A nonparametric test to detect quantitative trait loci where the phenotypic distribution differs by genotypes

A new test for trait mean and variance detects unreported loci for blood-pressure variation

Variability in quantitative traits has clinical, ecological, and evolutionary significance. Most genetic variants identified for complex quantitative traits have only a detectable effect on the mean of trait. We have developed the mean-variance test (MVtest) to simultaneously model the mean and log-variance of a quantitative trait as functions of genotypes and covariates by using estimating equations. The advantages of MVtest include the facts that it can detect effect modification, that multiple testing can follow conventional thresholds, that it is robust to non-normal outcomes, and that association statistics can be meta-analyzed. In simulations, we show control of type I error of MVtest over several alternatives. We identified 51 and 37 previously unreported associations for effects on blood-pressure variance and mean, respectively, in the UK Biobank. Transcriptome-wide association studies revealed 633 significant unique gene associations with blood-pressure mean variance. MVtest is broadly applicable to studies of complex quantitative traits and provides an important opportunity to detect novel loci.

Detecting genetic effects on phenotype variability to capture gene-by-environment interactions: a systematic method comparison

Genetically associated phenotypic variability has been widely observed across organisms and traits, including in humans. Both gene-gene and gene-environment interactions can lead to an increase in genetically associated phenotypic variability. Therefore, detecting the underlying genetic variants, or variance Quantitative Trait Loci (vQTLs), can provide novel insights into complex traits. Established approaches to detect vQTLs apply different methodologies from variance-only approaches to mean-variance joint tests, but a comprehensive comparison of these methods is lacking. Here, we review available methods to detect vQTLs in humans, carry out a simulation study to assess their performance under different biological scenarios of gene-environment interactions, and apply the optimal approaches for vQTL identification to gene expression data. Overall, with a minor allele frequency (MAF) of less than 0.2, the squared residual value linear model (SVLM) and the deviation regression model (DRM) are optimal when the data follow normal and non-normal distributions, respectively. In addition, the Brown-Forsythe (BF) test is one of the optimal methods when the MAF is 0.2 or larger, irrespective of phenotype distribution. Additionally, a larger sample size and more balanced sample distribution in different exposure categories increase the power of BF, SVLM, and DRM. Our results highlight vQTL detection methods that perform optimally under realistic simulation settings and show that their relative performance depends on the phenotype distribution, allele frequency, sample size, and the type of exposure in the interaction model underlying the vQTL.

FEATURE SELECTION FOR GENERALIZED VARYING COEFFICIENT MIXED-EFFECT MODELS WITH APPLICATION TO OBESITY GWAS

Motivated by an empirical analysis of data from a genome-wide association study on obesity, measured by the body mass index (BMI), we propose a two-step gene-detection procedure for generalized varying coefficient mixed-effects models with ultrahigh dimensional covariates. The proposed procedure selects significant single nucleotide polymorphisms (SNPs) impacting the mean BMI trend, some of which have already been biologically proven to be "fat genes." The method also discovers SNPs that significantly influence the age-dependent variability of BMI. The proposed procedure takes into account individual variations of genetic effects and can also be directly applied to longitudinal data with continuous, binary or count responses. We employ Monte Carlo simulation studies to assess the performance of the proposed method and further carry out causal inference for the selected SNPs.

A fast score test for generalized mixture models

In biomedical studies, testing for homogeneity between two groups, where one group is modeled by mixture models, is often of great interest. This paper considers the semiparametric exponential family mixture model proposed by Hong et al. (2017) and studies the score test for homogeneity under this model. The score test is nonregular in the sense that nuisance parameters disappear under the null hypothesis. To address this difficulty, we propose a modification of the score test, so that the resulting test enjoys the Wilks phenomenon. In finite samples, we show that with fixed nuisance parameters the score test is locally most powerful. In large samples, we establish the asymptotic power functions under two types of local alternative hypotheses. Our simulation studies illustrate that the proposed score test is powerful and computationally fast. We apply the proposed score test to an UK ovarian cancer DNA methylation data for identification of differentially methylated CpG sites.

