IMS (Univ. Bordeaux, CNRS, BINP), Talence, France, National Engineering School of Gabes (ENIG), University of Gabes, Gabes, Tunisia, CLIPP, Pôle de Recherche Université de Bourgogne, Dijon, France, NATO STO Centre for Maritime Research and Experimentation, La Spezia, Italy, Technology Research Department, Innovation Unit, bioMérieux SA, Marcy l’Étoile, France, Univ. Grenoble Alpes, Grenoble, France, CEA, LETI, MINATEC Campus, Grenoble, France, Service de Biostatistique - Bioinformatique, Hospices Civils de Lyon, Lyon, France, CNRS UMR 5558, LBBE, Équipe Biostatistique Santé, Villeurbanne, France, Université de Lyon, Université Claude Bernard Lyon 1, Lyon, France, Pôle Rhône-Alpes de Bioinformatique, Université Claude Bernard - Lyon 1, Villeurbanne, France

This paper addresses the question of biomarker discovery in proteomics. Given clinical data regarding a list of proteins for a set of individuals, the tackled problem is to extract a short subset of proteins the concentrations of which are an indicator of the biological status (healthy or pathological). In this paper, it is formulated as a specific instance of variable selection. The originality is that the proteins are not investigated one after the other but the best partition between discriminant and non-discriminant proteins is directly sought. In this way, correlations between the proteins are intrinsically taken into account in the decision. The developed strategy is derived in a Bayesian setting, and the decision is optimal in the sense that it minimizes a global mean error. It is finally based on the posterior probabilities of the partitions. The main difficulty is to calculate these probabilities since they are based on the so-called evidence that require marginalization of all the unknown model parameters. Two models are presented that relate the status to the protein concentrations, depending whether the latter are biomarkers or not. The first model accounts for biological variabilities by assuming that the concentrations are Gaussian distributed with a mean and a covariance matrix that depend on the status only for the biomarkers. The second one is an extension that also takes into account the technical variabilities that may significantly impact the observed concentrations. The main contributions of the paper are: (1) a new Bayesian formulation of the biomarker selection problem, (2) the closed-form expression of the posterior probabilities in the noiseless case, and (3) a suitable approximated solution in the noisy case. The methods are numerically assessed and compared to the state-of-the-art methods (t test, LASSO, Battacharyya distance, FOHSIC) on synthetic and real data from proteins quantified in human serum by mass spectrometry in selected reaction monitoring mode. © 2017, The Author(s).

Bayesian approach, Biomarker, Evidence, Hierarchical model, Model selection, Optimal decision, Proteomics, Variable selection

Bayesian networks, Biomarkers, Covariance matrix, Hierarchical systems, Inference engines, Mass spectrometry, Molecular biology, Probability, Bayesian approaches, Evidence, Hierarchical model, Model Selection, Optimal decisions, Proteomics, Variable selection, Proteins, biological marker, accuracy, Article, Bayes theorem, bioinformatics, conjugation, controlled study, evaluation study, human, mass spectrometry, proteomics, serum, synthesis