Adding Further Power to the Haseman and Elston Method for Detecting Linkage in Larger Sibships: Weighting Sums and Differences

Abstract

Haseman and Elston (H-E) proposed a robust test to detect linkage between a quantitative trait and a genetic marker. In their method the squared sib-pair trait difference is regressed on the estimated proportion of alleles at a locus shared identical by descent by sib pairs. This method has recently been improved by changing the dependent variable from the squared difference to the mean-corrected product of the sib-pair trait values, a significantly positive regression indicating linkage. Because situations arise in which the original test is more powerful, a further improvement of the H-E method occurs when the dependent variable is changed to a weighted average of the squared sib-pair trait difference and the squared sib-pair mean-corrected trait sum. Here we propose an optimal method of performing this weighting for larger sibships, allowing for the correlation between pairs within a sibship. The optimal weights are inversely proportional to the residual variances obtained from the two different regressions based on the squared sib-pair trait differences and the squared sib-pair mean-corrected trait sums, respectively, allowing for correlations among sib pairs. The proposed method is compared with the existing extension of the H-E approach for larger sibships. Control of the type I error probabilities for sibships of any size can be improved by using a generalized estimating equation approach and the robust sandwich estimate of the variance, or a Monte-Carlo permutation test.

Genome-Wide Linkage Study of Retinal Vessel Diameters in the Beaver Dam Eye Study

“…The robustness of the power of the t test, which was used in the model-free quantitative trait linkage method of this article, 18 in the presence of nonnormality, is not well guaranteed as the robustness of the type I error. 19,20 Therefore, we performed commingling analyses for the covariate-adjusted traits using the program SEGREG implemented in S.A.G.E., during the process of which a Box-Cox power transformation was performed to simultaneously obtain normal and homoscedastic residuals.…”

Genome-wide linkage scan for nicotine dependence in European Americans and its converging results with African Americans in the Mid-South Tobacco Family sample

“…As reported previously, 14,20 we transformed non-zero SQ values to a natural log-scale or an indexed SQ, in which and squared mean corrected trait sum; the former adjusts for the non-independence of sib pairs while the latter adjusts for the non-independence of sib pairs and the non-independence of squared trait sums and differences. 30 Otherwise, default options were used for all parameters in the trait regression method. Sex and age were included as covariates for all analyses in the EA sample, and sex, age and ethnicity were included as covariates for the combined sample.…”

Linkage and association studies in African- and Caucasian-American populations demonstrate that SHC3 is a novel susceptibility locus for nicotine dependence

“…Evidence for linkage was assessed by a HasemanElston regression with dependent variable options W3 and W4, which transforms the sib-pair's trait values to a weighted combination of the squared trait difference and squared-mean corrected trait sum, allowing for the non-independence of sib-pairs. 26 In SIBPAL, default options were used for all parameters in the trait regression method except that the options W3 (i.e., the weighted combination of squared trait difference and squared mean-corrected trait sum adjusting for the non-independence of sib-pairs) and W4 (i.e., the non-independence of squared trait sums and differences) were examined. Both options yielded essentially the same results on the three ND measures (SQ, HSI and FTND).…”