{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T16:29:34Z","timestamp":1762100974767,"version":"3.37.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Background<\/jats:title><jats:p>Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS) models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA) for modelling and analysis of short time-series data.<\/jats:p><\/jats:sec>","DOI":"10.1186\/1471-2105-9-105","type":"journal-article","created":{"date-parts":[[2009,8,4]],"date-time":"2009-08-04T15:07:57Z","timestamp":1249398477000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Piecewise multivariate modelling of sequential metabolic profiling data"],"prefix":"10.1186","volume":"9","author":[{"given":"Mattias","family":"Rantalainen","sequence":"first","affiliation":[]},{"given":"Olivier","family":"Cloarec","sequence":"additional","affiliation":[]},{"given":"Timothy MD","family":"Ebbels","sequence":"additional","affiliation":[]},{"given":"Torbj\u00f6rn","family":"Lundstedt","sequence":"additional","affiliation":[]},{"given":"Jeremy K","family":"Nicholson","sequence":"additional","affiliation":[]},{"given":"Elaine","family":"Holmes","sequence":"additional","affiliation":[]},{"given":"Johan","family":"Trygg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,2,19]]},"reference":[{"issue":"2","key":"2090_CR1","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1038\/nrd728","volume":"1","author":"JK Nicholson","year":"2002","unstructured":"Nicholson JK, Connelly J, Lindon JC, Holmes E: Metabonomics: a platform for studying drug toxicity and gene function. Nat Rev Drug Discov 2002, 1(2):153\u2013161. 10.1038\/nrd728","journal-title":"Nat Rev Drug Discov"},{"issue":"1-2","key":"2090_CR2","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1023\/A:1013713905833","volume":"48","author":"O Fiehn","year":"2002","unstructured":"Fiehn O: Metabolomics--the link between genotypes and phenotypes. Plant Mol Biol 2002, 48(1\u20132):155\u2013171. 10.1023\/A:1013713905833","journal-title":"Plant Mol Biol"},{"key":"2090_CR3","volume-title":"PLoS Med","author":"E Holmes","year":"2006","unstructured":"Holmes E, Tsang TM, Huang JT, Leweke FM, Koethe D, Gerth CW, Nolden BM, Gross S, Schreiber D, Nicholson JK, Bahn S: Metabolic Profiling of CSF: Evidence That Early Intervention May Impact on Disease Progression and Outcome in Schizophrenia. PLoS Med 2006., 3(8):"},{"issue":"1","key":"2090_CR4","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1002\/nbm.918","volume":"18","author":"VG Dunne","year":"2005","unstructured":"Dunne VG, Bhattachayya S, Besser M, Rae C, Griffin JL: Metabolites from cerebrospinal fluid in aneurysmal subarachnoid haemorrhage correlate with vasospasm and clinical outcome: a pattern-recognition 1H NMR study. NMR Biomed 2005, 18(1):24\u201333. 10.1002\/nbm.918","journal-title":"NMR Biomed"},{"issue":"5","key":"2090_CR5","doi-asserted-by":"publisher","first-page":"782","DOI":"10.1002\/ijc.20651","volume":"113","author":"K Odunsi","year":"2005","unstructured":"Odunsi K, Wollman RM, Ambrosone CB, Hutson A, McCann SE, Tammela J, Geisler JP, Miller G, Sellers T, Cliby W, Qian F, Keitz B, Intengan M, Lele S, Alderfer JL: Detection of epithelial ovarian cancer using 1H-NMR-based metabonomics. Int J Cancer 2005, 113(5):782\u2013788. 10.1002\/ijc.20651","journal-title":"Int J Cancer"},{"issue":"2","key":"2090_CR6","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s002040050144","volume":"69","author":"ML Anthony","year":"1994","unstructured":"Anthony ML, Beddell CR, Lindon JC, Nicholson JK: Studies on the comparative toxicity of S-(1,2-dichlorovinyl)-L-cysteine, S-(1,2-dichlorovinyl)-L-homocysteine and 1,1,2-trichloro-3,3,3-trifluoro-1-propene in the Fischer 344 rat. Arch Toxicol 1994, 69(2):99\u2013110. 10.1007\/s002040050144","journal-title":"Arch Toxicol"},{"issue":"8","key":"2090_CR7","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1021\/tx000231j","volume":"14","author":"AW Nicholls","year":"2001","unstructured":"Nicholls AW, Holmes E, Lindon JC, Shockcor JP, Farrant RD, Haselden JN, Damment SJ, Waterfield CJ, Nicholson JK: Metabonomic investigations into hydrazine toxicity in the rat. Chem Res Toxicol 2001, 14(8):975\u2013987. 10.1021\/tx000231j","journal-title":"Chem Res Toxicol"},{"issue":"3","key":"2090_CR8","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1002\/nbm.935","volume":"18","author":"ME Bollard","year":"2005","unstructured":"Bollard ME, Stanley EG, Lindon JC, Nicholson JK, Holmes E: NMR-based metabonomic approaches for evaluating physiological influences on biofluid composition. NMR Biomed 2005, 18(3):143\u2013162. 