Abstract
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.
Highlights
It is generally recognized that protein expression analysis is crucial in explaining the changes that occur as a part of disease pathogenesis [1, 2]
Dridi et al EURASIP Journal on Bioinformatics and Systems Biology (2017) 2017:9 the same biological status [5], and (2) the technical variability, which originates from the imperfections of the measurement process used to obtain the concentrations
Since the complexity of a status is unlikely to be manifested through the changes in the characteristics of just one protein, it has generally been acknowledged that a set of proteins should be considered [5,6,7,8]
Summary
It is generally recognized that protein expression analysis is crucial in explaining the changes that occur as a part of disease pathogenesis [1, 2]. For the subset of biomarkers, the parameters of the Gaussian distribution take different values depending on the biological status whereas this is not the case for the second subset of proteins.
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