Variable selection for noisy data applied in proteomics

The paper proposes a variable selection method for proteomics. It aims at selecting, among a set of proteins, those (named biomarkers) which enable to discriminate between two groups of individuals (healthy and pathological). To this end, data is available for a cohort of individuals: the biological state and a measurement of concentrations for a list of proteins. The proposed approach is based on a Bayesian hierarchical model for the dependencies between biological and instrumental variables. The optimal selection function minimizes the Bayesian risk, that is to say the selected set of variables maximizes the posterior probability. The two main contributions are: (1) we do not impose ad-hoc relationships between the variables such as a logistic regression model and (2) we account for instrumental variability through measurement noise. We are then dealing with indirect observations of a mixture of distributions and it results in intricate probability distributions. A closed-form expression of the posterior distributions cannot be derived. Thus, we discuss several approximations and study the robustness to the noise level. Finally, the method is evaluated both on simulated and clinical data.