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.
Highlights
There are three possible genotypes (AA,Aa, and aa) for a bi-allelic quantitative trait loci (QTL) with alleles A and a
We propose a bivariate null kernel (BNK) hypothesis testing method to characterize the joint distribution of the two test statistics in two dimensional space
To assess the performance of our newly proposed BNK approach, we work on one real genome wide association study (GWAS) dataset and three quite different simulation settings to give a comprehensive evaluation
Summary
There are three possible genotypes (AA,Aa, and aa) for a bi-allelic QTL with alleles A and a. Traditional QTL models perform only one hypothesis test related to the existence of a QTL, while using a recombination fraction r to model but not simultaneously test the linkage between the observed marker and the QTL1,3–5. Besides the general QTL existence test, another linkage disequilibrium (LD) strength test can be used to examine if the QTL and the observed genetic marker are linked[7,8,9,10,11,12]. The two-test structure tests how strong a genetic effect is and where the gene is located; and whether there is a QTL around the observed marker instead of just having a QTL by random chance. The BNK approach performs nicely in the LD-based QTL model from which it was developed, and in a simulation that was designed for traditional recombination based one-test QTL methods. The BNK approach detects six other genes that were found important for homeostasis/ metabolism expression, but that had not previously been detected from the same dataset
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