The Use of the Linear Mixed Model in Human Genetics

Highly Efficient Methods with a Generalized Linear Mixed Model for the Quantitative Trait Locus Mapping of Resistance to Columnaris Disease in Rainbow Trout (Oncorhynchus mykiss)

Linear mixed models (LMMs) are commonly used in genome-wide association studies (GWASs) to evaluate population structures and relatedness. However, LMMs have been shown to be ineffective in controlling false positive errors for the analysis of resistance to Columnaris disease in Rainbow Trout. To solve this problem, we conducted a series of studies using generalized linear mixed-model association software such as GMMAT (v1.4.0) (generalized linear mixed-model association tests), SAIGE (v1.4.0) (Scalable and Accurate Implementation of Generalized mixed model), and Optim-GRAMMAR for scanning a total of 25,853 SNPs. Seven different SNPs (single-nucleotide polymorphisms) associated with the trait of resistance to Columnaris were detected by Optim-GRAMMAR, four SNPs were detected by GMMAT, and three SNPs were detected by SAIGE, and all of these SNPs can explain 8.87% of the genetic variance of the trait of resistance to Columnaris disease. The heritability of the trait of resistance to Columnaris re-evaluated by GMMAT was calibrated and was found to amount to a total of 0.71 other than 0.35, which was seriously underestimated in previous research. The identification of LOC110520307, LOC110520314, and LOC110520317 associated with the resistance to Columnaris disease will provide us more genes to improve the genetic breeding by molecular markers. Finally, we continued the haplotype and gene-based analysis and successfully identified some haplotypes and a gene (TTf-2) associated with resistance to Columnaris disease.

Detecting inbreeding depression in structured populations

Measuring inbreeding and its consequences on fitness is central for many areas in biology including human genetics and the conservation of endangered species. However, there is no consensus on the best method, neither for quantification of inbreeding itself nor for the model to estimate its effect on specific traits. We simulated traits based on simulated genomes from a large pedigree and empirical whole-genome sequences of human data from populations with various sizes and structures (from the 1,000 Genomes project). We compare the ability of various inbreeding coefficients ([Formula: see text]) to quantify the strength of inbreeding depression: allele-sharing, two versions of the correlation of uniting gametes which differ in the weight they attribute to each locus and two identical-by-descent segments-based estimators. We also compare two models: the standard linear model and a linear mixed model (LMM) including a genetic relatedness matrix (GRM) as random effect to account for the nonindependence of observations. We find LMMs give better results in scenarios with population or family structure. Within the LMM, we compare three different GRMs and show that in homogeneous populations, there is little difference among the different [Formula: see text] and GRM for inbreeding depression quantification. However, as soon as a strong population or family structure is present, the strength of inbreeding depression can be most efficiently estimated only if i) the phenotypes are regressed on [Formula: see text] based on a weighted version of the correlation of uniting gametes, giving more weight to common alleles and ii) with the GRM obtained from an allele-sharing relatedness estimator.

Ravages: An R package for the simulation and analysis of rare variants in multicategory phenotypes

Current software packages for the analysis and the simulations of rare variants are only available for binary and continuous traits. Ravages provides solutions in a single R package to perform rare variant association tests for multicategory, binary and continuous phenotypes, to simulate datasets under different scenarios and to compute statistical power. Association tests can be run in the whole genome thanks to C++ implementation of most of the functions, using either RAVA-FIRST, a recently developed strategy to filter and analyse genome-wide rare variants, or user-defined candidate regions. Ravages also includes a simulation module that generates genetic data for cases who can be stratified into several subgroups and for controls. Through comparisons with existing programmes, we show that Ravages complements existing tools and will be useful to study the genetic architecture of complex diseases. Ravages is available on the CRAN at https://cran.r-project.org/web/packages/Ravages/ and maintained on Github at https://github.com/genostats/Ravages.

Mendelian Randomization Analysis Reveals Causal Effects of Plasma Proteome on Body Composition Traits

CONTEXT

Observational studies have demonstrated associations between plasma proteins and obesity, but evidence of causal relationship remains to be studied.

