{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T03:15:45Z","timestamp":1773717345448,"version":"3.50.1"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"10","license":[{"start":{"date-parts":[[2024,10,14]],"date-time":"2024-10-14T00:00:00Z","timestamp":1728864000000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFA1302500"],"award-info":[{"award-number":["2021YFA1302500"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12126605"],"award-info":[{"award-number":["12126605"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key-Area Research and Development of Guangdong Province","award":["2020B1111190001"],"award-info":[{"award-number":["2020B1111190001"]}]},{"name":"CAS Project for Young Scientists in Basic Research","award":["YSBR-034"],"award-info":[{"award-number":["YSBR-034"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022M723328"],"award-info":[{"award-number":["2022M723328"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Motivation<\/jats:title>\n                    <jats:p>Spatial transcriptomics (ST) technologies provide richer insights into the molecular characteristics of cells by simultaneously measuring gene expression profiles and their relative locations. However, each slice can only contain limited biological variation, and since there are almost always non-negligible batch effects across different slices, integrating numerous slices to account for batch effects and locations is not straightforward. Performing multi-slice integration, dimensionality reduction, and other downstream analyses separately often results in suboptimal embeddings for technical artifacts and biological variations. Joint modeling integrating these steps can enhance our understanding of the complex interplay between technical artifacts and biological signals, leading to more accurate and insightful results.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>In this context, we propose a hierarchical hidden Markov random field model STADIA to reduce batch effects, extract common biological patterns across multiple ST slices, and simultaneously identify spatial domains. We demonstrate the effectiveness of STADIA using five datasets from different species (human and mouse), various organs (brain, skin, and liver), and diverse platforms (10x Visium, ST, and Slice-seqV2). STADIA can capture common tissue structures across multiple slices and preserve slice-specific biological signals. In addition, STADIA outperforms the other three competing methods (PRECAST, fastMNN, and Harmony) in terms of the balance between batch mixing and spatial domain identification, and it demonstrates the advantage of joint modeling when compared to STAGATE and GraphST.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability and implementation<\/jats:title>\n                    <jats:p>The source code implemented by R is available at https:\/\/github.com\/zhanglabtools\/STADIA and archived with version 1.01 on Zenodo https:\/\/zenodo.org\/records\/13637744.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btae611","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T09:08:32Z","timestamp":1728551312000},"source":"Crossref","is-referenced-by-count":12,"title":["Statistical batch-aware embedded integration, dimension reduction, and alignment for spatial transcriptomics"],"prefix":"10.1093","volume":"40","author":[{"given":"Yanfang","family":"Li","sequence":"first","affiliation":[{"name":"NCMIS, CEMS, RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing 100190,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0192-7118","authenticated-orcid":false,"given":"Shihua","family":"Zhang","sequence":"additional","affiliation":[{"name":"NCMIS, CEMS, RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing 100190,","place":["China"]},{"name":"School of Mathematical Sciences, University of Chinese Academy of Sciences , Beijing 100049,","place":["China"]},{"name":"Key Laboratory of Systems Health Science of Zhejiang Province, School of Life Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences , Hangzhou 310024,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,10,14]]},"reference":[{"key":"2024102618501652300_btae611-B1","doi-asserted-by":"crossref","first-page":"2644","DOI":"10.1093\/bioinformatics\/btab164","article-title":"Sepal: identifying transcript profiles with spatial patterns by diffusion-based modeling","volume":"37","author":"Andersson","year":"2021","journal-title":"Bioinformatics"},{"key":"2024102618501652300_btae611-B2","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.3390\/cancers14071847","article-title":"MMP9: a tough target for targeted