Performance of PLS regression coefficients in selecting variables for each response of a multivariate PLS for omics-type data

Multivariate partial least square (PLS) regression allows the modeling of complex biological events, by considering different factors at the same time. It is unaffected by data collinearity, representing a valuable method for modeling high-dimensional biological data (as derived from genomics, proteomics and peptidomics). In presence of multiple responses, it is of particular interest how to appropriately "dissect" the model, to reveal the importance of single attributes with regard to individual responses (for example, variable selection). In this paper, performances of multivariate PLS regression coefficients, in selecting relevant predictors for different responses in omics-type of data, were investigated by means of a receiver operating characteristic (ROC) analysis. For this purpose, simulated data, mimicking the covariance structures of microarray and liquid chromatography mass spectrometric data, were used to generate matrices of predictors and responses. The relevant predictors were set a priori. The influences of noise, the source of data with different covariance structure and the size of relevant predictors were investigated. Results demonstrate the applicability of PLS regression coefficients in selecting variables for each response of a multivariate PLS, in omics-type of data. Comparisons with other feature selection methods, such as variable importance in the projection scores, principal component regression, and least absolute shrinkage and selection operator regression were also provided.