OBJECTIVE

We aimed to evaluate the causal relationship between plasma proteins and body composition.

METHODS

We conducted a 2-sample Mendelian randomization (MR) analysis based on the genome-wide association study (GWAS) summary statistics of 23 body composition traits and 2656 plasma proteins. We then performed hierarchical cluster analysis to evaluate the structure and pattern of the identified causal associations, and we performed gene ontology enrichment analysis to explore the functional relevance of the identified proteins.

RESULTS

We identified 430 putatively causal effects of 96 plasma proteins on 22 body composition traits (except obesity status) with strong MR evidence (P < 2.53 × 10 - 6, at a Bonferroni-corrected threshold). The top 3 causal associations are follistatin (FST) on trunk fat-free mass (Beta = -0.63, SE = 0.04, P = 2.00 × 10-63), insulin-like growth factor-binding protein 1 (IGFBP1) on trunk fat-free mass (Beta = -0.54, SE = 0.03, P = 1.79 × 10-57) and r-spondin-3 (RSPO3) on WHR (waist circumference/hip circumference) (Beta = 0.01, SE = 4.47 × 10-4, P = 5.45 × 10-60), respectively. Further clustering analysis and pathway analysis demonstrated that the pattern of causal effect to fat mass and fat-free mass may be different.

CONCLUSION

Our findings may provide evidence for causal relationships from plasma proteins to various body composition traits and provide basis for further targeted functional studies.

RAVAQ: An integrative pipeline from quality control to region-based rare variant association analysis

Next-generation sequencing technologies have opened up the possibility to sequence large samples of cases and controls to test for association with rare variants. To limit cost and increase sample sizes, data from controls could be used in multiple studies and might thus be generated on different sequencing platforms. This could pose some problems of comparability between cases and controls due to batch effects that could be confounding factors, leading to false-positive association signals. To limit batch effects and ensure comparability of datasets, stringent quality controls are required. We propose an integrative five-steps pipeline, RAVAQ, that (a) performs a specific three-step quality control taking into account the case-control status to ensure data comparability, (b) selects qualifying variants as defined by the user, and (c) performs rare variant association tests per genomic region. The RAVAQ pipeline is wrapped in an R package. It is user-friendly and flexible in its arguments to adapt to the specificity of each research project. We provide examples showing how RAVAQ improves rare variant association tests. The default RAVAQ quality control outperformed the widely used Variant Quality Score Recalibration method, removing inflation due to spurious signals. RAVAQ is open source and freely available at https://gitlab.com/gmarenne/ravaq.

Extension of SKAT to multi-category phenotypes through a geometrical interpretation

Rare genetic variants are expected to play an important role in disease and several statistical methods have been developed to test for disease association with rare variants, including variance-component tests. These tests however deal only with binary or continuous phenotypes and it is not possible to take advantage of a suspected heterogeneity between subgroups of patients. To address this issue, we extended the popular rare-variant association test SKAT to compare more than two groups of individuals. Simulations under different scenarios were performed that showed gain in power in presence of genetic heterogeneity and minor lack of power in absence of heterogeneity. An application on whole-exome sequencing data from patients with early- or late-onset moyamoya disease also illustrated the advantage of our SKAT extension. Genetic simulations and SKAT extension are implemented in the R package Ravages available on GitHub ( https://github.com/genostats/Ravages ).

Exploring the Link Between Additive Heritability and Prediction Accuracy From a Ridge Regression Perspective

Genome-Wide Association Studies (GWAS) explain only a small fraction of heritability for most complex human phenotypes. Genomic heritability estimates the variance explained by the SNPs on the whole genome using mixed models and accounts for the many small contributions of SNPs in the explanation of a phenotype. This paper approaches heritability from a machine learning perspective, and examines the close link between mixed models and ridge regression. Our contribution is two-fold. First, we propose estimating genomic heritability using a predictive approach via ridge regression and Generalized Cross Validation (GCV). We show that this is consistent with classical mixed model based estimation. Second, we derive simple formulae that express prediction accuracy as a function of the ratio n p , where n is the population size and p the total number of SNPs. These formulae clearly show that a high heritability does not imply an accurate prediction when p > n. Both the estimation of heritability via GCV and the prediction accuracy formulae are validated using simulated data and real data from UK Biobank.

