Resampling-based methods for the error control of variable selection in high-dimensional genomic data

In analysis of high-dimensional data, penalized regression models have been commonly employed to select relevant variables. The most popularly used model is a least absolute shrinkage and selection operator, i.e., lasso. Recent studies proposed resampling-based methods to control the false discovery rate of variables selected by lasso. They include a data splitting method and a Gaussian mirror method. The former randomly splits samples into two different sets to estimate two independent coefficients for the same variable, while the later randomly generates Gaussian errors to construct a pair of variables and to estimate two different coefficients. Then, mirror statistics based on the coefficients estimated by each method were used for the error control. In this article, we proposed new approach to control FDR, combining a selection probability and a mirror statistic motivated by two resampling-based methods. In our simulation study, we demonstrated that the proposed approach controls FDR at a designated level better than other resampling-based methods while it maintains selection power. We also identified potentially cancer-related genes in analysis of microarray gene expression data from a breast cancer study.