A versatile omnibus test for detecting mean and variance heterogeneity

Abstract

Recent research has revealed loci that display variance heterogeneity through various means such as biological disruption, linkage disequilibrium (LD), gene-by-gene (G × G), or gene-by-environment interaction. We propose a versatile likelihood ratio test that allows joint testing for mean and variance heterogeneity (LRT(MV)) or either effect alone (LRT(M) or LRT(V)) in the presence of covariates. Using extensive simulations for our method and others, we found that all parametric tests were sensitive to nonnormality regardless of any trait transformations. Coupling our test with the parametric bootstrap solves this issue. Using simulations and empirical data from a known mean-only functional variant, we demonstrate how LD can produce variance-heterogeneity loci (vQTL) in a predictable fashion based on differential allele frequencies, high D', and relatively low r² values. We propose that a joint test for mean and variance heterogeneity is more powerful than a variance-only test for detecting vQTL. This takes advantage of loci that also have mean effects without sacrificing much power to detect variance only effects. We discuss using vQTL as an approach to detect G × G interactions and also how vQTL are related to relationship loci, and how both can create prior hypothesis for each other and reveal the relationships between traits and possibly between components of a composite trait.

Figure 1

Test statistics (−log₁₀(P values)) for association between SNPs within 100kb of functional SNP rs679620 and MMP3 protein levels in Cerebralspinal Fluid. A. Lowess of test statistics (−log₁₀(P values)) against LD (|r|) with the functional SNP rs679620, from 5′ and 3′ separately. B. Lowess of test statistics (−log₁₀(P values)) against LD (|r|) with the SNP having the smallest p-value of LRT_V, from 5′ and 3′ separately. (See supplemental Figure 1 for plots without smoothing.) LR: linear regression; LRT_MV: likelihood ratio test testing both mean and variance heterogeneity; LRT_M: likelihood ratio test testing mean heterogeneity; LRT_V: likelihood ratio test testing variance heterogeneity.

Figure 1

Test statistics (−log₁₀(P values)) for association between SNPs within 100kb of functional SNP rs679620 and MMP3 protein levels in Cerebralspinal Fluid. A. Lowess of test statistics (−log₁₀(P values)) against LD (|r|) with the functional SNP rs679620, from 5′ and 3′ separately. B. Lowess of test statistics (−log₁₀(P values)) against LD (|r|) with the SNP having the smallest p-value of LRT_V, from 5′ and 3′ separately. (See supplemental Figure 1 for plots without smoothing.) LR: linear regression; LRT_MV: likelihood ratio test testing both mean and variance heterogeneity; LRT_M: likelihood ratio test testing mean heterogeneity; LRT_V: likelihood ratio test testing variance heterogeneity.