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