Large-scale inference for detecting QTL hotspots in hierarchically-related sparse regression models

There is a broad consensus in the biostatistical community about the merits of collectively accounting
for large numbers of genetic loci while leveraging information across correlated outcomes to uncover shared
regulation patterns. However, many also acknowledge the mathematical and computational diculties hampering
these practices in genetic association problems.

Here we present a scalable sparse regression framework for joint molecular quantitative trait locus (QTL)
analysis, where associations between genetic variants and molecular gene products are sought. Speci cally,
we devise two complementary approaches based on a series of parallel regressions combined in a hierarchical
manner to exibly accommodate high-dimensional responses (molecular outcomes) and predictors (genetic
variants), thereby allowing information-sharing across outcomes and variants. We also directly model the
propensity of variants to be hotspots, i.e., to remotely control the levels of many gene products, via a dedicated
top-level representation. We implement variational inference procedures augmented with simulated annealing
schemes to enhance exploration of highly multimodal spaces and allow simultaneous analysis of thousands of
samples, responses, predictors and predictor-level annotations. This uni ed learning boosts statistical power
and helps shed light on the biological processes underlying genetic regulation. We illustrate the advantages of
our approaches in simulations emulating real-data conditions and in a monocyte expression QTL study, which
con rms known hotspots and reveals new ones, as well as plausible mechanisms of action.