Analytical strategies to include the X-chromosome in variance heterogeneity analyses: Evidence for trait-specific polygenic variance structure

Genotype-stratified variance of a quantitative trait could differ in the presence of gene-gene or gene-environment interactions. Genetic markers associated with phenotypic variance are thus considered promising candidates for follow-up interaction or joint location-scale analyses. However, as in studies of main effects, the X-chromosome is routinely excluded from "whole-genome" scans due to analytical challenges. Specifically, as males carry only one copy of the X-chromosome, the inherent sex-genotype dependency could bias the trait-genotype association, through sexual dimorphism in quantitative traits with sex-specific means or variances. Here we investigate phenotypic variance heterogeneity associated with X-chromosome single nucleotide polymorphisms (SNPs) and propose valid and powerful strategies. Among those, a generalized Levene's test has adequate power and remains robust to sexual dimorphism. An alternative approach is a sex-stratified analysis but at the cost of slightly reduced power and modeling flexibility. We applied both methods to an Estonian study of gene expression quantitative trait loci (eQTL; n = 841), and two complex trait studies of height, hip, and waist circumferences, and body mass index from Multi-Ethnic Study of Atherosclerosis (MESA; n = 2,073) and UK Biobank (UKB; n = 327,393). Consistent with previous eQTL findings on mean, we found some but no conclusive evidence for cis regulators being enriched for variance association. SNP rs2681646 is associated with variance of waist circumference (p = 9.5E-07) at X-chromosome-wide significance in UKB, with a suggestive female-specific effect in MESA (p = 0.048). Collectively, an enrichment analysis using permutated UKB (p < 0.1) and MESA (p < 0.01) datasets, suggests a possible polygenic structure for the variance of human height.

QTL Mapping on a Background of Variance Heterogeneity

Standard QTL mapping procedures seek to identify genetic loci affecting the phenotypic mean while assuming that all individuals have the same residual variance. But when the residual variance differs systematically between groups, perhaps due to a genetic or environmental factor, such standard procedures can falter: in testing for QTL associations, they attribute too much weight to observations that are noisy and too little to those that are precise, resulting in reduced power and and increased susceptibility to false positives. The negative effects of such "background variance heterogeneity" (BVH) on standard QTL mapping have received little attention until now, although the subject is closely related to work on the detection of variance-controlling genes. Here we use simulation to examine how BVH affects power and false positive rate for detecting QTL affecting the mean (mQTL), the variance (vQTL), or both (mvQTL). We compare linear regression for mQTL and Levene's test for vQTL, with tests more recently developed, including tests based on the double generalized linear model (DGLM), which can model BVH explicitly. We show that, when used in conjunction with a suitable permutation procedure, the DGLM-based tests accurately control false positive rate and are more powerful than the other tests. We also find that some adverse effects of BVH can be mitigated by applying a rank inverse normal transform. We apply our novel approach, which we term "mean-variance QTL mapping", to publicly available data on a mouse backcross and, after accommodating BVH driven by sire, detect a new mQTL for bodyweight.

QTL Mapping on a Background of Variance Heterogeneity

Standard QTL mapping procedures seek to identify genetic loci affecting the phenotypic mean while assuming that all individuals have the same residual variance. But when the residual variance differs systematically between groups, perhaps due to a genetic or environmental factor, such standard procedures can falter: in testing for QTL associations, they attribute too much weight to observations that are noisy and too little to those that are precise, resulting in reduced power and and increased susceptibility to false positives. The negative effects of such "background variance heterogeneity" (BVH) on standard QTL mapping have received little attention until now, although the subject is closely related to work on the detection of variance-controlling genes. Here we use simulation to examine how BVH affects power and false positive rate for detecting QTL affecting the mean (mQTL), the variance (vQTL), or both (mvQTL). We compare linear regression for mQTL and Levene's test for vQTL, with tests more recently developed, including tests based on the double generalized linear model (DGLM), which can model BVH explicitly. We show that, when used in conjunction with a suitable permutation procedure, the DGLM-based tests accurately control false positive rate and are more powerful than the other tests. We also find that some adverse effects of BVH can be mitigated by applying a rank inverse normal transform. We apply our novel approach, which we term "mean-variance QTL mapping", to publicly available data on a mouse backcross and, after accommodating BVH driven by sire, detect a new mQTL for bodyweight.