10.1002\/nbm.935","journal-title":"NMR Biomed"},{"issue":"11","key":"2090_CR9","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1038\/81137","volume":"18","author":"O Fiehn","year":"2000","unstructured":"Fiehn O, Kopka J, Dormann P, Altmann T, Trethewey RN, Willmitzer L: Metabolite profiling for plant functional genomics. Nat Biotechnol 2000, 18(11):1157\u20131161. 10.1038\/81137","journal-title":"Nat Biotechnol"},{"issue":"1-2","key":"2090_CR10","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0003-2670(03)00121-1","volume":"490","author":"T Ebbels","year":"2003","unstructured":"Ebbels T, Keun H, Beckonert O, Antti H, Bollard M, Holmes E, Lindon J, Nicholson J: Toxicity classification from metabonomic data using a density superposition approach: `CLOUDS'. Analytica Chimica Acta 2003, 490(1\u20132):109\u2013122. 10.1016\/S0003-2670(03)00121-1","journal-title":"Analytica Chimica Acta"},{"issue":"2","key":"2090_CR11","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1021\/pr060594q","volume":"6","author":"J Trygg","year":"2007","unstructured":"Trygg J, Holmes E, Lundstedt T: Chemometrics in metabonomics. J Proteome Res 2007, 6(2):469\u2013479. 10.1021\/pr060594q","journal-title":"J Proteome Res"},{"key":"2090_CR12","first-page":"559\u2013572","volume-title":"Phil Mag","author":"K Pearson","year":"1901","unstructured":"Pearson K: On lines and planes of closest fit to systems of points in space. Phil Mag 1901, 559\u2013572."},{"issue":"8","key":"2090_CR13","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1080\/00498250500297940","volume":"35","author":"J Azmi","year":"2005","unstructured":"Azmi J, Griffin JL, Shore RF, Holmes E, Nicholson JK: Chemometric analysis of biofluids following toxicant induced hepatotoxicity: a metabonomic approach to distinguish the effects of 1-naphthylisothiocyanate from its products. Xenobiotica 2005, 35(8):839\u2013852. 10.1080\/00498250500297940","journal-title":"Xenobiotica"},{"issue":"12","key":"2090_CR14","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1039\/b208254n","volume":"127","author":"E Holmes","year":"2002","unstructured":"Holmes E, Antti H: Chemometric contributions to the evolution of metabonomics: mathematical solutions to characterising and interpreting complex biological NMR spectra. Analyst 2002, 127(12):1549\u20131557. 10.1039\/b208254n","journal-title":"Analyst"},{"issue":"2","key":"2090_CR15","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1039\/b500852b","volume":"1","author":"RE Williams","year":"2005","unstructured":"Williams RE, Lenz EM, Lowden JS, Rantalainen M, Wilson ID: The metabonomics of aging and development in the rat: an investigation into the effect of age on the profile of endogenous metabolites in the urine of male rats using 1H NMR and HPLC-TOF MS. Mol Biosyst 2005, 1(2):166\u2013175. 10.1039\/b500852b","journal-title":"Mol Biosyst"},{"issue":"5","key":"2090_CR16","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1016\/S0026-895X(25)09200-4","volume":"42","author":"E Holmes","year":"1992","unstructured":"Holmes E, Bonner FW, Sweatman BC, Lindon JC, Beddell CR, Rahr E, Nicholson JK: Nuclear magnetic resonance spectroscopy and pattern recognition analysis of the biochemical processes associated with the progression of and recovery from nephrotoxic lesions in the rat induced by mercury(II) chloride and 2-bromoethanamine. Mol Pharmacol 1992, 42(5):922\u2013930.","journal-title":"Mol Pharmacol"},{"issue":"4","key":"2090_CR17","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1021\/tx9700679","volume":"11","author":"BM Beckwith-Hall","year":"1998","unstructured":"Beckwith-Hall BM, Nicholson JK, Nicholls AW, Foxall PJ, Lindon JC, Connor SC, Abdi M, Connelly J, Holmes E: Nuclear magnetic resonance spectroscopic and principal components analysis investigations into biochemical effects of three model hepatotoxins. Chem Res Toxicol 1998, 11(4):260\u2013272. 10.1021\/tx9700679","journal-title":"Chem Res Toxicol"},{"key":"2090_CR18","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1137\/0905052","volume":"5","author":"S Wold","year":"1984","unstructured":"Wold S, Ruhe A, Wold H, Dunn WJIII: The collinearity problem in linear regression. The partial least squares approach to generalized inverses. SIAM J Sci Stat Comput 1984, 5: 735\u2013743. 