Mixed logistic regression in genome-wide association studies

Background

Mixed linear models (MLM) have been widely used to account for population structure in case-control genome-wide association studies, the status being analyzed as a quantitative phenotype. Chen et al. proved in 2016 that this method is inappropriate in some situations and proposed GMMAT, a score test for the mixed logistic regression (MLR). However, this test does not produces an estimation of the variants’ effects. We propose two computationally efficient methods to estimate the variants’ effects. Their properties and those of other methods (MLM, logistic regression) are evaluated using both simulated and real genomic data from a recent GWAS in two geographically close population in West Africa.

Results

We show that, when the disease prevalence differs between population strata, MLM is inappropriate to analyze binary traits. MLR performs the best in all circumstances. The variants’ effects are well evaluated by our methods, with a moderate bias when the effect sizes are large. Additionally, we propose a stratified QQ-plot, enhancing the diagnosis of p values inflation or deflation when population strata are not clearly identified in the sample.

Conclusion

The two proposed methods are implemented in the R package milorGWAS available on the CRAN. Both methods scale up to at least 10,000 individuals. The same computational strategies could be applied to other models (e.g. mixed Cox model for survival analysis).

JEM: A joint test to estimate the effect of multiple genetic variants on DNA methylation

Multiple methods have been proposed to aggregate genetic variants in a gene or a region and jointly test their association with a trait of interest. However, these joint tests do not provide estimates of the individual effect of each variant. Moreover, few methods have evaluated the joint association of multiple variants with DNA methylation. We propose a method based on linear mixed models to estimate the joint and individual effect of multiple genetic variants on DNA methylation leveraging genomic annotations. Our approach is flexible, can incorporate covariates and annotation features, and takes into account relatedness and linkage disequilibrium (LD). Our method had correct Type-I error and overall high power for different simulated scenarios where we varied the number and specificity of functional annotations, number of causal and total genetic variants, frequency of genetic variants, LD, and genetic variant effect. Our method outperformed the family Sequence Kernel Association Test and had more stable estimations of effects than a classical single-variant linear mixed-effect model. Applied genome-wide to the Framingham Heart Study data, our method identified 921 DNA methylation sites influenced by at least one rare or low-frequency genetic variant located within 50 kilobases (kb) of the DNA methylation site.

A family of linear mixed-effects models using the generalized Laplace distribution

We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm.

Variability of post-void residual urine volume and bladder voiding efficiency in patients with underactive bladder

OBJECTIVES

Post-void residual urine volume (PVR) and bladder voiding efficiency (BVE) are widely used as clinical parameters to evaluate patients with voiding dysfunction. The present study was conducted to assess the variability of PVR and BVE determinations in patients with underactive bladder (UAB). In addition, we focused on the bladder volume prior to voiding (BV_void ) that may influence PVR and BVE, and investigated a correlation between PVR and BV_void , and between BVE and BV_void .

METHODS

Ten patients with a symptom complex of UAB, who had PVR of 50 mL or greater, were admitted to hospital during a 24-hour period for the measurement of voided volume (VV) and PVR. PVR was measured by transabdominal ultrasonography. BVE was expressed by a fraction (%) of bladder volume evacuated ([VV/BV_void ] × 100).

RESULTS

Ten patients, five men (mean age of 65.0 years) and five women (mean age of 70.2 years), participated in this study. Regardless of gender, there was a large variation in repeated measurements of PVR in an individual patient. PVR increased with an increase in BV_void , and there was a significant linear relationship between PVR and BV_void . BVE was approximately constant after every voiding in each patient, and there was no significant linear relationship between BVE and BV_void .

