Identifying individual mechanisms involved in complex diseases, such as cancer, is essential for precision medicine. Their characterization is particularly challenging due to the unknown relationships of high-dimensional omics data and their inter-patient heterogeneity. We propose to model individual gene expression as a combination of unobserved molecular mechanisms (molecular components) that may differ between the individuals. Considering a baseline molecular profile common to all individuals, these molecular components may represent molecular pathways differing from the population background. We defined an infinite sparse graphical independent component analysis (isgICA) to identify these molecular components. This model relies on double sparseness: the source matrix sparseness defines the subset of genes involved in each molecular component, whereas the weight matrix sparseness identifies the subset of molecular components associated with each patient. As the number of molecular components is unknown but likely high, we simultaneously inferred it and the weight matrix sparseness using the beta-Bernoulli process (BBP). We simulated data from a double sparse ICA with 10/30 components with specific sparseness structures for 100/500 individuals and 500/1000/5000 genes with different noise variance levels to evaluate the reconstruction of the latent structures by our model. For all simulations, the isgICA was able to reconstruct with higher accuracy than 2 state-of-the-art methods ( ica and fastICA) the number of components, the weight and source matrix sparsenesses (correlation simulated/estimated >.8). Applying our model to the expression of 1063 genes of 614 breast cancer patients, the isgICA identified 22 components. According to the source matrix, 7 of these 22 components seemed to be specifically related to 3 known molecular pathways with a prognostic effect in early breast cancer (immune system, proliferation, and stroma invasion). This proposed algorithm provides an insight into individual molecular heterogeneity to better understand complex disease mechanisms.

The development of prognostic molecular signatures considering the inter-patient heterogeneity is a key challenge for the precision medicine. We propose a joint model of this heterogeneity and the patient survival, assuming that tumor expression results from a mixture of a subset of independent signatures. We deconvolute the omics data using a non-parametric independent component analysis with a double sparseness structure for the source and the weight matrices, corresponding to the gene-component and individual-component associations, respectively. In a simulation study, our approach identified the correct number of components and reconstructed with high accuracy the weight ([Formula: see text]0.85) and the source ([Formula: see text]0.75) matrices sparseness. The selection rate of components with high-to-moderate prognostic impacts was close to 95%, while the weak impacts were selected with a frequency close to the observed false positive rate ([Formula: see text]25%). When applied to the expression of 1063 genes from 614 breast cancer patients, our model identified 15 components, including six associated to patient survival, and related to three known prognostic pathways in early breast cancer (i.e. immune system, proliferation, and stromal invasion). The proposed algorithm provides a new insight into the individual molecular heterogeneity that is associated with patient prognosis to better understand the complex tumor mechanisms.