Introducing Sparse Weighted Sum Regression (SWSR): Variable Selection for Correlated Chemical Exposures

• Activity Number: 81 - Contributed Poster Presentations: Section on Statistics in Epidemiology
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Grace Lyden* and David Vock and Shanna H. Swan and Emily S. Barrett and Sheela Sathyanarayana and Ruby H.N. Nguyen
• Companies: and University of Minnesota and Mount Sinai School of Medicine and Rutgers University and University of Washington and University of Minnesota
• Keywords: variable selection; chemical mixtures; collinearity; phthalates

Abstract

There is a growing demand for methods to determine the effects of chemical mixtures on human health. One statistical challenge is identifying true “bad actors” from a set of highly correlated predictors. Linear regression becomes highly variable in this setting, and shrinkage estimators tend to select either one or all of the correlated exposures. Weighted Quantile Sum (WQS) regression has been proposed to address this problem, but WQS is limited by a lack of sparsity in coefficient estimates and a reliance on data splitting. We propose a new method called Sparse Weighted Sum Regression that has the ability to set weights to exactly zero, thus performing true variable selection while simultaneously estimating model parameters such as the overall mixture effect. Two options are presented for significance testing, including a permutation test that maintains nominal Type I error rates without data splitting. In extensive simulation studies, we demonstrate our method’s minimal bias and improved selection accuracy compared to WQS and linear regression. We apply our method to a national pregnancy cohort study with a focus on prenatal phthalate exposure and child development.