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High-dimensional longitudinal data is increasingly used in a wide range ofscientific studies. However, there are few statistical methods forhigh-dimensional linear mixed models (LMMs), as most Bayesian variableselection or penalization methods are designed for independent observations.Additionally, the few available software packages for high-dimensional LMMssuffer from scalability issues. This work presents an efficient and accurateBayesian framework for high-dimensional LMMs. We use empirical Bayes estimatorsof hyperparameters for increased flexibility and anExpectation-Conditional-Minimization (ECM) algorithm for computationallyefficient maximum a posteriori probability (MAP) estimation of parameters. Thenovelty of the approach lies in its partitioning and parameter expansion aswell as its fast and scalable computation. We illustrate Linear Mixed Modelingwith PaRtitiOned empirical Bayes ECM (LMM-PROBE) in simulation studiesevaluating fixed and random effects estimation along with computation time. Areal-world example is provided using data from a study of lupus in children,where we identify genes and clinical factors associated with a new lupusbiomarker and predict the biomarker over time.

Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm