Grouped Variable Selection via Hierarchical Linear Models

• Activity Number: 227
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Sihai Dave Zhao*+ and Yi Li
• Companies: Harvard University/Dana-Farber Cancer Institute and Dana-Farber Cancer Institute/Harvard School of Public Health
• Keywords: Biological pathways ; Grouped variables ; Hierarchical linear model ; High-dimensional data ; Variable selection

Abstract

Incorporating prior information into predictive models can often lead to better prediction and model selection. For example, in many genomic studies this prior information takes the form of grouped covariates, or biological pathways. Current methods can achieve variable selection at the group level as well as the within-group level. Framing these methods as hierarchical linear models, we find that they are actually suboptimal when used with the small samples, high-dimensional covariates, and large group sizes that are characteristic of modern high-throughput datasets. Motivated by a Bayes argument, we propose a new class of penalty functions that are designed to correct the deficiencies of existing techniques. We show that they can achieve the oracle property under mild regularity conditions. Simulation studies illustrate the advantages of our proposal, which are further demonstrated by an application to a clinical study of multiple myeloma.