title: Covariate Selection for Multilevel Models with Missing Data.
abstract: Missing covariate data hampers variable selection in multilevel regression settings. Current variable selection techniques for multiply-imputed data commonly address missingness in the predictors through list-wise deletion and stepwise-selection methods which are problematic. Moreover, most variable selection methods are developed for independent linear regression models and do not accommodate multilevel mixed effects regression models with incomplete covariate data. We develop a novel methodology that is able to perform covariate selection across multiply-imputed data for multilevel random effects models when missing data is present. Specifically, we propose to stack the multiply-imputed data sets from a multiple imputation procedure and to apply a group variable selection procedure through group lasso regularization to assess the overall impact of each predictor on the outcome across the imputed data sets. Simulations confirm the advantageous performance of the proposed method compared with the competing methods. We applied the method to reanalyze the Healthy Directions-Small Business cancer prevention study, which evaluated a behavioral intervention program targeting multiple risk-related behaviors in a working-class, multi-ethnic population.
authors.affiliation: Department of Family Medicine, Department of Public Health, Division of Biostatistics, Oregon Health and Science University, Portland, OR 97239 USA.
authors.forename: Miguel
authors.initials: M
authors.lastname: Marino
authors.affiliation: Associate Professor, Department of Biobehavioral Health, Pennsylvania State University, University Park, PA 16802. Lecturer on Medicine, Division of Sleep Medicine, Harvard Medical School, Boston, MA 02115. Associate Neuroscientist, Department of Medicine, Brigham and Women's Hospital, Boston, MA 02115. Adjunct Associate Professor, Department of Social and Behavioral Sciences, Harvard T.H. Chan School of Public Health, Boston, MA 02115.
authors.forename: Orfeu M
authors.initials: OM
authors.lastname: Buxton
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109 USA.
authors.forename: Yi
authors.initials: Y
authors.lastname: Li
keywords: BIC; Rubin’s rules; cancer prevention; group lasso; intervention studies; multilevel; multiple imputation; regularization