therapy for cancer","volume":"14","author":"Augoff","year":"2022","journal-title":"Cancers (Basel)"},{"key":"2024102618501652300_btae611-B3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1214\/20-BA1240","article-title":"Heterogeneous large datasets integration using bayesian factor regression","volume":"17","author":"Avalos-Pacheco","year":"2022","journal-title":"Bayesian Anal"},{"key":"2024102618501652300_btae611-B4","doi-asserted-by":"crossref","first-page":"3246","DOI":"10.1002\/cam4.934","article-title":"CXCL9: evidence and contradictions for its role in tumor progression","volume":"5","author":"Ding","year":"2016","journal-title":"Cancer Med"},{"key":"2024102618501652300_btae611-B5","doi-asserted-by":"crossref","first-page":"1739","DOI":"10.1038\/s41467-022-29439-6","article-title":"Deciphering spatial domains from spatially resolved transcriptomics with an adaptive graph attention auto-encoder","volume":"13","author":"Dong","year":"2022","journal-title":"Nat Commun"},{"key":"2024102618501652300_btae611-B6","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1038\/nmeth.4634","article-title":"Identification of spatial expression trends in single-cell gene expression data","volume":"15","author":"Edsg\u00e4rd","year":"2018","journal-title":"Nat Methods"},{"key":"2024102618501652300_btae611-B7","doi-asserted-by":"crossref","first-page":"e50","DOI":"10.1093\/nar\/gkab043","article-title":"SPOTlight: seeded NMF regression to deconvolute spatial transcriptomics spots with single-cell transcriptomes","volume":"49","author":"Elosua-Bayes","year":"2021","journal-title":"Nucleic Acids Res"},{"key":"2024102618501652300_btae611-B8","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1186\/s12935-020-01296-7","article-title":"The expression profiles and prognostic values of hsps family members in head and neck cancer","volume":"20","author":"Fan","year":"2020","journal-title":"Cancer Cell Int"},{"key":"2024102618501652300_btae611-B9","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1198\/016214502760047131","article-title":"Model-based clustering, discriminant analysis, and density estimation","volume":"97","author":"Fraley","year":"2002","journal-title":"J. Am. Stat. Assoc"},{"key":"2024102618501652300_btae611-B10","article-title":"Unsupervised spatially embedded deep representation of spatial transcriptomics","volume":"16","author":"Fu","year":"2024","journal-title":"Genome Medicine"},{"key":"2024102618501652300_btae611-B11","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1093\/biostatistics\/kxi042","article-title":"Probabilistic segmentation and intensity estimation for microarray images","volume":"7","author":"Gottardo","year":"2006","journal-title":"Biostatistics"},{"key":"2024102618501652300_btae611-B12","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1103\/PhysRevLett.69.2013","article-title":"Simulation of biological cell sorting using a two-dimensional extended potts model","volume":"69","author":"Graner","year":"1992","journal-title":"Phys Rev Lett"},{"key":"2024102618501652300_btae611-B13","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1038\/nbt.4091","article-title":"Batch effects in single-cell RNA-sequencing data are corrected by matching mutual nearest neighbors","volume":"36","author":"Haghverdi","year":"2018","journal-title":"Nat Biotechnol"},{"key":"2024102618501652300_btae611-B14","doi-asserted-by":"crossref","first-page":"2639","DOI":"10.1162\/0899766042321814","article-title":"Canonical correlation analysis: an overview with application to learning methods","volume":"16","author":"Hardoon","year":"2004","journal-title":"Neural Comput"},{"key":"2024102618501652300_btae611-B15","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1038\/s41587-019-0113-3","article-title":"Efficient integration of heterogeneous single-cell transcriptomes using scanorama","volume":"37","author":"Hie","year":"2019","journal-title":"Nat Biotechnol"},{"key":"2024102618501652300_btae611-B16","doi-asserted-by":"crossref","first-page":"7046","DOI":"10.1038\/s41467-021-27354-w","article-title":"Spatial transcriptomics to define transcriptional patterns of zonation and structural components in the mouse liver","volume":"12","author":"Hildebrandt","year":"2021","journal-title":"Nat Commun"},{"key":"2024102618501652300_btae611-B17","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1038\/s41592-021-01255-8","article-title":"SpaGCN: integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network","volume":"18","author":"Hu","year":"2021","journal-title":"Nat