Abstract
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.