A more powerful robust sib‐pair test of linkage for quantitative traits

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Abstract
A more powerful robust test for linkage is developed from the methodology of Haseman and Elston [Behav Genet 2(1):3–19, 1972]. This new robust test uses weighted least-squares (WLS) methods to detect linkage between a quantitative trait and a polymorphic marker. For comparison, the characteristics of a test for linkage that uses known trait genotypes for the parents are also studied. Sample sizes needed to detect linkage, calculated using asymptotic results, are compared for 1) the usual Haseman-Elston method, 2) the WLS method, and 3) the method that uses parental trait genotype data. The WLS method needs at most twice the number of sib pairs as does the method that used information on the trait genotypes of the parents. The small sample properties of the Haseman-Elston (H-E) and WLS tests are investigated by simulation. The power calculations for the H-E method are found to be accurate. The power of the WLS method is overestimated when fewer than 300 sib pairs are studied, but the WLS method is nonetheless more powerful than the usual H-E method. In samples of fewer than 300 sib pairs, the WLS test tends to be anticonservative. Treating all sib pairs from sibships of size 3 or 5 as independent does not increase the significance of the tests.