Accounting for Established Predictors with the Multi-Step Elastic Net

• Activity Number: 256 - Contributed Poster Presentations: Section on Statistical Learning and Data Science
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Elizabeth C Chase* and Phil Boonstra
• Companies: University of Michigan and University of Michigan
• Keywords: penalized regression; nested models; grouped data; lasso; grouped lasso

Abstract

Multivariable models are rarely built in isolation. Instead, they are based on a mixture of covariates that have been evaluated in earlier studies (e.g. age, sex, or common biomarkers) and covariates that were collected specifically for the current study (e.g. novel biomarkers or other hypothesized risk factors). For that context, we present the multi-step elastic net (MSN), which considers penalized regression with variables that can be qualitatively grouped based upon their degree of prior research support: established predictors vs. unestablished predictors. The MSN chooses between uniform penalization of all predictors (the standard elastic net) and weaker penalization of the established predictors in a cross-validated framework, and includes the option to impose zero penalty on the established predictors. In simulation studies that reflect the motivating context, we show the comparability or superiority of the MSN over the standard elastic net, the Integrative LASSO with Penalty Factors, the sparse group lasso, and the group lasso, and we investigate the importance of not penalizing the established predictors at all.