Mixed-effects high-dimensional multivariate regression via group-lasso regularization = Regressione multivariata con effetti misti per dati ad alta dimensionalit`a: un approccio con regolarizzazione di tipo group-lasso

Linear mixed modeling is a well-established technique widely employed when observations possess a grouping structure. Nonetheless, this standard methodology is no longer applicable when the learning framework encompasses a multivariate response and high-dimensional predictors. To overcome these issues, in the present paper a penalized estimation procedure for multivariate linear mixed-effects models (MLMM) is introduced. In details, we propose to regularize the likelihood via a group-lasso penalty, forcing only a subset of the estimated parameters to be preserved across all components of the multivariate response. The methodology is employed to develop novel surrogate biomarkers for cardiovascular risk factors, such as lipids and blood pressure, from whole-genome DNA methylation data in a multi-center study. The described methodology performs better than current stateof- art alternatives in predicting a multivariate continuous outcome.