MegaLMM: Mega-scale linear mixed models for genomic predictions with thousands of traits.
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ABSTRACT:
SUBMITTER: Runcie DE
PROVIDER: S-EPMC8299638 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Large-scale phenotype data are expected to increase the accuracy of genome-wide prediction and the power of genome-wide association analyses. However, genomic analyses of high-dimensional, highly correlated traits are challenging. We developed a method for implementing high-dimensional Bayesian multivariate regression to simultaneously analyze genetic variants underlying thousands of traits. As a demonstration, we implemented the BayesC prior in the R package MegaLMM. Applied to Genomic Prediction, MegaBayesC effectively integrated hyperspectral reflectance data from 620 hyperspectral wavelengths to improve the accuracy of genetic value prediction on grain yield in a wheat dataset. Applied to Genome-Wide Association Studies, we used simulations to show that MegaBayesC can accurately estimate the effect sizes of QTL across a range of genetic architectures and causes of correlations among traits. To apply MegaBayesC to a realistic scenario involving whole-genome marker data, we developed a 2-stage procedure involving a preliminary step of candidate marker selection prior to multivariate regression. We then used MegaBayesC to identify genetic associations with flowering time in Arabidopsis thaliana, leveraging expression data from 20,843 genes. MegaBayesC selected 15 single nucleotide polymorphisms as important for flowering time, with 13 located within 100 kb of known flowering-time related genes, a higher validation rate than achieved by a single-stage analysis using only the flowering time data itself. These results demonstrate that MegaBayesC can efficiently and effectively leverage high-dimensional phenotypes in genetic analyses.
| S-EPMC9991502 | biostudies-literature
Project description:Brain imaging outcomes are important for Alzheimer's disease (AD) detection, and their prediction based on both genetic and demographic risk factors can facilitate the ongoing prevention and treatment of AD. Existing studies have identified numerous significantly AD-associated SNPs. However, how to make the best use of them for prediction analyses remains unknown. In this research, we first explored the relationship between genetic architecture and prediction accuracy of linear mixed models via visualizing the Manhattan plots generated based on the data obtained from the Wellcome Trust Case Control Consortium, and then constructed prediction models for eleven AD-related brain imaging outcomes using data from United Kingdom Biobank and Alzheimer's Disease Neuroimaging Initiative studies. We found that the simple Manhattan plots can be informative for the selection of prediction models. For traits that do not exhibit any significant signals from the Manhattan plots, the simple genomic best linear unbiased prediction (gBLUP) model is recommended due to its robust and accurate prediction performance as well as its computational efficiency. For diseases and traits that show spiked signals on the Manhattan plots, the latent Dirichlet process regression is preferred, as it can flexibly accommodate both the oligogenic and omnigenic models. For the prediction of AD-related traits, the Manhattan plots suggest their polygenic nature, and gBLUP has achieved robust performance for all these traits. We found that for these AD-related traits, genetic factors themselves only explain a very small proportion of the heritability, and the well-known AD risk factors can substantially improve the prediction model.
| S-EPMC9581223 | biostudies-literature
Project description:Spatial probit generalized linear mixed models (spGLMM) with a linear fixed effect and a spatial random effect, endowed with a Gaussian Process prior, are widely used for analysis of binary spatial data. However, the canonical Bayesian implementation of this hierarchical mixed model can involve protracted Markov Chain Monte Carlo sampling. Alternate approaches have been proposed that circumvent this by directly representing the marginal likelihood from spGLMM in terms of multivariate normal cummulative distribution functions (cdf). We present a direct and fast rendition of this latter approach for predictions from a spatial probit linear mixed model. We show that the covariance matrix of the cdf characterizing the marginal cdf of binary spatial data from spGLMM is amenable to approximation using Nearest Neighbor Gaussian Processes (NNGP). This facilitates a scalable prediction algorithm for spGLMM using NNGP that only involves sparse or small matrix computations and can be deployed in an embarrassingly parallel manner. We demonstrate the accuracy and scalability of the algorithm via numerous simulation experiments and an analysis of species presence-absence data.
