Correcting for relatedness in Bayesian models for genomic data association analysis

Pikkuhookana, P; Sillanpää, Mikko J.

doi:10.1038/hdy.2009.56

Cited by 22 publications

(41 citation statements)

References 87 publications

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“…Although many authors have found the impact of the polygene insignificant (e.g., Calus and Veerkamp 2007;Pikkuhookana and Sillanpää 2009), some are convinced of its importance (e.g., de los Lund et al 2009). In our example analyses the estimates of the polygenic component are negligible and have no influence on the estimated breeding value.…”

Section: Discussionmentioning

confidence: 99%

“…Due to its weaker shrinking ability the Student's t prior is more prone to the problem than the Laplace prior. In fact, Pikkuhookana andHayashi andIwata (2010) have noted that adding a point mass at zero to a Student's t prior model improves the performance, due to the elimination of the cumulative effect of a multitude of insignificant but nonzero marker effects. Although the Laplace prior generates more sparseness, there is evidence in support of the usefulness of the Laplace and point mass mixture prior (Shepherd et al 2010).…”

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confidence: 99%

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Back to Basics for Bayesian Model Building in Genomic Selection

Kärkkäinen¹,

Sillanpää

2012

Genetics

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Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.T HE availability of the genome-wide sets of molecular markers has opened new avenues to animal and plant breeders for estimating breeding values on the basis of molecular markers with and without pedigree information (Bernardo and Yu 2007;Hayes et al. 2009;Lorenzano and Bernando 2009). The same holds true for phenotype prediction in human genetics (Lee et al. 2008;de los Campos et al. 2010). There are clearly two very different model approaches to estimate genomic breeding values, the first of which applies simultaneous estimation and variable selection to multilocus association models, where all markers are included as potential explanatory variables (e.g., Meuwissen et al. 2001;Xu 2003). Multilocus association models assign different, possibly zero, effects to every marker allele or genotype and determine the genetic value of an individual as a sum of the marker effects. The second approach is to utilize the marker information for estimating realized relationships between individuals and use the marker-estimated genomic relationship matrix instead of the pedigree-based numerator relationship matrix in a mixed-model context (e.g., VanRaden 2008;Powell et al. 2010).In recent literature there are numerous Bayesian methods of phenotype prediction and breeding value estimation based on multilocus association models, from Meuwissen et al. (2001) BayesA and BayesB onward (e.g., Xu 2003;Yi et al. 2003;Yi and Xu 2008;de los Campos et al. 2009;Verbyla et al. 2009Verbyla et al. , 2010Mutshinda and Sillanpää 2010;Sun et al. 2010;Habier et al. 2011;Knürr et al. 2011). The Bayesian methods have proved workable, efficient, and flexible, but the tremendous number of markers in the modern SNP data sets makes the computational methods traditionally connected to Bayesian estimation, e.g., Markov chain Monte Carlo (MCMC), rather cumbersome or even infeasible. For the same models fast alternative estimation procedures have been proposed, most commonly ...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Back to Basics for Bayesian Model Building in Genomic Selection

Kärkkäinen¹,

Sillanpää

2012

Genetics

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“…Setakis et al (2006) suggested the use of a much larger number of null markers as regression covariates to eliminate most of the variation due to population structure. In addition, multilocus models have been shown to possess the potential to account for population stratification, potentially as the variable selection process selects also those markers that explain a part of the confounding variation (Iwata et al, 2007;Pikkuhookana and Sillanpää, 2009;Kärkkäinen and Sillanpää, 2012). Another benefit of simultaneously taking multiple QTL into account in the model is that the QTL detection power may also be enhanced (Iwata et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Würschum

Kraft²

2014

Heredity

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Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multilocus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledgebased breeding.

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“…As in Pikkuhookana and Sillanpää, (2009), there is another source of sparseness in our model, given by the indicator variables. In principle, the degree of sparseness can be controlled by specifying a small prior probability to include each marker into the model.…”

Section: Model Selectionmentioning

confidence: 99%

“…Although these indicators provide a natural way to monitor posterior occupancy of QTLs, the real reason for having them in the model is to improve heritability estimation as shown by Pikkuhookana and Sillanpää (2009). For details, see the subsection dealing with Heritabilities and genetic covariances/correlations.…”

Section: Multiple Trait Qtl Modelmentioning

confidence: 99%

Simultaneous estimation of multiple quantitative trait loci and growth curve parameters through hierarchical Bayesian modeling

et al. 2011

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A novel hierarchical quantitative trait locus (QTL) mapping method using a polynomial growth function and a multiple-QTL model (with no dependence in time) in a multitrait framework is presented. The method considers a populationbased sample where individuals have been phenotyped (over time) with respect to some dynamic trait and genotyped at a given set of loci. A specific feature of the proposed approach is that, instead of an average functional curve, each individual has its own functional curve. Moreover, each QTL can modify the dynamic characteristics of the trait value of an individual through its influence on one or more growth curve parameters. Apparent advantages of the approach include: (1) assumption of time-independent QTL and environmental effects, (2) alleviating the necessity for an autoregressive covariance structure for residuals and (3) the flexibility to use variable selection methods. As a by-product of the method, heritabilities and genetic correlations can also be estimated for individual growth curve parameters, which are considered as latent traits. For selecting trait-associated loci in the model, we use a modified version of the wellknown Bayesian adaptive shrinkage technique. We illustrate our approach by analysing a sub sample of 500 individuals from the simulated QTLMAS 2009 data set, as well as simulation replicates and a real Scots pine (Pinus sylvestris) data set, using temporal measurements of height as dynamic trait of interest.

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Correcting for relatedness in Bayesian models for genomic data association analysis

Cited by 22 publications

References 87 publications

Back to Basics for Bayesian Model Building in Genomic Selection

Back to Basics for Bayesian Model Building in Genomic Selection

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Simultaneous estimation of multiple quantitative trait loci and growth curve parameters through hierarchical Bayesian modeling

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