10.1137\/0905052","journal-title":"SIAM J Sci Stat Comput"},{"issue":"2","key":"2090_CR19","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1039\/b109430k","volume":"127","author":"J Azmi","year":"2002","unstructured":"Azmi J, Griffin JL, Antti H, Shore RF, Johansson E, Nicholson JK, Holmes E: Metabolic trajectory characterisation of xenobiotic-induced hepatotoxic lesions using statistical batch processing of NMR data. Analyst 2002, 127(2):271\u2013276. 10.1039\/b109430k","journal-title":"Analyst"},{"issue":"3-4","key":"2090_CR20","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1039\/b517195d","volume":"2","author":"RE Williams","year":"2006","unstructured":"Williams RE, Lenz EM, Rantalainen M, Wilson ID: The comparative metabonomics of age-related changes in the urinary composition of male Wistar-derived and Zucker (fa\/fa) obese rats. Mol Biosyst 2006, 2(3\u20134):193\u2013202. 10.1039\/b517195d","journal-title":"Mol Biosyst"},{"key":"2090_CR21","first-page":"1","volume":"16","author":"RA Harshman","year":"1970","unstructured":"Harshman RA: Foundations of the PARAFAC procedure: Models and conditions for an \"explanatory\" multi-modal factor analysis. UCLA Working Papers in Phonetics 1970, 16: 1--84.","journal-title":"UCLA Working Papers in Phonetics"},{"issue":"2","key":"2090_CR22","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/S0169-7439(97)00032-4","volume":"38","author":"R Bro","year":"1997","unstructured":"Bro R: Parafac. Tutorial and Applications. Chemometr Intell Lab Chemometr Intell Lab 1997, 38(2):149\u2013171. 10.1016\/S0169-7439(97)00032-4","journal-title":"Chemometr Intell Lab Chemometr Intell Lab"},{"issue":"13","key":"2090_CR23","doi-asserted-by":"publisher","first-page":"3043","DOI":"10.1093\/bioinformatics\/bti476","volume":"21","author":"AK Smilde","year":"2005","unstructured":"Smilde AK, Jansen JJ, Hoefsloot HC, Lamers RJ, van der Greef J, Timmerman ME: ANOVA-simultaneous component analysis (ASCA): a new tool for analyzing designed metabolomics data. Bioinformatics 2005, 21(13):3043\u20133048. 10.1093\/bioinformatics\/bti476","journal-title":"Bioinformatics"},{"issue":"4","key":"2090_CR24","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1093\/bioinformatics\/btg014","volume":"19","author":"Y Luan","year":"2003","unstructured":"Luan Y, Li H: Clustering of time-course gene expression data using a mixed-effects model with B-splines. Bioinformatics 2003, 19(4):474\u2013482. 10.1093\/bioinformatics\/btg014","journal-title":"Bioinformatics"},{"issue":"3","key":"2090_CR25","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1093\/bib\/4.3.228","volume":"4","author":"SY Kim","year":"2003","unstructured":"Kim SY, Imoto S, Miyano S: Inferring gene networks from time series microarray data using dynamic Bayesian networks. Brief Bioinform 2003, 4(3):228\u2013235. 10.1093\/bib\/4.3.228","journal-title":"Brief Bioinform"},{"key":"2090_CR26","volume-title":"The Handbook of Metabonomics and Metabolomics","author":"J Trygg","year":"2006","unstructured":"Trygg J, Lundstedt T: Chemometrics Techniques for Metabonomics. In The Handbook of Metabonomics and Metabolomics. Edited by: Lindon JCNJKHE. Elsevier; 2006."},{"issue":"1-2","key":"2090_CR27","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/S0169-7439(98)00162-2","volume":"44","author":"S Wold","year":"1998","unstructured":"Wold S, Kettaneh N, Friden H, Holmberg A: Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems 1998, 44(1\u20132):331\u2013340. 10.1016\/S0169-7439(98)00162-2","journal-title":"Chemometrics and Intelligent Laboratory Systems"},{"issue":"16","key":"2090_CR28","doi-asserted-by":"publisher","first-page":"2493","DOI":"10.1093\/bioinformatics\/bth283","volume":"20","author":"Z Bar-Joseph","year":"2004","unstructured":"Bar-Joseph Z: Analyzing time series gene expression data. Bioinformatics 2004, 20(16):2493\u20132503. 10.1093\/bioinformatics\/bth283","journal-title":"Bioinformatics"},{"issue":"3","key":"2090_CR29","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1002\/cem.695","volume":"16","author":"J Trygg","year":"2002","unstructured":"Trygg J, Wold S: Orthogonal projections to latent structures (O-PLS). Journal of Chemometrics 2002, 16(3):119\u2013128. 10.1002\/cem.695","journal-title":"Journal of Chemometrics"},{"issue":"1-2","key":"2090_CR30","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/S0169-7439(98)00109-9","volume":"44","author":"S Wold","year":"1998","unstructured":"Wold S, Antti H, Lindgren F, \u00d6hman J: Orthogonal signal correction of near-infrared spectra. Chemometr Intell Lab Chemometr Intell Lab 1998, 44(1\u20132):175\u2013185. 