GWAS by GBLUP: Single and Multimarker EMMAX and Bayes Factors, with an Example in Detection of a Major Gene for Horse Gait

Bayesian models for genomic prediction and association mapping are being increasingly used in genetics analysis of quantitative traits. Given a point estimate of variance components, the popular methods SNP-BLUP and GBLUP result in joint estimates of the effect of all markers on the analyzed trait; single and multiple marker frequentist tests (EMMAX) can be constructed from these estimates. Indeed, BLUP methods can be seen simultaneously as Bayesian or frequentist methods. So far there is no formal method to produce Bayesian statistics from GBLUP. Here we show that the Bayes Factor, a commonly admitted statistical procedure, can be computed as the ratio of two normal densities: the first, of the estimate of the marker effect over its posterior standard deviation; the second of the null hypothesis (a value of 0 over the prior standard deviation). We extend the BF to pool evidence from several markers and of several traits. A real data set that we analyze, with ours and existing methods, analyzes 630 horses genotyped for 41711 polymorphic SNPs for the trait "outcome of the qualification test" (which addresses gait, or ambling, of horses) for which a known major gene exists. In the horse data, single marker EMMAX shows a significant effect at the right place at Bonferroni level. The BF points to the same location although with low numerical values. The strength of evidence combining information from several consecutive markers increases using the BF and decreases using EMMAX, which comes from a fundamental difference in the Bayesian and frequentist schools of hypothesis testing. We conclude that our BF method complements frequentist EMMAX analyses because it provides a better pooling of evidence across markers, although its use for primary detection is unclear due to the lack of defined rejection thresholds.

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