CONCLUSIONS

Measurement of PVR was unreliable because of wide variation in the same individual. The variation of BVE was much smaller than PVR. BVE would be a reliable parameter with good reproducibility for the assessment of emptying function.

Contribution of Genome-Wide Significant Single Nucleotide Polymorphisms in Myopia Prediction: Findings from a 10-year Cohort of Chinese Twin Children

PURPOSE

To determine the added predictive ability of genome-wide significant single nucleotide polymorphisms (SNPs) in refraction prediction in children and investigate the earliest age threshold for an accurate prediction of high myopia.

DESIGN

Prospective longitudinal study.

PARTICIPANTS

A total of 1063 first-born twins followed annually between 2006 and 2015 in China. The exposures were genetic factors (parental myopia, SNPs) and environmental factors (near work, outdoor activity).

METHODS

Five linear mixed-effect models, consisting of different combinations of age, gender, genetic, and environmental factors, were built to predict myopia development. All predictions were performed on the basis of spherical equivalent (SE) at baseline and the measurements on the second and third visits.

MAIN OUTCOME MEASURES

The primary outcome measure was SE at the last visit among all subjects, and the secondary outcome measure was the presence of high myopia at the age of 18 years.

RESULTS

Mean age of the study population was 10.5±2.2 years (range, 7-15 years) at baseline, and 48.6% were male. In linear mixed-effect models, age, age square, gender, paternal SE, maternal SE, and genetic risk scores (GRSs) showed a significant fixed effect, whereas outdoor and near-work time were not significant to SE at the last visit. Incorporating more follow-up data into the model showed better performance across all models. In the prediction of the presence of high myopia at 18 years of age, the model consisting of only age and gender showed a good performance (area under the curve [AUC] = 0.95), whereas the addition of SNPs did not enhance the model performance significantly. The AUC for predicting high myopia was >0.95 after the age of 13 years for participants with a single visit and after the age of 12 years for those with 1 more visit data.

CONCLUSIONS

A simple model incorporating age, sex, and relevant refraction data is sufficient to accurately predict high myopia; there was limited improvement in the prediction model after adding genetic information. Furthermore, this prediction on the outcome at 18 years is possible when the child is aged 12 to 13 years.

Prediction of gene expression with cis-SNPs using mixed models and regularization methods

Background

It has been shown that gene expression in human tissues is heritable, thus predicting gene expression using only SNPs becomes possible. The prediction of gene expression can offer important implications on the genetic architecture of individual functional associated SNPs and further interpretations of the molecular basis underlying human diseases.

Methods

We compared three types of methods for predicting gene expression using only cis-SNPs, including the polygenic model, i.e. linear mixed model (LMM), two sparse models, i.e. Lasso and elastic net (ENET), and the hybrid of LMM and sparse model, i.e. Bayesian sparse linear mixed model (BSLMM). The three kinds of prediction methods have very different assumptions of underlying genetic architectures. These methods were evaluated using simulations under various scenarios, and were applied to the Geuvadis gene expression data.

Results

The simulations showed that these four prediction methods (i.e. Lasso, ENET, LMM and BSLMM) behaved best when their respective modeling assumptions were satisfied, but BSLMM had a robust performance across a range of scenarios. According to R² of these models in the Geuvadis data, the four methods performed quite similarly. We did not observe any clustering or enrichment of predictive genes (defined as genes with R² ≥ 0.05) across the chromosomes, and also did not see there was any clear relationship between the proportion of the predictive genes and the proportion of genes in each chromosome. However, an interesting finding in the Geuvadis data was that highly predictive genes (e.g. R² ≥ 0.30) may have sparse genetic architectures since Lasso, ENET and BSLMM outperformed LMM for these genes; and this observation was validated in another gene expression data. We further showed that the predictive genes were enriched in approximately independent LD blocks.

Conclusions

Gene expression can be predicted with only cis-SNPs using well-developed prediction models and these predictive genes were enriched in some approximately independent LD blocks. The prediction of gene expression can shed some light on the functional interpretation for identified SNPs in GWASs.