{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T06:50:45Z","timestamp":1790837445403,"version":"4.1.0"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2019,12,6]],"date-time":"2019-12-06T00:00:00Z","timestamp":1575590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Metagenomics sequencing is routinely applied to quantify bacterial abundances in microbiome studies, where bacterial composition is estimated based on the sequencing read counts. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which tend to result in inaccurate estimates of bacterial abundance and diversity. This paper takes a multisample approach to estimation of bacterial abundances in order to borrow information across samples and across species. Empirical results from real datasets suggest that the composition matrix over multiple samples is approximately low rank, which motivates a regularized maximum likelihood estimation with a nuclear norm penalty. An efficient optimization algorithm using the generalized accelerated proximal gradient and Euclidean projection onto simplex space is developed. Theoretical upper bounds and the minimax lower bounds of the estimation errors, measured by the Kullback\u2013Leibler divergence and the Frobenius norm, are established. Simulation studies demonstrate that the proposed estimator outperforms the naive estimators. The method is applied to an analysis of a human gut microbiome dataset.<\/jats:p>","DOI":"10.1093\/biomet\/asz062","type":"journal-article","created":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T19:26:11Z","timestamp":1569957971000},"page":"75-92","source":"Crossref","is-referenced-by-count":29,"title":["Multisample estimation of bacterial composition matrices in metagenomics data"],"prefix":"10.1093","volume":"107","author":[{"given":"Yuanpei","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anru","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Wisconsin-Madison, 1300 University Avenue, Madison, Wisconsin 53706, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongzhe","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,12,6]]},"reference":[{"key":"2020021310532348100_B1","volume-title":"The Statistical Analysis of Compositional Data","author":"Aitchison,","year":"2003"},{"key":"2020021310532348100_B2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck,","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"key":"2020021310532348100_B3","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s12532-011-0029-5","article-title":"Templates for convex cone problems with applications to sparse signal recovery","volume":"3","author":"Becker,","year":"2011","journal-title":"Math. Prog. Comput."},{"key":"2020021310532348100_B4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-20192-9","volume-title":"Statistics for High-Dimensional Data: Methods, Theory and Applications","author":"B\u00fchlmann,","year":"2011"},{"key":"2020021310532348100_B5","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","article-title":"A singular value thresholding algorithm for matrix completion","volume":"20","author":"Cai,","year":"2010","journal-title":"SIAM J. Optim."},{"key":"2020021310532348100_B6","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1093\/biomet\/asz012","article-title":"Differential Markov random field analysis with an application to detecting differential microbial community networks","volume":"106","author":"Cai,","year":"2019","journal-title":"Biometrika"},{"key":"2020021310532348100_B7","doi-asserted-by":"crossref","first-page":"4643","DOI":"10.1109\/TSP.2013.2270464","article-title":"Unbiased risk estimates for singular value thresholding and spectral estimators","volume":"61","author":"Cand\u00e8s,","year":"2013","journal-title":"IEEE Trans. Sig. Proces."},{"key":"2020021310532348100_B8","first-page":"1","article-title":"Large covariance estimation for compositional data via composition-adjusted thresholding","volume":"114","author":"Cao,","year":"2018","journal-title":"J. Am. Statist. 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