A global-local approach for detecting hotspots in multiple-response regression. (English) Zbl 1446.62288

Ruffieux, Hélène; Davison, Anthony C.; Hager, Jörg; Inshaw, Jamie; Fairfax, Benjamin P.; Richardson, Sylvia; Bottolo, Leonardo

Ann. Appl. Stat. 14, No. 2, 905-928 (2020).

Summary: 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62F07	Statistical ranking and selection procedures
62J15	Paired and multiple comparisons; multiple testing
92D20	Protein sequences, DNA sequences

Keywords:

annealed variational inference; hierarchical model; horseshoe prior; molecular quantitative trait locus analyses; multiplicity control; normal scale mixture; regulation hotspot; shrinkage; statistical genetics; variable selection

Software:

EMVS; TreeQTL; Matrix eQTL

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