Beyond the traditional simulation design for evaluating type 1 error control: From the "theoretical" null to "empirical" null

When evaluating a newly developed statistical test, an important step is to check its type 1 error (T1E) control using simulations. This is often achieved by the standard simulation design S0 under the so-called "theoretical" null of no association. In practice, the whole-genome association analyses scan through a large number of genetic markers ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> s) for the ones associated with an outcome of interest ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> ), where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> comes from an alternative while the majority of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> s are not associated with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> ; the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi> <mml:mo>-</mml:mo> <mml:mi>G</mml:mi></mml:math> relationships are under the "empirical" null. This reality can be better represented by two other simulation designs, where design S1.1 simulates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> from analternative model based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> , then evaluates its association with independently generated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow/> <mml:msub><mml:mi>G</mml:mi> <mml:mrow><mml:mi>n</mml:mi> <mml:mi>e</mml:mi> <mml:mi>w</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> ; while design S1.2 evaluates the association between permutated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> . More than a decade ago, Efron (2004) has noted the important distinction between the "theoretical" and "empirical" null in false discovery rate control. Using scale tests for variance heterogeneity, direct univariate, and multivariate interaction tests as examples, here we show that not all null simulation designs are equal. In examining the accuracy of a likelihood ratio test, while simulation design S0 suggested the method being accurate, designs S1.1 and S1.2 revealed its increased empirical T1E rate if applied in real data setting. The inflation becomes more severe at the tail and does not diminish as sample size increases. This is an important observation that calls for new practices for methods evaluation and T1E control interpretation.

A sibling method for identifying vQTLs

The propensity of a trait to vary within a population may have evolutionary, ecological, or clinical significance. In the present study we deploy sibling models to offer a novel and unbiased way to ascertain loci associated with the extent to which phenotypes vary (variance-controlling quantitative trait loci, or vQTLs). Previous methods for vQTL-mapping either exclude genetically related individuals or treat genetic relatedness among individuals as a complicating factor addressed by adjusting estimates for non-independence in phenotypes. The present method uses genetic relatedness as a tool to obtain unbiased estimates of variance effects rather than as a nuisance. The family-based approach, which utilizes random variation between siblings in minor allele counts at a locus, also allows controls for parental genotype, mean effects, and non-linear (dominance) effects that may spuriously appear to generate variation. Simulations show that the approach performs equally well as two existing methods (squared Z-score and DGLM) in controlling type I error rates when there is no unobserved confounding, and performs significantly better than these methods in the presence of small degrees of confounding. Using height and BMI as empirical applications, we investigate SNPs that alter within-family variation in height and BMI, as well as pathways that appear to be enriched. One significant SNP for BMI variability, in the MAST4 gene, replicated. Pathway analysis revealed one gene set, encoding members of several signaling pathways related to gap junction function, which appears significantly enriched for associations with within-family height variation in both datasets (while not enriched in analysis of mean levels). We recommend approximating laboratory random assignment of genotype using family data and more careful attention to the possible conflation of mean and variance effects.

Current Challenges and New Opportunities for Gene-Environment Interaction Studies of Complex Diseases

Recently, many new approaches, study designs, and statistical and analytical methods have emerged for studying gene-environment interactions (G×Es) in large-scale studies of human populations. There are opportunities in this field, particularly with respect to the incorporation of -omics and next-generation sequencing data and continual improvement in measures of environmental exposures implicated in complex disease outcomes. In a workshop called "Current Challenges and New Opportunities for Gene-Environment Interaction Studies of Complex Diseases," held October 17-18, 2014, by the National Institute of Environmental Health Sciences and the National Cancer Institute in conjunction with the annual American Society of Human Genetics meeting, participants explored new approaches and tools that have been developed in recent years for G×E discovery. This paper highlights current and critical issues and themes in G×E research that need additional consideration, including the improved data analytical methods, environmental exposure assessment, and incorporation of functional data and annotations.

