methodology of generalized estimating equations is used to provide an estimate of the robust covariance matrix of the estimates of the set of relative-pair-type-specific regression parameters. Using this matrix, an asymptotically most powerful test of linkage which optimally combines the information contained in the different types of relative pairs is constructed. This test requires optimal weights that depend on unknown values of heritability and recombination fraction to be chosen a priori. However, simulations show that, in the regions of recombination fraction and heritability of practical interest, the power of the test does not depend strongly on the assumptions made when choosing the optimal weights; as a result, weights that depend only on the number of each type of relative pair and the variability of the marker identity-by-descent probabilities work well in practice. In addition, an approximation to the regression model leads to a simple approach to testing linkage in which only a single regression parameter is estimated from data containing different types of relative pairs. The resulting test is slightly less powerful than the test described above, but its computational simplicity and lack of dependence on a priori weighting schemes suggest potential usefulness in large linkage studies.