<p><span style="color: rgb(0, 0, 0);">When testing for treatment effects in large-scale, observational (i.e., non-randomized) genomic studies, investigators must address two important challenges: (i) bias from unmeasured confounders and (ii) multivariate outcomes that exhibit shared, biologically meaningful low-dimensional structure. A sensitivity analysis for unmeasured confounding quantifies the impact of unmeasured confounders, but it has been limited to scalar outcomes or multivariate outcomes without a low-dimensional structure. This work presents representation-powered sensitivity analysis, a novel test for both global and subgroup treatment effects under unmeasured confounding when the outcomes exhibit a low-dimensional structure. As long as the dimension reduction method used to discover the low-dimensional structure satisfies high-level rate conditions, the proposed test guarantees Type I error or false discovery rate control, and many off-the-shelf dimension reduction methods satisfy these rates. Also, the proposed test has non-trivial power to detect a wide variety of treatment effects, including dense, sparse, and small treatment effects. We conclude by investigating the effect of Amyloid-beta (i.e., treatment) on multiple DNA methylation regions (i.e., outcomes) from an observational epigenomic dataset. Our results discover DNA methylation regions that are significantly influenced by Amyloid-beta levels even in the presence of unmeasured confounders and these discoveries align with in-vitro experiments.</span></p>