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 ($>$0.85) and the source ($>$0.75) matrices sparseness. The selection rate of components with high-to-moderate prognostic impacts was close to 95%, while the weak impacts were selected with a frequency close to the observed false positive rate ($<$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.

考虑患者间异质性的预后分子特征的发展是精准医学的关键挑战。我们提出了这种异质性和患者生存的联合模型，假设肿瘤表达是由独立特征子集的混合产生的。我们使用非参数独立成分分析对组学数据进行反卷积，其中源矩阵和权重矩阵具有双稀疏结构，分别对应于基因成分和个体成分关联。在模拟研究中，我们的方法确定了正确数量的组件并高精度地重建了重量（$>$0.85) 和来源 ($>$0.75) 矩阵稀疏性。具有高到中等预后影响的组件的选择率接近 95%，而选择弱影响的频率接近观察到的假阳性率（$<$25%）。当应用于来自 614 名乳腺癌患者的 1063 个基因的表达时，我们的模型确定了 15 个成分，包括与患者生存相关的六个成分，以及与早期乳腺癌的三个已知预后途径（即免疫系统、增殖和间质浸润）相关的成分。所提出的算法提供了对与患者预后相关的个体分子异质性的新见解，以更好地理解复杂的肿瘤机制。