Multicollinearity in the statistical genomics era: Proposals to account for dependencies between molecular covariates with application to animal breeding

在动物育种中，将分子数据（例如单核苷酸多态性; SNP）作为预测变量纳入统计模型，以改善动物的基因组评估。这导致更精确地估计尚未表型化的动物的育种值，这对于育种目的是重要的，并且使得能够阐明某些性状的遗传结构。不仅效应大小相关，而且在基因组上的位置也相关。特别是当高维SNP数据可用时，可以将致病变体精确定位到基因组上的特定碱基对。由于模型参数的数量随着SNP数量的增加而增加，协变量之间的多重共线性会影响全基因组回归方法的结果。本研究的目的是另外纳入分子协变量之间的依赖关系，这是由于染色体片段之间的连锁和连锁不平衡，更准确地估计SNP的影响。SNP基因型之间的理论协方差可用于过滤SNP的整个集合，以便保持较少但具有代表性的预测变量。此外，提出了一种联合方法，允许同时选择和收缩相关的预测。假设该方法满足基因组评估的要求：考虑SNP之间的依赖性，在高度相关的SNP组内获得平滑估计，并且解决方案在这些组之间和这些组内是稀疏的。因此，可以鉴定影响性状的基因组区域。

In animal breeding, molecular data (e.g. single nucleotide polymorphisms; SNPs) are incorporated as predictor variables in statistical models to reach an improved genomic evaluation of animals. This leads to more precisely estimated breeding values of not-yet phenotyped animals, which is important for breeding purposes, and enables the genetic architecture of some traits to be elucidated. Not only is the effect size relevant but also the position on the genome. Particularly as high-dimensional SNP data are available, a causative variant can be pinpointed to a specific base pair on the genome. As the number of model parameters increases with a still growing number of SNPs, multicollinearity between covariates can affect the results of whole-genome regression methods. The objective of this study is to additionally incorporate dependencies between the molecular covariates, which are due to the linkage and linkage disequilibrium among chromosome segments, for more accurate estimates of SNP effects. The theoretical covariance between SNP genotypes can be used to filter the whole set of SNPs in order to remain at less but representative predictor variables. Furthermore, a joint approach is proposed that allows the simultaneous selection and shrinkage of relevant predictors. It is hypothesised that this method fulfils the requirements of genomic evaluation: the dependencies between SNPs are considered, smooth estimates are obtained within groups of highly correlated SNPs and the solution is sparse among and also within these groups. Thus, genomic regions that affect a trait can be identified.