Abstract
Cancer heterogeneity analysis is essential for precision medicine. Most of the existing heterogeneity analyses only consider a single type of data and ignore the possible sparsity of important features. In cancer clinical practice, it has been suggested that two types of data, pathological imaging and omics data, are commonly collected and can produce hierarchical heterogeneous structures, in which the refined sub-subgroup structure determined by omics features can be nested in the rough subgroup structure determined by the imaging features. Moreover, sparsity pursuit has extraordinary significance and is more challenging for heterogeneity analysis, because the important features may not be the same in different subgroups, which is ignored by the existing heterogeneity analyses. Fortunately, rich information from previous literature (for example, those deposited in PubMed) can be used to assist feature selection in the present study. Advancing from the existing analyses, in this study, we propose a novel sparse hierarchical heterogeneity analysis framework, which can integrate two types of features and incorporate prior knowledge to improve feature selection. The proposed approach has satisfactory statistical properties and competitive numerical performance. A TCGA real data analysis demonstrates the practical value of our approach in analyzing data heterogeneity and sparsity.