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

TL;DR

This paper introduces FNC screening, a novel data-driven method for retaining true signals in high-dimensional GWAS data under dependence, effectively controlling false negatives and improving power in limited sample scenarios.

Contribution

The paper develops FNC screening, a new method that controls false negatives in dependent high-dimensional data, with theoretical calibration and practical GWAS applications.

Findings

FNC screening effectively controls false negatives at a user-specified level.

The method outperforms existing approaches in simulations and real GWAS data.

FNC screening enhances power in two-stage GWAS with limited samples.

Abstract

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.