{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T21:07:58Z","timestamp":1789160878024,"version":"build-2803163510"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:00:00Z","timestamp":1780444800000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Lopez\u2013Loreta Foundation"},{"DOI":"10.13039\/501100000265","name":"UK Medical Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Union\u2019s Horizon Europe","award":["101126636"],"award-info":[{"award-number":["101126636"]}]},{"DOI":"10.13039\/501100000265","name":"UK Medical Research Council","doi-asserted-by":"publisher","award":["UKRI491"],"award-info":[{"award-number":["UKRI491"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,31]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Motivation<\/jats:title>\n                    <jats:p>In heterogeneous disease settings, accounting for intrinsic sample variability is crucial for obtaining reliable and interpretable omic network estimates. However, most graphical model analyses of biomedical data assume homogeneous conditional dependence structures, potentially leading to misleading conclusions. To address this, we propose a joint Gaussian graphical model that leverages sample-level ordinal covariates (e.g. disease stage) to account for heterogeneity and improve the estimation of partial correlation structures.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Our modelling framework, called NExON-Bayes, extends the graphical spike-and-slab framework to account for ordinal covariates, jointly estimating their relevance to the graph structure and leveraging them to improve the accuracy of network estimation. To scale to high-dimensional omic settings, we develop an efficient variational inference algorithm tailored to our model. Through simulations, we demonstrate that our method outperforms the vanilla graphical spike-and-slab (with no covariate information), as well as other state-of-the-art network approaches which exploit covariate information. Applying our method to reverse phase protein array data from patients diagnosed with stage I, II or III breast carcinoma, we estimate the behaviour of proteomic networks as cancer progresses. Our model provides insights not only through inspection of the estimated proteomic networks, but also of the estimated ordinal covariate dependencies of key groups of proteins within those networks, offering a comprehensive understanding of how biological pathways shift across disease stages.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability and implementation<\/jats:title>\n                    <jats:p>A user-friendly R package for NExON-Bayes with tutorials is available on Github at github.com\/jf687\/NExON, and archived at https:\/\/doi.org\/10.5281\/zenodo.20312938. The source of the dataset used is cited in the relevant section.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btag345","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T11:41:27Z","timestamp":1779882087000},"source":"Crossref","is-referenced-by-count":0,"title":["NExON-Bayes: a Bayesian approach to network estimation informed by ordinal covariates"],"prefix":"10.1093","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-2246-9031","authenticated-orcid":false,"given":"Joseph","family":"Feest","sequence":"first","affiliation":[{"name":"MRC Biostatistics Unit, University of Cambridge , Cambridge CB2 0SR,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7113-2540","authenticated-orcid":false,"given":"H\u00e9l\u00e8ne","family":"Ruffieux","sequence":"additional","affiliation":[{"name":"MRC Biostatistics Unit, University of Cambridge , 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