Variable Selection with Multiply-Imputed Datasets: Choosing Between Stacked and Grouped Methods. Issue 4 (2nd October 2022)

• Record Type: Journal Article
• Authors: Du, Jiacong; Boss, Jonathan; Han, Peisong; Beesley, Lauren J.; Kleinsasser, Michael; Goutman, Stephen A.; Batterman, Stuart; Feldman, Eva L.; Mukherjee, Bhramar
• Is Part Of: Journal of computational and graphical statistics. Volume 31:Issue 4(2022)
• Page Start: 1063
• Page End: 1075
• Publication Date: 2022-10-02
• Subjects: Elastic net -- Group LASSO -- Majorization-minimization -- Missing data -- Multiple imputation -- Pooled objective function; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2022.2035739
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: Penalized regression methods are used in many biomedical applications for variable selection and simultaneous coefficient estimation. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors. This article considers a general class of penalized objective functions which, by construction, force selection of the same variables across imputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as "stacked" and "grouped" objective functions. Building on existing work, we (i) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for continuous and binary outcome data, (ii) incorporate adaptive shrinkage penalties, (iii) compare these methods through simulation, and (iv) develop an R package miselect . Simulations demonstrate that the "stacked" approaches are more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Biorepository aiming to identify the association between environmental pollutants and ALS risk. Supplementary materials for this article are available online.