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Recent studies have suggested that interconnections among omics variables, as reflected in network structures, can be more informative than simpler measures. Multiple types of omics variables can be connected via regulatory relationships, and there are studies modeling heterogeneity based on such regulations. Here, we conduct heterogeneity analysis based on both network structures and regulatory relationships. Significantly different from the existing literature, we consider network structures of regulators, as opposed to regulatees\u2014such networks describe more essential biological mechanisms and are less likely to be blurred by the mixture of direct and indirect interconnections. Another significant advancement is that we incorporate (unknown) blocking structures of regulators, which contain information complementary to network structures. A novel penalization approach is developed to simultaneously identify sample groups and estimate block structures, group\u2010specific networks, and regulation relationships. An effective computational algorithm is developed. It is rigorously proved that the proposed approach enjoys consistency in estimation, selection, and block identification. Simulation studies demonstrate its competitiveness against multiple alternatives. In the analysis of TCGA breast cancer data, we consider the (gene expression, protein expression) dual and make sensible findings that differ from those of the alternatives.<\/jats:p>","DOI":"10.1002\/sim.70779","type":"journal-article","created":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T23:42:46Z","timestamp":1792021366000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cancer Heterogeneity Modeling With Omics Data via Network\u2010Based Block\u2010Wise Regulatory Analysis"],"prefix":"10.1002","volume":"45","author":[{"given":"Rong","family":"Li","sequence":"first","affiliation":[{"name":"Center for Applied Statistics and School of Statistics Renmin University of China  Beijing China"},{"name":"Institute of Health Data Science, Renmin University of China  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9001-4999","authenticated-orcid":false,"given":"Shuangge","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Yale School of Public Health  Connecticut USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,14]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1093\/bib\/bbaa188"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.14348\/molcells.2021.0042"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12935-025-03944-2"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.3390\/cancers17030441"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-019-05855-6"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/bs.apcsb.2021.03.006"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csbj.2022.07.018"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2105-11-S3-S9"},{"issue":"217","key":"e_1_2_10_10_1","first-page":"1","article-title":"Simultaneous Clustering and Estimation of Heterogeneous Graphical Models","volume":"18","author":"Hao B.","year":"2018","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomtc\/ujae096"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssc.12575"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000281"},{"key":"e_1_2_10_14_1","first-page":"1340","article-title":"Conditional Structure Generation Through Graph Variational Generative Adversarial Nets","volume":"32","author":"Yang C.","year":"2019","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1214\/088342307000000113"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-25872-1"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2023.07.014"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.3390\/ijms25168830"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btt537"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.1186\/1752-0509-7-S2-S15"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12859-019-3253-z"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s42979-021-00865-5"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxae028"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csbj.2020.10.001"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btr288"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1507168112"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2105-9-559"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1214\/21-EJS1971"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1274"},{"key":"e_1_2_10_30_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-022-01716-7"},{"key":"e_1_2_10_31_1","first-page":"3808","article-title":"Learning Sparse Gaussian Graphical Models With Overlapping Blocks","volume":"29","author":"Hosseini M. 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