High-dimensional variable selection for genomics data, from both frequentist and Bayesian perspectives - Ren, Jie (Kansas State University, 2020)
Variable selection is one of the most popular tools for analyzing high-dimensional genomic data. It has been developed to accommodate complex data structures and lead to structured sparse identification of important genomics features. We focus on the network and interaction structure that commonly exist in genomic data, and develop novel variable selection methods from both frequentist and Bayesian perspectives. Network-based regularization has achieved success in variable selections for high-dimensional cancer genomic data, due to its ability to incorporate the correlations among genomic features. However, as survival time data usually follow skewed distributions, and are contaminated by outliers, network-constrained regularization that does not take the robustness into account leads to false identifications of network structure and biased estimation of patients’ survival. In the first project, we develop a novel robust network-based variable selection method under the accelerated failure time (AFT) model. Extensive simulation studies show the advantage of the proposed method over the alternative methods. Promising findings are made in two case studies of lung cancer datasets with high dimensional gene expression measurements. Gene-environment (G×E) interactions are important for the elucidation of disease etiology beyond the main genetic and environmental effects. In the second project, a novel and powerful semi-parametric Bayesian variable selection model has been proposed to investigate linear and nonlinear G×E interactions simultaneously. It can further conduct structural identification by distinguishing nonlinear interactions from main-effects-only case within the Bayesian framework. The proposed method conducts Bayesian variable selection more efficiently and accurately than alternatives. Simulation shows that the proposed model outperforms competing alternatives in terms of both identification and prediction. In the case study, the proposed Bayesian method leads to the identification of effects with important implications in a high-throughput profiling study with high-dimensional SNP data. In the last project, a robust Bayesian variable selection method has been developed for G×E interaction studies. The proposed robust Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. Spike and slab priors are incorporated on both individual and group levels to identify the sparse main and interaction effects. Extensive simulation studies and analysis of both the diabetes data with SNP measurements from the Nurses’ Health Study and TCGA melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives. To facilitate reproducible research and fast computation, we have developed open source R packages for each project, which provide highly efficient C++ implementation for all the proposed and alternative approaches. The R packages regnet and spinBayes, associated with the first and second project correspondingly, are available on CRAN. For the third project, the R package robin is available from GitHub and will be submitted to CRAN soon.
Keywords: High‐dimensional data; Network‐based regularization; Robust variable selection; Bayesian variable selection; Gene-environment interactions; Markov chain Monte Carlo