{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T16:41:39Z","timestamp":1775580099401,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010108","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000}}],"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T00:00:00Z","timestamp":1657065600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"Determining associations between intestinal bacteria and continuously measured physiological outcomes is important for understanding the bacteria-host relationship but is not straightforward since abundance data (compositional data) are not normally distributed. To address this issue, we developed a fully Bayesian linear regression model (BRACoD;B<\/jats:underline>ayesianR<\/jats:underline>egressionA<\/jats:underline>nalysis ofCo<\/jats:underline>mpositionalD<\/jats:underline>ata) with physiological measurements (continuous data) as a function of a matrix of relative bacterial abundances. Bacteria can be classified as operational taxonomic units or by taxonomy (genus, family, etc.). Bacteria associated with the physiological measurement were identified using a Bayesian variable selection method: Stochastic Search Variable Selection. The output is a list of inclusion probabilities (p<\/mml:mi><\/mml:mrow>^<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) and coefficients that indicate the strength of the association (\u03b2<\/mml:mi><\/mml:mrow>^<\/mml:mo><\/mml:mover><\/mml:mrow>i<\/mml:mi>n<\/mml:mi>c<\/mml:mi>l<\/mml:mi>u<\/mml:mi>d<\/mml:mi>e<\/mml:mi>d<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) for each bacterial taxa. Tests with simulated communities showed that adopting a cut point value ofp<\/mml:mi><\/mml:mrow>^<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u2265 0.3 for identifying included bacteria optimized the true positive rate (TPR) while maintaining a false positive rate (FPR) of \u2264 5%. At this point, the chances of identifying non-contributing bacteria were low and all well-established contributors were included. Comparison with other methods showed that BRACoD (atp<\/mml:mi><\/mml:mrow>^<\/mml:mo><\/mml:mover><\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u2265 0.3) had higher precision and a higher TPR than a commonly used center log transformed LASSO procedure (clr-LASSO) as well as higher TPR than an off-the-shelf Spike and Slab method after center log transformation (clr-SS). BRACoD was also less likely to include non-contributing bacteria that merely correlate with contributing bacteria. Analysis of a rat microbiome experiment identified 47 operational taxonomic units that contributed to fecal butyrate levels. Of these, 31 were positively and 16 negatively associated with butyrate. Consistent with their known role in butyrate metabolism, most of these fell within the Lachnospiraceae and Ruminococcaceae. We conclude that BRACoD provides a more precise and accurate method for determining bacteria associated with a continuous physiological outcome compared to clr-LASSO. It is more sensitive than a generalized clr-SS algorithm, although it has a higher FPR. Its ability to distinguish genuine contributors from correlated bacteria makes it better suited to discriminating bacteria that directly contribute to an outcome. The algorithm corrects for the distortions arising from compositional data making it appropriate for analysis of microbiome data.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010108","type":"journal-article","created":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T17:47:46Z","timestamp":1657129666000},"page":"e1010108","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Bayesian method for identifying associations between response variables and bacterial community composition"],"prefix":"10.1371","volume":"18","author":[{"given":"Adrian","family":"Verster","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0763-1214","authenticated-orcid":true,"given":"Nicholas","family":"Petronella","sequence":"additional","affiliation":[]},{"given":"Judy","family":"Green","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3594-1380","authenticated-orcid":true,"given":"Fernando","family":"Matias","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1169-6221","authenticated-orcid":true,"given":"Stephen P. 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Tibshirani","year":"1996","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)."},{"key":"pcbi.1010108.ref029","doi-asserted-by":"crossref","first-page":"e55","DOI":"10.7717\/peerj-cs.55","article-title":"Probabilistic programming in Python using PyMC3","volume":"2","author":"J Salvatier","year":"2016","journal-title":"PeerJ Computer Science"},{"issue":"1","key":"pcbi.1010108.ref030","first-page":"1593","article-title":"The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo.","volume":"15","author":"MD Hoffman","year":"2014","journal-title":"J Mach Learn Res"},{"issue":"2","key":"pcbi.1010108.ref031","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s11222-011-9299-z","article-title":"Sequential Monte Carlo on large binary sampling spaces","volume":"23","author":"C Sch\u00e4fer","year":"2013","journal-title":"Statistics and Computing"},{"issue":"5","key":"pcbi.1010108.ref032","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1093\/jn\/127.5.717","article-title":"Acarbose enhances human colonic butyrate production","volume":"127","author":"GA Weaver","year":"1997","journal-title":"J Nutr"},{"issue":"1","key":"pcbi.1010108.ref033","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1139\/m92-010","article-title":"A general method of isolating high molecular weight DNA from methanogenic archaea (archaebacteria).","volume":"38","author":"KF Jarrell","year":"1992","journal-title":"Can J Microbiol"},{"issue":"17","key":"pcbi.1010108.ref034","doi-asserted-by":"crossref","first-page":"5112","DOI":"10.1128\/AEM.01043-13","article-title":"Development of a dual-index sequencing strategy and curation pipeline for analyzing amplicon sequence data on the MiSeq Illumina sequencing platform","volume":"79","author":"JJ Kozich","year":"2013","journal-title":"Appl Environ 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Tang","year":"2019","journal-title":"Biostatistics"},{"issue":"1","key":"pcbi.1010108.ref038","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1080\/02664763.2018.1454894","article-title":"Clustering transformed compositional data using K-means, with applications in gene expression and bicycle sharing system data","volume":"46","author":"A Godichon-Baggioni","year":"2018","journal-title":"Journal of Applied Statistics"},{"issue":"10","key":"pcbi.1010108.ref039","doi-asserted-by":"crossref","first-page":"5186","DOI":"10.1128\/AEM.68.10.5186-5190.2002","article-title":"Acetate utilization and butyryl coenzyme A (CoA):acetate-CoA transferase in butyrate-producing bacteria from the human large intestine","volume":"68","author":"SH Duncan","year":"2002","journal-title":"Appl Environ Microbiol"},{"issue":"5","key":"pcbi.1010108.ref040","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1128\/aem.62.5.1589-1592.1996","article-title":"Pathways of acetate, propionate, and 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