A Bayesian Antedependence Model for Whole Genome Prediction

Abstract

Hierarchical mixed effects models have been demonstrated to be powerful for predicting genomic merit of livestock and plants, on the basis of high-density single-nucleotide polymorphism (SNP) marker panels, and their use is being increasingly advocated for genomic predictions in human health. Two particularly popular approaches, labeled BayesA and BayesB, are based on specifying all SNP-associated effects to be independent of each other. BayesB extends BayesA by allowing a large proportion of SNP markers to be associated with null effects. We further extend these two models to specify SNP effects as being spatially correlated due to the chromosomally proximal effects of causal variants. These two models, that we respectively dub as ante-BayesA and ante-BayesB, are based on a first-order nonstationary antedependence specification between SNP effects. In a simulation study involving 20 replicate data sets, each analyzed at six different SNP marker densities with average LD levels ranging from r 2 ¼ 0.15 to 0.31, the antedependence methods had significantly (P , 0.01) higher accuracies than their corresponding classical counterparts at higher LD levels (r 2 . 0. 24) with differences exceeding 3%. A cross-validation study was also conducted on the heterogeneous stock mice data resource (http:// mus.well.ox.ac.uk/mouse/HS/) using 6-week body weights as the phenotype. The antedependence methods increased cross-validation prediction accuracies by up to 3.6% compared to their classical counterparts (P , 0.001). Finally, we applied our method to other benchmark data sets and demonstrated that the antedependence methods were more accurate than their classical counterparts for genomic predictions, even for individuals several generations beyond the training data.

An Integrated Approach to Empirical Bayesian Whole Genome Prediction Modeling

“…(19) with respect to θ−σ by simply setting ∂ ∂θ −σ (log p (τ|θ −σ ) + log p (θ −σ )) dθ −σ , evaluated at the E-step, equal to 0. For all subsequent analyses in this paper, we considered p ν g ∝ 1 (1+νg) 2 and p (π ) to be a Beta(1,10) density, similar to what we have advocated in previous work (Yang et al 2015;Yang and Tempelman 2012).…”

Empirical Bayesian elastic net for multiple quantitative trait locus mapping

“…Several methods for predicting genetic values incorporate the spatial correlations among markers. Yang and Tempelman (2012) included a first-order antedependence correlation structure for regression coefficients b into their Bayesian hierarchical mixed effects model so that b j depends on b j À1 , 2pjpk, resulted in increased accuracy in predicting genetic values. Shen et al (2011) incorporated a specific correlation structure in their smoothed double hierarchical generalized linear model, and a spatial correlation parameter was introduced to control correlation between two markers.…”

“…Shen et al (2011) incorporated a specific correlation structure in their smoothed double hierarchical generalized linear model, and a spatial correlation parameter was introduced to control correlation between two markers. Although our EBEN exploits the possible correlations among QTLs, unlike those of Shen et al (2011), Yang andTempelman (2012), our EBEN does not specify a correlation structure for markers in the QTL model. Therefore, our EBEN is more robust, because a mis-specified correlation structure may significantly degrade performance.…”

“…Therefore, our EBEN is more robust, because a mis-specified correlation structure may significantly degrade performance. Our EBEN can shrink most variables in the QTL model to zero, yielding a sparse QTL model, which significantly decreases FDR without sacrificing the power of detection; whereas the method of Shen et al (2011) does not employ the shrinkage technique, and it is not clear if the method of Yang and Tempelman (2012) can shrink variables in the QTL model to zero. Although performance of predicting genetic values may not degrade without using the shrinkage technique or an appropriate variable selection method to identify QTLs, shrinkage is very important to the performance of QTL mapping.…”

Addressing scope of inference for global genetic evaluation of livestock

“…It might be wise to specify meaningful yet computationally tractable LD specifications between SNP. Our group (Yang & Tempelman, 2010) has proposed first order antedependence specifications between SNP as an extension to BayesA. Suppose that the subscripts of the elements of g specify the relative order of the SNPs on linkage groups such that the following antedependence structure is considered: …”