10.1016\/S0169-7439(98)00109-9","journal-title":"Chemometr Intell Lab Chemometr Intell Lab"},{"issue":"1","key":"2090_CR31","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/S0169-7439(99)00045-3","volume":"50","author":"T Fearn","year":"2000","unstructured":"Fearn T: On orthogonal signal correction. Chemometrics and Intelligent Laboratory Systems 2000, 50(1):47\u201352. 10.1016\/S0169-7439(99)00045-3","journal-title":"Chemometrics and Intelligent Laboratory Systems"},{"issue":"1-2","key":"2090_CR32","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/S0169-7439(00)00113-1","volume":"55","author":"A H\u00f6skuldsson","year":"2001","unstructured":"H\u00f6skuldsson A: Variable and subset selection in PLS regression. Chemometrics and Intelligent Laboratory Systems 2001, 55(1\u20132):23\u201338. 10.1016\/S0169-7439(00)00113-1","journal-title":"Chemometrics and Intelligent Laboratory Systems"},{"issue":"1-2","key":"2090_CR33","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/S0169-7439(98)00112-9","volume":"44","author":"J Sj\u00f6blom","year":"1998","unstructured":"Sj\u00f6blom J, Svensson O, Josefson M, Kullberg H, Wold S: An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra. Chemometrics and Intelligent Laboratory Systems 1998, 44(1\u20132):229\u2013244. 10.1016\/S0169-7439(98)00112-9","journal-title":"Chemometrics and Intelligent Laboratory Systems"},{"issue":"278","key":"2090_CR34","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1080\/01621459.1957.10501378","volume":"52","author":"JE Jackson","year":"1957","unstructured":"Jackson JE: An Application of Multivariate Quality Control to Photographic Processing. Journal of the American Statistical Association 1957, 52(278):186. 10.2307\/2280844","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2090_CR35","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/0031-3203(76)90014-5","volume":"8","author":"S Wold","year":"1976","unstructured":"Wold S: Pattern-Recognition by Means of Disjoint Principal Components Models. Pattern Recognition 1976, 8(3):127\u2013139. 10.1016\/0031-3203(76)90014-5","journal-title":"Pattern Recognition"},{"key":"2090_CR36","first-page":"569","volume-title":"Wiley series in probability and statistics","author":"JE Jackson","year":"2003","unstructured":"Jackson JE: A user's guide to principal components. In Wiley series in probability and statistics. Hoboken, N.J., Wiley; 2003:xvii, 569."},{"issue":"3","key":"2090_CR37","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1080\/00401706.1979.10489779","volume":"21","author":"JE Jackson","year":"1979","unstructured":"Jackson JE, Mudholkar GS: Control Procedures for Residuals Associated with Principal Component Analysis. Technometrics 1979, 21(3):341\u2013349. 10.2307\/1267757","journal-title":"Technometrics"},{"issue":"6","key":"2090_CR38","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1021\/pr050399w","volume":"5","author":"E Holmes","year":"2006","unstructured":"Holmes E, Cloarec O, Nicholson JK: Probing latent biomarker signatures and in vivo pathway activity in experimental disease states via statistical total correlation spectroscopy (STOCSY) of biofluids: application to HgCl2 toxicity. J Proteome Res 2006, 5(6):1313\u20131320. 10.1021\/pr050399w","journal-title":"J Proteome Res"},{"key":"2090_CR39","unstructured":"The R project for statistical computing[http:\/\/www.r-project.org\/]"},{"key":"2090_CR40","volume-title":"Time Series Analysis: Forecasting and Control","author":"J Box","year":"1976","unstructured":"Box J: Time Series Analysis: Forecasting and Control. Holden-Day; 1976."},{"issue":"2","key":"2090_CR41","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1162\/15324430260185556","volume":"2","author":"R Rosipal","year":"2002","unstructured":"Rosipal R, Trejo LJ: Kernel partial least squares regression in Reproducing Kernel Hilbert Space. J Mach Learn Res 2002, 2(2):97\u2013123. 10.1162\/15324430260185556","journal-title":"J Mach Learn Res"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-9-105.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T16:41:37Z","timestamp":1739292097000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-9-105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2,19]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["2090"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-9-105","relation":{},"ISSN":["1471-2105"],"issn-type":[{"type":"electronic","value":"1471-2105"}],"subject":[],"published":{"date-parts":[[2008,2,19]]},"assertion":[{"value":"4 August 2007","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2008","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2008","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"105"}}