Methods"},{"key":"2024102618501652300_btae611-B18","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1038\/s42003-020-01590-0","article-title":"Decorin-mediated suppression of tumorigenesis, invasion, and metastasis in inflammatory breast cancer","volume":"4","author":"Hu","year":"2021","journal-title":"Commun Biol"},{"key":"2024102618501652300_btae611-B19","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/jop.12109","article-title":"The role of NEFL in cell growth and invasion in head and neck squamous cell carcinoma cell lines","volume":"43","author":"Huang","year":"2014","journal-title":"J Oral Pathol Med"},{"key":"2024102618501652300_btae611-B20","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.cell.2020.05.039","article-title":"Multimodal analysis of composition and spatial architecture in human squamous cell carcinoma","volume":"182","author":"Ji","year":"2020","journal-title":"Cell"},{"key":"2024102618501652300_btae611-B21","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1111\/j.1467-9868.2009.00730.x","article-title":"On the use of non-local prior densities in bayesian hypothesis tests","volume":"72","author":"Johnson","year":"2010","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"},{"key":"2024102618501652300_btae611-B22","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1080\/01621459.2012.682536","article-title":"Bayesian model selection in high-dimensional settings","volume":"107","author":"Johnson","year":"2012","journal-title":"J Am Stat Assoc"},{"key":"2024102618501652300_btae611-B23","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1093\/biostatistics\/kxj037","article-title":"Adjusting batch effects in microarray expression data using empirical bayes methods","volume":"8","author":"Johnson","year":"2007","journal-title":"Biostatistics"},{"key":"2024102618501652300_btae611-B24","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1038\/s41592-019-0619-0","article-title":"Fast, sensitive and accurate integration of single-cell data with harmony","volume":"16","author":"Korsunsky","year":"2019","journal-title":"Nat Methods"},{"key":"2024102618501652300_btae611-B25","first-page":"19","article-title":"ML estimation of the t distribution using EM and its extensions, ECM and ECME","volume":"5","author":"Liu","year":"1995","journal-title":"Stat Sin"},{"key":"2024102618501652300_btae611-B26","doi-asserted-by":"crossref","first-page":"583","DOI":"10.3892\/ol.2011.300","article-title":"The emerging role of cxcl10 in cancer","volume":"2","author":"Liu","year":"2011","journal-title":"Oncol Lett"},{"key":"2024102618501652300_btae611-B27","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1038\/s41467-023-35947-w","article-title":"Probabilistic embedding, clustering, and alignment for integrating spatial transcriptomics data with PRECAST","volume":"14","author":"Liu","year":"2023","journal-title":"Nat Commun"},{"key":"2024102618501652300_btae611-B28","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1038\/s41467-023-36796-3","article-title":"Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst","volume":"14","author":"Long","year":"2023","journal-title":"Nat Commun"},{"key":"2024102618501652300_btae611-B29","article-title":"SPADE: spatial deconvolution for domain specific cell-type estimation","volume":"7","author":"Lu","journal-title":"Commun Biol"},{"key":"2024102618501652300_btae611-B30","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1080\/01621459.2018.1497494","article-title":"Batch effects correction with unknown subtypes","volume":"114","author":"Luo","year":"2019","journal-title":"J Am Stat Assoc"},{"key":"2024102618501652300_btae611-B31","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1038\/s41587-022-01273-7","article-title":"Spatially informed cell-type deconvolution for spatial transcriptomics","volume":"40","author":"Ma","year":"2022","journal-title":"Nat Biotechnol"},{"key":"2024102618501652300_btae611-B32","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1038\/s41593-020-00787-0","article-title":"Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex","volume":"24","author":"Maynard","year":"2021","journal-title":"Nat Neurosci"},{"key":"2024102618501652300_btae611-B33","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1146\/annurev-statistics-031017-100325","article-title":"Finite mixture models","volume":"6","author":"McLachlan","year":"2019","journal-title":"Annu Rev Stat Appl"},{"key":"2024102618501652300_btae611-B34","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1080\/00273171.2015.1065398","article-title":"A comparison of inverse-wishart prior specifications for covariance matrices in multilevel autoregressive