Genome-wide association studies (GWAS) are traditionally carried out by using the single marker regression model that, if a small number of individuals is involved, often lead to very few associations. The Bayesian methods, such as BayesR, have obtained encouraging results when they are applied to the GWAS. However, these approaches, require that an a priori posterior inclusion probability threshold be fixed, thus arbitrarily affecting the obtained associations. To partially overcome these problems, a multivariate statistical algorithm was proposed. The basic idea was that animals with different phenotypic values of a specific trait share different allelic combinations for genes involved in its determinism. Three multivariate techniques were used to highlight the differences between the individuals assembled in high and low phenotype groups: the canonical discriminant analysis, the discriminant analysis and the stepwise discriminant analysis. The multivariate method was tested both on simulated and on real data. The results from the simulation study highlighted that the multivariate GWAS detected a greater number of true associated single nucleotide polymorphisms (SNPs) and Quantitative trait loci (QTLs) than the single marker model and the Bayesian approach. For example, with 3000 animals, the traditional GWAS highlighted only 29 significantly associated markers and 13 QTLs, whereas the multivariate method found 127 associated SNPs and 65 QTLs. The gap between the two approaches slowly decreased as the number of animals increased. The Bayesian method gave worse results than the other two. On average, with the real data, the multivariate GWAS found 108 associated markers for each trait under study and among them, around 63% SNPs were also found in the single marker approach. Among the top 118 associated markers, 76 SNPs harbored putative candidate genes.

中文翻译：

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将多元判别分析用于牛的全基因组关联研究。

传统上，全基因组关联研究（GWAS）是使用单标记回归模型进行的，如果涉及的个体数量很少，通常会导致很少的关联。当将贝叶斯方法（例如BayesR）应用于GWAS时，已经获得了令人鼓舞的结果。但是，这些方法要求先验后验包含概率阈值是固定的，从而任意影响获得的关联。为了部分克服这些问题，提出了一种多元统计算法。基本思想是，具有特定性状的不同表型值的动物对于参与其确定性的基因共享不同的等位基因组合。使用三种多变量技术来突出显示在高和低表型组中组装的个体之间的差异：规范判别分析，判别分析和逐步判别分析。在模拟和真实数据上都测试了多元方法。模拟研究的结果强调，与单标记模型和贝叶斯方法相比，多变量GWAS检测出更多的真实相关单核苷酸多态性（SNP）和定量性状基因座（QTL）。例如，对于3000只动物，传统的GWAS仅突出显示29个显着相关的标记和13个QTL，而多变量方法发现127个相关的SNP和65个QTL。随着动物数量的增加，两种方法之间的差距逐渐减小。贝叶斯方法给出的结果比其他两种方法差。平均而言，根据实际数据，多变量GWAS为研究中的每个性状发现了108个相关标记，其中在单标记法中也发现了约63％的SNP。在前118个相关标记中，有76个SNP包含推定的候选基因。