Department of Mathematics, Brigham Young University-Idaho, Rexburg, ID, 83460, USA.
Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA.
Sci Rep. 2017 Oct 9;7(1):12798. doi: 10.1038/s41598-017-10177-5.
The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test statistics in two-dimensional space. The power of this BNK approach is verified by three different simulation designs and one whole genome dataset. It solves a few challenging open statistical questions, closely separates the confounding between 'linkage' and 'QTL effect', makes a fine genome division, provides a comprehensive understanding of the entire genome, overcomes limitations of traditional QTL approaches, and connects traditional QTL mapping with the newest genotyping technologies. The proposed approach contributes to both the genetics literature and the statistics literature, and has a potential to be extended to broader fields where a bivariate test is needed.
基于连锁不平衡 (LD) 的数量性状基因座 (QTL) 模型涉及两个不可或缺的假设检验：检验是否存在 QTL，以及检验 QTL 与观察到的标记之间的 LD 强度。这种两检验框架的优点在于检验是否在观察到的标记周围存在有影响的 QTL，而不是仅仅因为随机机会而存在 QTL。关于检验统计量的不准确渐近分布，存在未解决的、开放的统计问题。我们提出了一种双变量零核 (BNK) 假设检验方法，该方法用二维空间中的两个检验统计量来描述联合分布。通过三种不同的模拟设计和一个全基因组数据集验证了这种 BNK 方法的功效。它解决了一些具有挑战性的开放统计问题，紧密分离了“连锁”和“QTL 效应”之间的混杂，进行了精细的基因组划分，提供了对整个基因组的全面了解，克服了传统 QTL 方法的局限性，并将传统的 QTL 映射与最新的基因分型技术联系起来。该方法为遗传学文献和统计学文献做出了贡献，并有可能扩展到需要双变量检验的更广泛领域。
