Rank-based Bayesian variable selection for genome-wide transcriptomic analyses

Variable selection is crucial in high-dimensional omics-based analyses, since it is biologically reasonable to assume only a subset of non-noisy features contributes to the data structures. However, the task is particularly hard in an unsupervised setting, and a priori ad hoc variable selection is still a very frequent approach, despite the evident drawbacks and lack of reproducibility. We propose a Bayesian variable selection approach for rank-based transcriptomic analysis. Making use of data rankings instead of the actual continuous measurements increases the robustness of conclusions when compared to classical statistical methods, and embedding variable selection into the inferential tasks allows complete reproducibility. Specifically, we develop a novel extension of the Bayesian Mallows model for variable selection that allows for a full probabilistic analysis, leading to coherent quantification of uncertainties. We test our approach on simulated data using several data generating procedures, demonstrating the versatility and robustness of the method under different scenarios. We then use the novel approach to analyse genome-wide RNAseq gene expression data from ovarian cancer samples: several genes that affect cancer development are correctly detected in a completely unsupervised fashion, showing the method usefulness in the context of signature discovery for cancer genomics. Moreover, the possibility to also perform uncertainty quantification plays a key role in the subsequent biological investigation.