Update on the State of the Science for Analytical Methods for Gene-Environment Interactions

The analysis of gene-environment interaction (G×E) may hold the key for further understanding the etiology of many complex traits. The current availability of high-volume genetic data, the wide range in types of environmental data that can be measured, and the formation of consortiums of multiple studies provide new opportunities to identify G×E but also new analytical challenges. In this article, we summarize several statistical approaches that can be used to test for G×E in a genome-wide association study. These include traditional models of G×E in a case-control or quantitative trait study as well as alternative approaches that can provide substantially greater power. The latest methods for analyzing G×E with gene sets and with data in a consortium setting are summarized, as are issues that arise due to the complexity of environmental data. We provide some speculation on why detecting G×E in a genome-wide association study has thus far been difficult. We conclude with a description of software programs that can be used to implement most of the methods described in the paper.

A semiparametric model for vQTL mapping

Quantitative trait locus analysis has been used as an important tool to identify markers where the phenotype or quantitative trait is linked with the genotype. Most existing tests for single locus association with quantitative traits aim at the detection of the mean differences across genotypic groups. However, recent research has revealed functional genetic loci that affect the variance of traits, known as variability-controlling quantitative trait locus. In addition, it has been suggested that many genotypes have both mean and variance effects, while the mean effects or variance effects alone may not be strong enough to be detected. The existing methods accounting for unequal variances include the Levene's test, the Lepage test, and the D-test, but suffer from their limitations of lack of robustness or lack of power. We propose a semiparametric model and a novel pairwise conditional likelihood ratio test. Specifically, the semiparametric model is designed to identify the combined differences in higher moments among genotypic groups. The pairwise likelihood is constructed based on conditioning procedure, where the unknown reference distribution is eliminated. We show that the proposed pairwise likelihood ratio test has a simple asymptotic chi-square distribution, which does not require permutation or bootstrap procedures. Simulation studies show that the proposed test performs well in controlling Type I errors and having competitive power in identifying the differences across genotypic groups. In addition, the proposed test has certain robustness to model mis-specifications. The proposed test is illustrated by an example of identifying both mean and variances effects in body mass index using the Framingham Heart Study data.

Screening for interaction effects in gene expression data

Expression quantitative trait (eQTL) studies are a powerful tool for identifying genetic variants that affect levels of messenger RNA. Since gene expression is controlled by a complex network of gene-regulating factors, one way to identify these factors is to search for interaction effects between genetic variants and mRNA levels of transcription factors (TFs) and their respective target genes. However, identification of interaction effects in gene expression data pose a variety of methodological challenges, and it has become clear that such analyses should be conducted and interpreted with caution. Investigating the validity and interpretability of several interaction tests when screening for eQTL SNPs whose effect on the target gene expression is modified by the expression level of a transcription factor, we characterized two important methodological issues. First, we stress the scale-dependency of interaction effects and highlight that commonly applied transformation of gene expression data can induce or remove interactions, making interpretation of results more challenging. We then demonstrate that, in the setting of moderate to strong interaction effects on the order of what may be reasonably expected for eQTL studies, standard interaction screening can be biased due to heteroscedasticity induced by true interactions. Using simulation and real data analysis, we outline a set of reasonable minimum conditions and sample size requirements for reliable detection of variant-by-environment and variant-by-TF interactions using the heteroscedasticity consistent covariance-based approach.

A perspective on interaction effects in genetic association studies

The identification of gene–gene and gene–environment interaction in human traits and diseases is an active area of research that generates high expectation, and most often lead to high disappointment. This is partly explained by a misunderstanding of the inherent characteristics of standard regression‐based interaction analyses. Here, I revisit and untangle major theoretical aspects of interaction tests in the special case of linear regression; in particular, I discuss variables coding scheme, interpretation of effect estimate, statistical power, and estimation of variance explained in regard of various hypothetical interaction patterns. Linking this components it appears first that the simplest biological interaction models—in which the magnitude of a genetic effect depends on a common exposure—are among the most difficult to identify. Second, I highlight the demerit of the current strategy to evaluate the contribution of interaction effects to the variance of quantitative outcomes and argue for the use of new approaches to overcome this issue. Finally, I explore the advantages and limitations of multivariate interaction models, when testing for interaction between multiple SNPs and/or multiple exposures, over univariate approaches. Together, these new insights can be leveraged for future method development and to improve our understanding of the genetic architecture of multifactorial traits.

