A variable selection approach in the multivariate linear model: an application to LC-MS metabolomics data

• Published in: Statistical applications in genetics and molecular biology Vol. 17; no. 5
• Main Authors: Perrot-Dockès, Marie, Lévy-Leduc, Céline, Chiquet, Julien, Sansonnet, Laure, Brégère, Margaux, Étienne, Marie-Pierre, Robin, Stéphane, Genta-Jouve, Grégory
• Format: Journal Article
• Language: English
• Published: Germany De Gruyter 08.09.2018; Walter de Gruyter GmbH
• Subjects: Applications; Biochemistry, Molecular Biology; Biological activity; Biomarkers - metabolism; Chromatography, Liquid - methods; Covariance matrix; Data Interpretation, Statistical; Dependence; Humans; Life Sciences; Linear Models; Liquid chromatography; Mass spectrometry; Mathematical models; metabolomics; Metabolomics - methods; Metabolomics - statistics & numerical data; multivariate linear model; Random errors; Stationary processes; Statistical analysis; Statistical methods; Statistics; Tandem Mass Spectrometry - methods; time series; variable selection; time series; variable selection; multivariate linear model; metabolomics
• ISSN: 2194-6302; 1544-6115; 1544-6115
• DOI: 10.1515/sagmb-2017-0077

Omic data are characterized by the presence of strong dependence structures that result either from data acquisition or from some underlying biological processes. Applying statistical procedures that do not adjust the variable selection step to the dependence pattern may result in a loss of power and the selection of spurious variables. The goal of this paper is to propose a variable selection procedure within the multivariate linear model framework that accounts for the dependence between the multiple responses. We shall focus on a specific type of dependence which consists in assuming that the responses of a given individual can be modelled as a time series. We propose a novel Lasso-based approach within the framework of the multivariate linear model taking into account the dependence structure by using different types of stationary processes covariance structures for the random error matrix. Our numerical experiments show that including the estimation of the covariance matrix of the random error matrix in the Lasso criterion dramatically improves the variable selection performance. Our approach is successfully applied to an untargeted LC-MS (Liquid Chromatography-Mass Spectrometry) data set made of African copals samples. Our methodology is implemented in the R package which is available from the Comprehensive R Archive Network (CRAN).