Comparison of Multivariate Tests for Genetic Linkage

Abstract

Objectives: Multivariate tests for linkage can provide improved power over univariate tests but the type I error rates and comparative power of commonly used methods have not previously been compared. Here we studied the behavior of bivariate formulations of the variance component (VC) and Haseman-Elston (H-E) approaches. Methods: We compared through simulation studies the bivariate H-E test with the unconstrained bivariate VC approach and with a VC approach in which the major-gene correlation is constrained to ±1. We also compared these methods to univariate methods. Results: Bivariate approaches are more powerful than univariate analyses unless the traits are very highly positively correlated. The power of the bivariate H-E test was less than the VC procedures. The constrained test was often less powerful than the unconstrained test. The empirical distributions of the bivariate H-E test and the unconstrained bivariate VC test conformed with asymptotic distributions for samples of 100 or more sibships of size 4. Conclusions: The unconstrained VC test is valuable for testing for preliminary linkages using multivariate phenotypes. The bivariate H-E test was less powerful than the bivariate VC tests.

Bivariate genome-wide scan for metabolic phenotypes in non-diabetic Chinese individuals from the Stanford, Asia and Pacific Program of Hypertension and Insulin Resistance Family Study

“…As for the interaction between fasting insulin and glucose levels, we cannot exclude the possibility of partial pleiotropy. These findings are consistent with previous studies showing that trait pairs exhibiting low to moderate overall genetic and phenotypic correlations appear more informative for bivariate analyses than pairs with high genetic correlations [19,27,30,31]. On the other hand, the QTL responsible for fasting insulin together with BMI or HOMA-IR could be due to co-incident linkage, suggesting that the susceptibility genes are independently responsible for fasting insulin or BMI and simply happen to cluster together.…”

“…Genome-wide bivariate multipoint linkage analyses The univariate variance component method [25] decomposes the variability of a trait into components for a QTL, the residual polygenic component and the random environmental component [26], which has been extended to a multivariate framework [27]. In the bivariate model, the additive genetic (ρ g ) and environmental (ρ e ) correlations between the two traits represent the effects of shared genes or pleiotropy and shared environmental factors, respectively on the phenotypic variance in a trait.…”

“…Under this model, we tested the null hypothesis that the variance component attributed from the QTL equals zero for both traits by comparing the likelihood of this restricted model to that of a model in which this variance component was estimated for the traits. Twice the difference in log likelihoods of these models yields a test statistic that is asymptotically distributed as a mixture of 1/4 χ 2 0 , 1/2 χ 2 1 and 1/4 χ 2 3 [27]. Bivariate linkage analyses were performed for each pairwise combination of metabolic traits.…”

“…In the case of ρ q being constrained to 0, the difference between these likelihoods is distributed as a chi-square with 1 degree of freedom. When ρ q is constrained to 1 or −1, a boundary, the difference in likelihoods, is distributed as a 1/2:1/2 mixture of χ 2 1 and a point mass at 0 [27]. The hypothesis of ρ q =1 or −1 (complete pleiotropy) or the hypothesis of ρ q =0 (co-incident linkage) was rejected when p was less than 0.05.…”

Bivariate association analysis in selected samples: application to a GWAS of two bone mineral density phenotypes in males with high or low BMD

“…Joint analysis of correlated phenotypes can theoretically provide greater power than that provided by analysis of individual phenotypes. 3,[5][6][7] Multivariate analysis can also alleviate the multiple testing problem, caused by testing different traits separately, and thereby improve the ability to detect genetic variants whose effects are too small to be detected in univariate analysis. 8 Several multivariate approaches have been applied to linkage studies of correlated complex phenotypes, such as osteoporosis and bone-related phenotypes.…”