A Joint Location-Scale Test Improves Power to Detect Associated SNPs, Gene Sets, and Pathways

Gene-based, pathway, and other multivariate association methods are motivated by the possibility of GxG and GxE interactions; however, accounting for such interactions is limited by the challenges associated with adequate modeling information. Here we propose an easy-to-implement joint location-scale (JLS) association testing framework for single-variant and multivariate analysis that accounts for interactions without explicitly modeling them. We apply the JLS method to a gene-set analysis of cystic fibrosis (CF) lung disease, which is influenced by multiple environmental and genetic factors. We identify and replicate an association between the constituents of the apical plasma membrane and CF lung disease (p = 0.0099 and p = 0.0180, respectively) and highlight a role for the SLC9A3-SLC9A3R1/2-EZR complex in contributing to CF lung disease. Many association studies could benefit from re-analysis with the JLS method that leverages complex genetic architecture for SNP, gene, and pathway identification. Analytical verification, simulation, and additional proof-of-principle applications support our approach.

dslice: an R package for nonparametric testing of associations with application in QTL and gene set analysis

Many statistical problems in bioinformatics and genetics can be formulated as the testing of associations between a categorical variable and a continuous variable. A dynamic slicing method was proposed for non-parametric dependence testing, which has been demonstrated to have higher powers compared with traditional methods such as Kolmogorov-Smirnov test. We introduce an R package dslice to facilitate the use of dynamic slicing method in bioinformatic applications such as quantitative trait loci study and gene set enrichment analysis.

AVAILABILITY AND IMPLEMENTATION

dslice is implemented in Rcpp and available in the Comprehensive R Archive Network. The package is distributed under the GNU General Public License (version 2 or later).

Pathway-guided identification of gene-gene interactions

Assessing gene-gene interactions (GxG) at the gene level can permit examination of epistasis at biologically functional units with amplified interaction signals from marker-marker pairs. While current gene-based GxG methods tend to be designed for two or a few genes, for complex traits, it is often common to have a list of many candidate genes to explore GxG. We propose a regression model with pathway-guided regularization for detecting interactions among genes. Specifically, we use the principal components to summarize the SNP-SNP interactions between a gene pair, and use an L1 penalty that incorporates adaptive weights based on biological guidance and trait supervision to identify important main and interaction effects. Our approach aims to combine biological guidance and data adaptiveness, and yields credible findings that may be likely to shed insights in order to formulate biological hypotheses for further molecular studies. The proposed approach can be used to explore the GxG with a list of many candidate genes and is applicable even when sample size is smaller than the number of predictors studied. We evaluate the utility of the proposed method using simulation and real data analysis. The results suggest improved performance over methods not utilizing pathway and trait guidance.

A versatile omnibus test for detecting mean and variance heterogeneity

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.

Maximizing the power of principal-component analysis of correlated phenotypes in genome-wide association studies

Many human traits are highly correlated. This correlation can be leveraged to improve the power of genetic association tests to identify markers associated with one or more of the traits. Principal component analysis (PCA) is a useful tool that has been widely used for the multivariate analysis of correlated variables. PCA is usually applied as a dimension reduction method: the few top principal components (PCs) explaining most of total trait variance are tested for association with a predictor of interest, and the remaining components are not analyzed. In this study we review the theoretical basis of PCA and describe the behavior of PCA when testing for association between a SNP and correlated traits. We then use simulation to compare the power of various PCA-based strategies when analyzing up to 100 correlated traits. We show that contrary to widespread practice, testing only the top PCs often has low power, whereas combining signal across all PCs can have greater power. This power gain is primarily due to increased power to detect genetic variants with opposite effects on positively correlated traits and variants that are exclusively associated with a single trait. Relative to other methods, the combined-PC approach has close to optimal power in all scenarios considered while offering more flexibility and more robustness to potential confounders. Finally, we apply the proposed PCA strategy to the genome-wide association study of five correlated coagulation traits where we identify two candidate SNPs that were not found by the standard approach.