  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.
