Statistically robust approaches for sib‐pair linkage analysis

Abstract

summaryMany 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 & Elston (1972) 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, 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.

Comparison of Multivariate Tests for Genetic Linkage

“…However, recent studies [33,34] have shown lack of convergence of the test for linkage to a limiting ¯2 distribution when the data are not normally distributed and there is a strong residual correlation among sibs, after allowing for the major gene effect. Methods to allow the construction of accurate tests for nonnormal data include data trimming [35], application of generalized estimating equations or robust variance estimation [22], or the construction of permutation tests [36]. Application of each of these approaches for multivariate data could be rather complex, and tests using either permutation tests or generalized estimating equations are computationally intensive.…”

Nonparametric Trend Statistic Incorporating Dispersion Differences in Sib Pair Linkage for Quantitative Traits

“…Thirdly, we generated 2,000 replicates with 500 sib pairs per replicate. A sample size of 100 sib pairs has been demonstrated to be robust to non-normal data for the ordinary least squares methods [11,22,23] . The phenotypic value for each sib consisted of mean displacement due to the QTL and a residual value.…”

“…Recently Fernandez et al [10] proposed Winsorizing the sib pair phenotypes before applying the approaches of the HE regression in order to overcome the problem of non-normality of the squared phenotypic differences. Wang et al [11] proposed a robust version of the HE method based on M-estimator of slope, and showed that it is substantially more powerful than the method of HE, the nonparametric Wilcoxon rank-sum and JonckheereTerpstra trend test [12,13] for the non-normally distributed quantitative trait values. In order to test linkage with this M-estimated slope, one is required to generate by a Monte Carlo simulation an empirical null distribution of this M-estimated slope, since the sampling distribution of this slope is not known.…”

Improving the Power of Sib Pair Quantitative Trait Loci Detection by Phenotype Winsorization

“…One revision is the use of a robust version of the Haseman-Elston test using M estimation [15] to increase statistical power when outliers are present. Another such revision considered the correlation between sibs as the index of phenotypic similarity such that the mean-corrected cross products of sib pairs Z j = (X 1j -X -)…”