Bayesian Linear Mixed Models with Polygenic Effects

We considered Bayesian estimation of polygenic effects, in particular heritability in relation to a class of linear mixed models implemented in R (R Core Team 2018). Our approach is applicable to both family-based and population-based studies in human genetics with which a genetic relationship matrix can be derived either from family structure or genome-wide data. Using a simulated and a real data, we demonstrate our implementation of the models in the generic statistical software systems JAGS (Plummer 2017) and Stan (Carpenter et al. 2017) as well as several R packages. In doing so, we have not only provided facilities in R linking standalone programs such as GCTA (Yang, Lee, Goddard, and Visscher 2011) and other packages in R but also addressed some technical issues in the analysis. Our experience with a host of general and special software systems will facilitate investigation into more complex models for both human and nonhuman genetics.

[1]  R. Varga.  Geršgorin And His Circles , 2004 .

[2]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[3]  Katrina J Scurrah,et al.  Covariance components models for longitudinal family data. , 2005, International journal of epidemiology.

[4]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[5]  M. Sillanpää,et al.  Efficient Markov Chain Monte Carlo Implementation of Bayesian Analysis of Additive and Dominance Genetic Variances in Noninbred Pedigrees , 2008, Genetics.

[6]  Jing hua Zhao,et al.  Mixed-effects Cox models of alcohol dependence in extended families , 2005, BMC Genetics.

[7]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[8]  Endong Wang,et al.  Intel Math Kernel Library , 2014 .

[9]  Sara Martino,et al.  Animal Models and Integrated Nested Laplace Approximations , 2013, G3: Genes, Genomes, Genetics.

[10]  Kevin Fiedler,et al.  Likelihood Bayesian And Mcmc Methods In Quantitative Genetics , 2016 .

[11]  D. Allison,et al.  Heritability of pulmonary function estimated from pedigree and whole-genome markers , 2013, Front. Genet..

[12]  M. Firat,et al.  Bayesian inference of genetic parameters for ultrasound scanning traits of Kivircik lambs. , 2017, Animal : an international journal of animal bioscience.

[13]  Patrik Waldmann,et al.  Easy and Flexible Bayesian Inference of Quantitative Genetic Parameters , 2009, Evolution; international journal of organic evolution.

[14]  José Crossa,et al.  Genome-enabled prediction using the BLR (Bayesian Linear Regression) R-package. , 2013, Methods in molecular biology.

[15]  N. Yi,et al.  Bayesian mapping of quantitative trait loci for complex binary traits. , 2000, Genetics.

[16]  Paola Sebastiani,et al.  An efficient technique for Bayesian modeling of family data using the BUGS software , 2014, Front. Genet..

[17]  N E Morton,et al.  Analysis of family resemblance. 3. Complex segregation of quantitative traits. , 1974, American journal of human genetics.

[18]  L. Penrose,et al.  THE CORRELATION BETWEEN RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE , 2022 .

[19]  J. Noguera,et al.  Bayesian analysis of quantitative trait loci for boar taint in a Landrace outbred population. , 2005, Journal of animal science.

[20]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[21]  Jing Hua Zhao,et al.  gap: Genetic Analysis Package , 2007 .

[22]  M. Sillanpää,et al.  Bayesian Inference of Genetic Parameters Based on Conditional Decompositions of Multivariate Normal Distributions , 2010, Genetics.

[23]  José Crossa,et al.  Genomic‐Enabled Prediction Based on Molecular Markers and Pedigree Using the Bayesian Linear Regression Package in R , 2010, The plant genome.

[24]  Terry M. Therneau,et al.  Mixed Effects Cox Models , 2015 .

[25]  Jack Dongarra,et al.  LAPACK Users' Guide, 3rd ed. , 1999 .

[26]  John K. Kruschke,et al.  Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan , 2014 .

[27]  L H Damgaard,et al.  Technical note: how to use Winbugs to draw inferences in animal models. , 2007, Journal of animal science.

[28]  Andrew Gelman,et al.  R2WinBUGS: A Package for Running WinBUGS from R , 2005 .

[29]  P. Visscher,et al.  Common SNPs explain a large proportion of heritability for human height , 2011 .

[30]  Jing Hua Zhao,et al.  Mixed Modeling with Whole Genome Data , 2012 .

[31]  Luis R. Pericchi,et al.  Model Selection and Hypothesis Testing based on Objective Probabilities and Bayes Factors , 2005 .

[32]  P. Visscher,et al.  GCTA: a tool for genome-wide complex trait analysis. , 2011, American journal of human genetics.

[33]  E. Thompson,et al.  Monte Carlo estimation of variance component models for large complex pedigrees. , 1991, IMA journal of mathematics applied in medicine and biology.

[34]  D Gianola,et al.  Technical note: an R package for fitting generalized linear mixed models in animal breeding. , 2010, Journal of animal science.

[35]  Martyn Plummer,et al.  JAGS: Just Another Gibbs Sampler , 2012 .

[36]  Jarrod Had.  MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package , 2010 .

[37]  K. Meyer,et al.  Restricted maximum likelihood to estimate variance components for animal models with several random effects using a derivative-free algorithm , 1989, Genetics Selection Evolution.

[38]  Mikko J. Sillanpää,et al.  Rapid Bayesian inference of heritability in animal models without convergence problems , 2013 .

[39]  Shinichi Nakagawa,et al.  A general and simple method for obtaining R2 from generalized linear mixed‐effects models , 2013 .