Variable screening with multiple studies

TL;DR

This paper introduces a novel two-step variable screening method for high-dimensional data across multiple studies, improving accuracy and robustness over existing single-study approaches.

Contribution

It proposes a new multi-study screening framework with a two-step procedure using self-normalized estimators, reducing false negatives and relaxing distributional assumptions.

Findings

Reduces false negative errors significantly.

Maintains low false positive rate.

Performs well in simulations and real data applications.

Abstract

Advancement in technology has generated abundant high-dimensional data that allows integration of multiple relevant studies. Due to their huge computational advantage, variable screening methods based on marginal correlation have become promising alternatives to the popular regularization methods for variable selection. However, all these screening methods are limited to single study so far. In this paper, we consider a general framework for variable screening with multiple related studies, and further propose a novel two-step screening procedure using a self-normalized estimator for high-dimensional regression analysis in this framework. Compared to the one-step procedure and rank-based sure independence screening (SIS) procedure, our procedure greatly reduces false negative errors while keeping a low false positive rate. Theoretically, we show that our procedure possesses the sure screening property with weaker assumptions on signal strengths and allows the number of features to grow at an exponential rate of the sample size. In addition, we relax the commonly used normality assumption and allow sub-Gaussian distributions. Simulations and a real transcriptomic application illustrate the advantage of our method as compared to the rank-based SIS method.