Stable Variable Selection for High-Dimensional Genomic Data with Strong Correlations

High-dimensional genomic data studies are often found to exhibit strong correlations, which results in instability and inconsistency in the estimates obtained using commonly used regularization approaches including the Lasso and MCP, etc. In this paper, we perform comparative study of regularization approaches for variable selection under different correlation structures and propose a two-stage procedure named rPGBS to address the issue of stable variable selection in various strong correlation settings. This approach involves repeatedly running a two-stage hierarchical approach consisting of a random pseudo-group clustering and bi-level variable selection. Extensive simulation studies and high-dimensional genomic data analysis on real datasets have demonstrated the advantage of the proposed rPGBS method over some of the most used regularization methods. In particular, rPGBS results in more stable selection of variables across a variety of correlation settings, as compared to some recent methods addressing variable selection with strong correlations: Precision Lasso (Wang et al. in Bioinformatics 35:1181–1187, 2019) and Whitening Lasso (Zhu et al. in Bioinformatics 37:2238–2244, 2021). Moreover, rPGBS has been shown to be computationally efficient across various settings.