A global-local approach for detecting hotspots in multiple-response regression

Abstract

We tackle modelling and inference for variable selection in regression problems with many predictors and many responses. We focus on detecting hotspots, that is, predictors associated with several responses. Such a task is critical in statistical genetics, as hotspot genetic variants shape the architecture of the genome by controlling the expression of many genes and may initiate decisive functional mechanisms underlying disease endpoints. Existing hierarchical regression approaches designed to model hotspots suffer from two limitations: their discrimination of hotspots is sensitive to the choice of top-level scale parameters for the propensity of predictors to be hotspots, and they do not scale to large predictor and response vectors, for example, of dimensions 10 3 -10 5 in genetic applications. We address these shortcomings by introducing a flexible hierarchical regression framework that is tailored to the detection of hotspots and scalable to the above dimensions. Our proposal implements a fully Bayesian model for hotspots based on the horseshoe shrinkage prior. Its global-local formulation shrinks noise globally and, hence, accommodates the highly sparse nature of genetic analyses while being robust to individual signals, thus leaving the effects of hotspots unshrunk. Inference is carried out using a fast variational algorithm coupled with a novel simulated annealing procedure that allows efficient exploration of multimodal distributions.

EPISPOT: an epigenome-driven approach for detecting and interpreting hotspots in molecular QTL studies

“…Finally, the propensity of each SNP to be associated with many traits, i.e., to be a hotspot, is explicitly modelled using a SNP-specific parameter, θ s , similarly as in our earlier work [5].…”

“…We first describe the type of posterior output produced by EPISPOT and its performance in a simple problem where no modules are involved, i.e., the active epigenetic marks exert their influence on all associated SNP-trait pairs. We benchmark our approach against our earlier joint model, ATLASQTL [5], also tailored to the modelling of hotspots but which does not accommodate the epigenetic marks, as well as with the purely marginal screening approach, MATRIXEQTL [2], which tests each SNP-trait pair one-by-one and does not involve any epigenetic information. Figure 2 is attributable to an effective use of the three informative marks and not to other intrinsic differences between the two models; more evidence on this is provided in the next simulation experiment.…”

“…Parameter θ s has a central role in pleiotropic molecular QTL settings as it represents the propensity of each predictor to be associated with multiple responses, i.e., its propensity to be a hotspot. Its Gaussian prior specification involves a local-scale feature (via s 0s ) which effectively prevents overshrinkage; see our previous work on the modelling of hotspots from which this formulation is borrowed [5]. The value of s 0s is set by empirical Bayes, and so are the epigenetic effect hyperparameters ω l and s (see hereafter).…”

“…Indeed, widely-used marginal screening approaches [1,2] suffer from a large multiplicity burden and tend to lack of statistical power as they do not exploit the regulation patterns shared by the molecular entities, whereas joint modelling approaches [3,4] are often limited by the computational burden implied by the exploration of high-dimensional spaces of candidate variants and traits. To manage this tension between scalable inference and comprehensive joint modelling, we recently proposed a variational inference approach, called ATLASQTL [5], which explicitly borrows information across thousands of molecular traits controlled by shared pathways, and offers a robust fully Bayesian parametrisation of hotspots; its increased sensitivity and that of earlier related models have been demonstrated in different molecular QTL studies [4][5][6][7].…”

“…We introduce a novel approach, called EPISPOT, which infers the role of sparse sets of marksfrom hundreds of candidate epigenetic marks -in the activation of both cis and trans mechanisms affecting a whole network of molecular traits. Importantly, our proposal combines this epigenomedriven feature with the flexible hotspot modelling feature from our previous work [5], thereby offering a unified toolkit to refine the detection of master trans-hotspots from panels of candidate loci, aided by the epigenetic information at hand. The base version of EPISPOT assesses the action of the marks uniformly for the full set of analysed transcripts.…”