  Motivated by the inquiries of weak signals in underpowered genome-wide
association studies (GWASs), we consider the problem of retaining true signals
that are not strong enough to be individually separable from a large amount of
noise. We address the challenge from the perspective of false negative control
and present false negative control (FNC) screening, a data-driven method to
efficiently regulate false negative proportion at a user-specified level. FNC
screening is developed in a realistic setting with arbitrary covariance
dependence between variables. We calibrate the overall dependence through a
parameter whose scale is compatible with the existing phase diagram in
high-dimensional sparse inference. Utilizing the new calibration, we
asymptotically explicate the joint effect of covariance dependence, signal
sparsity, and signal intensity on the proposed method. We interpret the results
using a new phase diagram, which shows that FNC screening can efficiently
select a set of candidate variables to retain a high proportion of signals even
when the signals are not individually separable from noise. Finite sample
performance of FNC screening is compared to those of several existing methods
in simulation studies. The proposed method outperforms the others in adapting
to a user-specified false negative control level. We implement FNC screening to
empower a two-stage GWAS procedure, which demonstrates substantial power gain
when working with limited sample sizes in real applications.
