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Understanding the genetic underpinnings of complex traits and diseases has been greatly advanced by genome-wide association studies (GWAS). However, a significant portion of trait heritability remains unexplained, known as ``missing heritability". Most GWAS loci reside in non-coding regions, posing challenges in understanding their functional impact. Integrating GWAS with functional genomic data, such as expression quantitative trait loci (eQTLs), can bridge this gap. This study introduces a novel approach to discover candidate genes regulated by GWAS signals in both cis and trans. Unlike existing eQTL studies that focus solely on cis-eQTLs or consider cis- and trans-QTLs separately, we utilize adaptive statistical metrics that can reflect both the strong, sparse effects of cis-eQTLs and the weak, dense effects of trans-eQTLs. Consequently, candidate genes regulated by the joint effects can be prioritized. We demonstrate the efficiency of our method through theoretical and numerical analyses and apply it to adipose eQTL data from the METabolic Syndrome in Men (METSIM) study, uncovering genes playing important roles in the regulatory networks influencing cardiometabolic traits. Our findings offer new insights into the genetic regulation of complex traits and present a practical framework for identifying key regulatory genes based on joint eQTL effects.

Accurate delineation of tumor-adjacent functional brain regions is essential for planning function-preserving neurosurgery. Functional magnetic resonance imaging (fMRI) is increasingly used for presurgical counseling and planning. When analyzing presurgical fMRI data, false negatives are more dangerous to the patients than false positives because patients are more likely to experience significant harm from failing to identify functional regions and subsequently resecting critical tissues. In this paper, we propose a novel spatially adaptive variable screening procedure to enable effective control of false negatives while leveraging the spatial structure of fMRI data. Compared to existing statistical methods in fMRI data analysis, the new procedure directly controls false negatives at a desirable level and is completely data-driven. The new method is also substantially different from existing false-negative control procedures which do not take spatial information into account. Numerical examples show that the new method outperforms several state-of-the-art methods in retaining signal voxels, especially the subtle ones at the boundaries of functional regions, while providing cleaner separation of functional regions from background noise. Such results could be valuable to preserve critical tissues in neurosurgery.

We study the problem of high-dimensional variable selection via some two-step procedures. First we show that given some good initial estimator which is $\ell_{\infty}$-consistent but not necessarily variable selection consistent, we can apply the nonnegative Garrote, adaptive Lasso or hard-thresholding procedure to obtain a final estimator that is both estimation and variable selection consistent. Unlike the Lasso, our results do not require the irrepresentable condition which could fail easily even for moderate $p_n$ (Zhao and Yu, 2007) and it also allows $p_n$ to grow almost as fast as $\exp(n)$ (for hard-thresholding there is no restriction on $p_n$). We also study the conditions under which the Ridge regression can be used as an initial estimator. We show that under a relaxed identifiable condition, the Ridge estimator is $\ell_{\infty}$-consistent. Such a condition is usually satisfied when $p_n\le n$ and does not require the partial orthogonality between relevant and irrelevant covariates which is needed for the univariate regression in (Huang et al., 2008). Our numerical studies show that when using the Lasso or Ridge as initial estimator, the two-step procedures have a higher sparsity recovery rate than the Lasso or adaptive Lasso with univariate regression used in (Huang et al., 2008)., Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)