models","volume":"51","author":"Schuurman","year":"2016","journal-title":"Multivariate Behav Res"},{"key":"2024102618501652300_btae611-B35","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1089\/cmb.2021.0617","article-title":"Deciphering the spatial modular patterns of tissues by integrating spatial and single-cell transcriptomic data","volume":"29","author":"Shan","year":"2022","journal-title":"J Comput Biol"},{"key":"2024102618501652300_btae611-B36","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1126\/science.aaf2403","article-title":"Visualization and analysis of gene expression in tissue sections by spatial transcriptomics","volume":"353","author":"St\u00e5hl","year":"2016","journal-title":"Science"},{"key":"2024102618501652300_btae611-B37","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1038\/s41587-020-0739-1","article-title":"Highly sensitive spatial transcriptomics at near-cellular resolution with slide-seqv2","volume":"39","author":"Stickels","year":"2021","journal-title":"Nat Biotechnol"},{"key":"2024102618501652300_btae611-B38","doi-asserted-by":"crossref","first-page":"1888","DOI":"10.1016\/j.cell.2019.05.031","article-title":"Comprehensive integration of single-cell data","volume":"177","author":"Stuart","year":"2019","journal-title":"Cell"},{"key":"2024102618501652300_btae611-B39","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1038\/s41592-019-0701-7","article-title":"Statistical analysis of spatial expression patterns for spatially resolved transcriptomic studies","volume":"17","author":"Sun","year":"2020","journal-title":"Nat Methods"},{"key":"2024102618501652300_btae611-B40","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1038\/nmeth.4636","article-title":"SpatialDE: identification of spatially variable genes","volume":"15","author":"Svensson","year":"2018","journal-title":"Nat Methods"},{"key":"2024102618501652300_btae611-B41","first-page":"231475","article-title":"Molecular markers in cutaneous squamous cell carcinoma","volume":"2011","author":"Tufaro","year":"2011","journal-title":"Int J Surg Oncol"},{"key":"2024102618501652300_btae611-B42","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1038\/s41592-022-01459-6","article-title":"Alignment and integration of spatial transcriptomics data","volume":"19","author":"Zeira","year":"2022","journal-title":"Nat Methods"},{"key":"2024102618501652300_btae611-B43","doi-asserted-by":"crossref","first-page":"e103","DOI":"10.1093\/nar\/gkad801","article-title":"STAMarker: determining spatial domain-specific variable genes with saliency maps in deep learning","volume":"51","author":"Zhang","year":"2023","journal-title":"Nucleic Acids Res"},{"key":"2024102618501652300_btae611-B44","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1038\/s41587-021-00935-2","article-title":"Spatial transcriptomics at subspot resolution with BayesSpace","volume":"39","author":"Zhao","year":"2021","journal-title":"Nat Biotechnol"},{"key":"2024102618501652300_btae611-B45","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1038\/s43588-023-00528-w","article-title":"Integrating spatial transcriptomics data across different conditions, technologies and developmental stages","volume":"3","author":"Zhou","year":"2023","journal-title":"Nat Comput Sci"},{"key":"2024102618501652300_btae611-B46","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1186\/s13059-021-02404-0","article-title":"SPARK-X: non-parametric modeling enables scalable and robust detection of spatial expression patterns for large spatial transcriptomic studies","volume":"22","author":"Zhu","year":"2021","journal-title":"Genome Biol"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/advance-article-pdf\/doi\/10.1093\/bioinformatics\/btae611\/59748034\/btae611.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/40\/10\/btae611\/60105498\/btae611.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/40\/10\/btae611\/60105498\/btae611.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T14:51:15Z","timestamp":1729954275000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/doi\/10.1093\/bioinformatics\/btae611\/7821185"}},"subtitle":[],"editor":[{"given":"Anthony","family":"Mathelier","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2024,10,1]]},"references-count":46,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2024,10,1]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btae611","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.06.10.598190","asserted-by":"object"}]},"ISSN":["1367-4811"],"issn-type":[{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,10]]},"published":{"date-parts":[[2024,10,1]]},"article-number":"btae611"}}