Many traits that distinguish one individual from another, such as height or weight, are clearly heritable and yet vary continuously in populations. Continuous, heritable variation in trait levels presumably reflects the segregation of multiple genes, but elucidation of the genetic architecture of quantitative traits has been limited. Haseman and Elston developed a genetically robust method (HE) for detecting linkage to quantitative trait loci using sib-pairs. The method is based on a simple linear regression of the squared sib-pairs trait difference on the proportion of alleles shared identical by descent at a marker locus. Linkage is detected by a negative slope which has been traditionally assessed by a standard t-test. Wan, Cohen and Guerra have shown that the standard t-test is robust to the violations of the stochastic assumptions underlying the test. In practice, however, the standard t-test, based on least-squares regression, is sensitive to outliers. The presence of outliers in the data can lead to false positive and false negative linkage results. Accordingly we have developed and evaluated a statistically robust procedure for the HE approach to linkage. The procedure is based on robust regression. Simulation studies show that this robust procedure has greater power than the standard t-test in the presence of outliers, and has similar power to the standard t-test in the absence of outliers. This robust procedure also shows greater power than rank-based approaches either in the absence or presence of outliers. To illustrate the methods using real data we reanalyse data from two lipoprotein systems that motivated this work.
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