Score test for detecting linkage to quantitative traits

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Abstract
The two most popular methods to detect linkage of a quantitative trait to a marker are the Haseman‐Elston regression method and the variance components likelihood‐ratio test. In the literature, these methods are frequently compared and the relative advantages and disadvantages of each method are well known. In this article, we derive a score test for the variance component attributable to a specific quantitative trait locus and show that for sib‐pairs it is mathematically equivalent to a recently proposed version of the Haseman‐Elston method that optimally combines the sum squared and the difference squared of the centered phenotype values of the sibs. Because score tests and likelihood‐ratio tetsts are equivalent for large sample sizes, the variance components likelihood‐ratio test is also asymptotically equivalent to this optimal Haseman‐Elston test. This fact gives a theoretical explanation of the empirical observation from simulation studies reporting similar power of the variance components likelihood‐ratio test and the optimal Haseman‐Elston method. Perhaps more importantly for practical purposes, the score test can also be extended in a natural way to support the simultaneous analysis of more than two subjects and multivariate phenotypes. Genet. Epidemiol. 22:345–355, 2002.