Gene expression (GE) levels have important biological and clinical implications. They are regulated by copy number alterations (CNAs). Modeling the regulatory relationships between GEs and CNAs facilitates understanding disease biology and can also have value in translational medicine. The expression level of a gene can be regulated by its cis-acting as well as trans-acting CNAs, and the set of trans-acting CNAs is usually not known, which poses a high-dimensional selection and estimation problem. Most of the existing studies share a common limitation in that they cannot accommodate long-tailed distributions or contamination of GE data. In this study, we develop a high-dimensional robust regression approach to infer the regulatory relationships between GEs and CNAs. A high-dimensional regression model is used to accommodate the effects of both cis-acting and trans-acting CNAs. A DPD (density power divergence) loss function is used to accommodate long-tailed GE distributions and contamination. Penalization is adopted for regularized estimation and selection of relevant CNAs. The proposed approach is effectively realized using a coordinate descent algorithm. Simulation shows that it has competitive performance compared to the nonrobust benchmark and the robust LAD (least absolute deviation) approach. We analyze TCGA (The Cancer Genome Atlas) data on cutaneous melanoma and study GE-CNA regulations in the RAP (regulation of apoptosis) pathway, which further demonstrates satisfactory performance of the proposed approach.
For the prognosis of complex diseases, beyond the main effects of genetic (G) and environmental (E) factors, gene-environment (G-E) interactions also play an important role. Many approaches have been developed for detecting important G-E interactions, most of which assume that measurements are complete. In practical data analysis, missingness in E measurements are not uncommon, and failing to properly accommodate such missingness leads to biased estimation and false marker identification. In this study, we conduct G-E interaction analysis with prognosis data under an accelerated failure time (AFT) model. To accommodate missingness in E measurements, we adopt a nonparametric kernel-based data augmentation approach. With a well-designed weighting scheme, a nice “byproduct” is that the proposed approach enjoys a certain robustness property. A penalization approach, which respects the “main effects, interactions” hierarchy, is adopted for selection (of important interactions and main effects) and regularized estimation. The proposed approach has sound interpretations and a solid statistical basis. It outperforms multiple alternatives in simulation. The analysis of TCGA data on lung cancer and melanoma leads to interesting findings and models with superior prediction.
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