| S-EPMC10544813 | biostudies-literature
Project description:BackgroundLinear mixed-effects models (LMM) are a leading method in conducting genome-wide association studies (GWAS) but require residual maximum likelihood (REML) estimation of variance components, which is computationally demanding. Previous work has reduced the computational burden of variance component estimation by replacing direct matrix operations with iterative and stochastic methods and by employing loose tolerances to limit the number of iterations in the REML optimization procedure. Here, we introduce two novel algorithms, stochastic Lanczos derivative-free REML (SLDF_REML) and Lanczos first-order Monte Carlo REML (L_FOMC_REML), that exploit problem structure via the principle of Krylov subspace shift-invariance to speed computation beyond existing methods. Both novel algorithms only require a single round of computation involving iterative matrix operations, after which their respective objectives can be repeatedly evaluated using vector operations. Further, in contrast to existing stochastic methods, SLDF_REML can exploit precomputed genomic relatedness matrices (GRMs), when available, to further speed computation.ResultsResults of numerical experiments are congruent with theory and demonstrate that interpreted-language implementations of both algorithms match or exceed existing compiled-language software packages in speed, accuracy, and flexibility.ConclusionsBoth the SLDF_REML and L_FOMC_REML algorithms outperform existing methods for REML estimation of variance components for LMM and are suitable for incorporation into existing GWAS LMM software implementations.
| S-EPMC6668092 | biostudies-literature
Project description:We develop linear mixed models (LMMs) and functional linear mixed models (FLMMs) for gene-based tests of association between a quantitative trait and genetic variants on pedigrees. The effects of a major gene are modeled as a fixed effect, the contributions of polygenes are modeled as a random effect, and the correlations of pedigree members are modeled via inbreeding/kinship coefficients. F -statistics and ? 2 likelihood ratio test (LRT) statistics based on the LMMs and FLMMs are constructed to test for association. We show empirically that the F -distributed statistics provide a good control of the type I error rate. The F -test statistics of the LMMs have similar or higher power than the FLMMs, kernel-based famSKAT (family-based sequence kernel association test), and burden test famBT (family-based burden test). The F -statistics of the FLMMs perform well when analyzing a combination of rare and common variants. For small samples, the LRT statistics of the FLMMs control the type I error rate well at the nominal levels ? = 0.01 and 0.05 . For moderate/large samples, the LRT statistics of the FLMMs control the type I error rates well. The LRT statistics of the LMMs can lead to inflated type I error rates. The proposed models are useful in whole genome and whole exome association studies of complex traits.
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Project description:Large-scale cohorts with combined genetic and phenotypic data, coupled with methodological advances, have produced increasingly accurate genetic predictors of complex human phenotypes called polygenic risk scores (PRSs). In addition to the potential translational impacts of identifying at-risk individuals, PRS are being utilized for a growing list of scientific applications, including causal inference, identifying pleiotropy and genetic correlation, and powerful gene-based and mixed-model association tests. Existing PRS approaches rely on external large-scale genetic cohorts that have also measured the phenotype of interest. They further require matching on ancestry and genotyping platform or imputation quality. In this work, we present a novel reference-free method to produce a PRS that does not rely on an external cohort. We show that naive implementations of reference-free PRS either result in substantial overfitting or prohibitive increases in computational time. We show that our algorithm avoids both of these issues and can produce informative in-sample PRSs over a single cohort without overfitting. We then demonstrate several novel applications of reference-free PRSs, including detection of pleiotropy across 246 metabolic traits and efficient mixed-model association testing.
| S-EPMC7185352 | biostudies-literature
Project description:This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size. We further propose a group variable selection strategy to simultaneously select and estimate important random effects, where the unknown covariance matrix of random effects is replaced with a proxy matrix. We prove that, with the proxy matrix appropriately chosen, the proposed procedure can identify all true random effects with asymptotic probability one, where the dimension of random effects vector is allowed to increase exponentially with the sample size. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. We further illustrate the proposed procedures via a real data example.
| S-EPMC4026175 | biostudies-other
Project description:BACKGROUND:Multiple hypothesis testing is a major issue in genome-wide association studies (GWAS), which often analyze millions of markers. The permutation test is considered to be the gold standard in multiple testing correction as it accurately takes into account the correlation structure of the genome. Recently, the linear mixed model (LMM) has become the standard practice in GWAS, addressing issues of population structure and insufficient power. However, none of the current multiple testing approaches are applicable to LMM. RESULTS:We were able to estimate per-marker thresholds as accurately as the gold standard approach in real and simulated datasets, while reducing the time required from months to hours. We applied our approach to mouse, yeast, and human datasets to demonstrate the accuracy and efficiency of our approach. CONCLUSIONS:We provide an efficient and accurate multiple testing correction approach for linear mixed models. We further provide an intuition about the relationships between per-marker threshold, genetic relatedness, and heritability, based on our observations in real data.
| S-EPMC4818520 | biostudies-literature
Project description:Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.
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Project description:Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.
| S-EPMC3755911 | biostudies-literature