In quantitative proteomics, mass tag labeling techniques have been widely adopted in mass spectrometry experiments. These techniques allow peptides (short amino acid sequences) and proteins from multiple samples of a batch being detected and quantified in a single experiment, and as such greatly improve the efficiency of protein profiling. However, the batch-processing of samples also results in severe batch effects and non-ignorable missing data occurring at the batch level. Motivated by the breast cancer proteomic data from the Clinical Proteomic Tumor Analysis Consortium, in this work, we developed two tailored multivariate MIxed-effects SElection models (mvMISE) to jointly analyze multiple correlated peptides/proteins in labeled proteomics data, considering the batch effects and the non-ignorable missingness. By taking a multivariate approach, we can borrow information across multiple peptides of the same protein or multiple proteins from the same biological pathway, and thus achieve better statistical efficiency and biological interpretation. These two different models account for different correlation structures among a group of peptides or proteins. Specifically, to model multiple peptides from the same protein, we employed a factor-analytic random effects structure to characterize the high and similar correlations among peptides. To model biological dependence among multiple proteins in a functional pathway, we introduced a graphical lasso penalty on the error precision matrix, and implemented an efficient algorithm based on the alternating direction method of multipliers. Simulations demonstrated the advantages of the proposed models. Applying the proposed methods to the motivating data set, we identified phosphoproteins and biological pathways that showed different activity patterns in triple negative breast tumors versus other breast tumors. The proposed methods can also be applied to other high-dimensional multivariate analyses based on clustered data with or without non-ignorable missingness.

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