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Omic data are characterized by the presence of strong dependence structuresthat result either from data acquisition or from some underlying biologicalprocesses. In metabolomics, for instance, data resulting from LiquidChromatography-Mass Spectrometry (LC-MS) -- a technique which gives access to alarge coverage of metabolites -- exhibit such patterns. These data sets aretypically used to find the metabolites characterizing a phenotype of interestassociated with the samples. However, applying some statistical procedures thatdo not adjust the variable selection step to the dependence pattern may resultin a loss of power and the selection of spurious variables. The goal of thispaper is to propose a variable selection procedure in the multivariate linearmodel that accounts for the dependence structure of the multiple outputs whichmay lead in the LC-MS framework to the selection of more relevant metabolites.We propose a novel Lasso-based approach in the multivariate framework of thegeneral linear model taking into account the dependence structure by usingvarious modelings of the covariance matrix of the residuals. Our numericalexperiments show that including the estimation of the covariance matrix of theresiduals in the Lasso criterion dramatically improves the variable selectionperformance. Our approach is also successfully applied to a LC-MS data set madeof African copals samples for which it is able to provide a small list ofmetabolites without altering the phenotype discrimination. Our methodology isimplemented in the R package MultiVarSel which is available from the CRAN(Comprehensive R Archive Network).

A multivariate variable selection approach for analyzing LC-MS metabolomics data