Robust Inference Based on High-Dimensional Multiple Regressions with Application to Biomarker Screening

• Activity Number: 663 - Regression, Clustering and Gene Set Methods in Genomics
• Type: Contributed
• Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Genomics and Genetics
• Author(s): Youngseok Song* and Wen Zhou and Wenxin Zhou and Kim Hoke
• Companies: Colorado State University and Colorado State University and University of California, San Diego and Colorado State University
• Keywords: High dimensional multiple regression; Large scale multiple testing; Huber loss

Abstract

Identifying genetically related markers from a candidate pool based on sequencing data has been playing critical roles in genetic and genomics studies for treating cancer, controlling experiment quality, and learning evolutionary pathways. The complex dependency and leptokurtic nature of the sequencing data, however, make the conventional statistical approaches unreliable due to the lose of controlling the false discovery rate (FDR) or compromising the empirical power. Motivated by Fan et al. (2017) and Chen and Zhou (2018), we consider a linear model by which we can identify genetically related markers through testing linear hypotheses like contrasts. In particular, we propose a robust multiple testing procedure to handle these heavy tailed high dimensional data. The proposed method can simultaneously resolve the difficulties brought from the inter-gene dependence and heavy tailedness among data. We demonstrate that our procedure can improve power and control FDR when the data is generated by heavy-tailed distributions both theoretically and numerically. We apply our procedure to RNA sequencing data from Fischer et al. (2019) and reveal interesting biological insights.