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 (GxG), or gene-by-environment (GxE) interaction. We propose a versatile likelihood ratio test that allows joint testing for mean and variance heterogeneity (LRTMV) or either effect alone (LRTM or LRTV) in the presence of covariates. Using extensive simulations for our method and others we found that all parametric tests were sensitive to non-normality 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 linkage disequilibrium (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 gene-by-gene interactions and also how vQTL are related to relationship loci (rQTL) and how both can create prior hypothesis for each other and reveal the relationships between traits and possibly between components of a composite trait.

On Robust Association Testing for Quantitative Traits and Rare Variants

“…In response, we further propose a robust version of the aSPU test, called aSPUr. While the traditional variant-by-variant association test for common SNVs (MAF $>5\text{\%}$) has been shown to be robust to nonnormal distributed traits (Cao et al 2014), here we demonstrate that RV association testing can be very sensitive to quantitative trait’s subtle deviation from normality. Based on type I error control and statistical power considerations, we further provide practitioners with some general guidelines and a new robust test to deal with nonnormal quantitative traits.…”

Genetic interactions matter more in less-optimal environments: a Focused Review of “Phenotype uniformity in combined-stress environments has a different genetic architecture than in single-stress treatments” (Makumburage and Stapleton, 2011)

“…A more recently developed method (Cao et al, 2014) for detecting quantitative trait loci with variance heterogeneity (vQTL) is a likelihood ratio test developed to test differences in means and variances simultaneously (LRT MV ). Derivatives of this test allow for single-purpose testing of variance heterogeneity (i.e., phenotype uniformity) and mean differences (notated LRT V and LRT M respectively).…”

“…In a second application to dairy traits, the environmental effect was again shown to contribute substantially to the variance (Mulder et al, 2013a). In the Cao et al (2014) work the new method was applied to a well-understood functional variant important for Alzheimer disease; the analysis showed that closely linked SNPs with different population distributions could be detected using the method. As yet, this omnibus method has not been applied to environment or modifier detection.…”

Covariate adjusted differential variability analysis of DNA methylation with propensity score method

“…As the list of DMC and DVC may provide complementary information, this motivates us to develop our model for DVC and DMC separately. Most of the existing approaches for testing mean and variance simultaneously (Opdyke, 2009;Cao et al, 2014) reduce to testing the null hypothesis: μ 1 = μ 2 and 2 2 1 2 = σ σ and the (Levene: Levene's test, Wt-Score: weighted score test; GLM: logistic regression on r ij and direct covariates adjustment; Pool-pv: χ 2 -test p-values pooling.) For the method "GLM without covariate adjustment", we fit a logistic regression y i ∼r ij , whereas for "GLM with covariate adjustment", we fit a logistic regression y i ∼r ij +age i +race i +stage i +alcohol i +smoking i , where y i is the binary indicator for luminal A and basal subtype and j denote CpG j.…”