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Motivated by the inquiries of weak signals in underpowered genome-wideassociation studies (GWASs), we consider the problem of retaining true signalsthat are not strong enough to be individually separable from a large amount ofnoise. We address the challenge from the perspective of false negative controland present false negative control (FNC) screening, a data-driven method toefficiently regulate false negative proportion at a user-specified level. FNCscreening is developed in a realistic setting with arbitrary covariancedependence between variables. We calibrate the overall dependence through aparameter whose scale is compatible with the existing phase diagram inhigh-dimensional sparse inference. Utilizing the new calibration, weasymptotically explicate the joint effect of covariance dependence, signalsparsity, and signal intensity on the proposed method. We interpret the resultsusing a new phase diagram, which shows that FNC screening can efficientlyselect a set of candidate variables to retain a high proportion of signals evenwhen the signals are not individually separable from noise. Finite sampleperformance of FNC screening is compared to those of several existing methodsin simulation studies. The proposed method outperforms the others in adaptingto a user-specified false negative control level. We implement FNC screening toempower a two-stage GWAS procedure, which demonstrates substantial power gainwhen working with limited sample sizes in real applications.

Weak Signal Inclusion Under Dependence and Applications in Genome-wide Association Study