Quantile-based Permutation Thresholds for QTL Hotspots

QTL hotspots (genomic locations affecting many traits) are a common feature in genetical genomics studies, and are biologically interesting since they may harbor critical regulators. Therefore, statistical procedures to assess the significance of hotspots are of key importance. One approach, randomly allocating observed QTLs across the genomic locations separately by trait, implicitly assumes all traits are uncorrelated. Recently, an empirical test for QTL hotspots was proposed based on the number of traits that exceed a predetermined LOD value, such as the standard permutation LOD threshold. The permutation null distribution of the maximum number of traits across all genomic locations preserves the correlation structure among the phenotypes, avoiding the detection of spurious hotspots due to non-genetic correlation induced by uncontrolled environmental factors and unmeasured variables. However, by only considering the number of traits above a threshold, without accounting for the magnitude of the LOD scores, relevant information is lost. In particular, biologically interesting hotspots composed of a moderate to small number of traits with strong LOD scores may be neglected as non-significant. In this paper we propose a quantile-based permutation approach that simultaneously accounts for the number and the LOD scores of traits within the hotspots. By considering a sliding scale of mapping thresholds, our method can assess the statistical significance of both small and large hotspots. Although the proposed approach can be applied to any type of heritable high volume ‘omic’ data set, we restrict our attention to eQTL analysis. We assess and compare the performances of these three methods in simulations and we illustrate how our approach can effectively assess the significance of moderate and small hotspots with strong LOD scores in a yeast expression data set.