Variable screening with multiple studies

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 highdimensional 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.

High-dimension to high-dimension screening for detecting genome-wide epigenetic regulators of gene expression

“…Fan and Lv (2008) proposed the first sure screening method called Sure Independence Screening (SIS) that only kept the predictors with large marginal correlation with the response in univariate linear model and showed its sure screening property that the set after screening will contain the true set of predictors with large probability. Alternative marginal association based screening methods, including those adopting robust and model-free statistics, were developed and generalized to a broader class of models (Fan and Song, 2010; Zhu et al, 2011; Ma et al, 2020). Other screening methods have been proposed to further consider the between-predictor correlation (Bühlmann et al, 2010; He et al, 2019).…”

Detecting survival-associated biomarkers from heterogeneous populations

“…The first general framework for variable selection with multiple studies was proposed by Ma et al 27 where active predictors is assumed to be common to all studies, but the signal strengths (i.e., magnitudes of ) of those active predictors can vary among the studies. Combining marginal correlations between an outcome and each feature across studies, Ma et al (2020) proposed the extension of sure independence screening to multiple studies in the linear models, the method known as Two-Step Aggregation Sure Independence Screening or “TSA-SIS”.…”

“…Our proposed methodology is a non-trivial extension of the sure screening procedure for multiple studies of Ma et al 27 to the multiple Cox proportional hazards models. Unlike simpler parametric models such as linear and logistic regression models, the Cox model has the baseline hazard function as an infinite dimensional function parameter beyond the regression coefficients of interest.…”

“…In this paper, we propose a novel Cox model based two-stage variable selection method for the detection of survival associated biomarkers common in multiple genomic studies. In the first stage, we extend the screening procedure for the linear model in Ma et al 27 to perform sure screening with multiple studies in high-dimensional Cox regression. In the second stage, we penalize the partial log-likelihoods with a group lasso penalty across multiple studies to select the final set of features in all studies simultaneously.…”

Feature screening for multi-response linear models by empirical likelihood

“…For example, the well-known DCSIS proposed by Li et al (2012) can be directly applied to the multi-response; Li et al (2017) proposed a projection-based screening method; Lu and Lin (2018) built a canonical correlation-based screening method for varying coefficient models. Ma et al (2020) developed a two-stage screening method for multi-response linear model; ? proposed a rank canonical correlation-based screening procedure.…”