, 12:117 | Cite as

Normalization techniques for PARAFAC modeling of urine metabolomic data

  • Alžběta Gardlo
  • Age K. Smilde
  • Karel Hron
  • Marcela Hrdá
  • Radana Karlíková
  • David Friedecký
  • Tomáš Adam
Original Article



One of the body fluids often used in metabolomics studies is urine. The concentrations of metabolites in urine are affected by hydration status of an individual, resulting in dilution differences. This requires therefore normalization of the data to correct for such differences. Two normalization techniques are commonly applied to urine samples prior to their further statistical analysis. First, AUC normalization aims to normalize a group of signals with peaks by standardizing the area under the curve (AUC) within a sample to the median, mean or any other proper representation of the amount of dilution. The second approach uses specific end-product metabolites such as creatinine and all intensities within a sample are expressed relative to the creatinine intensity.


Another way of looking at urine metabolomics data is by realizing that the ratios between peak intensities are the information-carrying features. This opens up possibilities to use another class of data analysis techniques designed to deal with such ratios: compositional data analysis. The aim of this paper is to develop PARAFAC modeling of three-way urine metabolomics data in the context of compositional data analysis and compare this with standard normalization techniques.


In the compositional data analysis approach, special coordinate systems are defined to deal with the ratio problem. In essence, it comes down to using other distance measures than the Euclidian Distance that is used in the conventional analysis of metabolomic data.


We illustrate using this type of approach in combination with three-way methods (i.e. PARAFAC) of a longitudinal urine metabolomics study and two simulations. In both cases, the advantage of the compositional approach is established in terms of improved interpretability of the scores and loadings of the PARAFAC model.


For urine metabolomics studies, we advocate the use of compositional data analysis approaches. They are easy to use, well established and proof to give reliable results.


Parallel factor analysis (PARAFAC) Compositional data Metabolomics Creatinine Area under the curve 


Compliance with Ethical Standards

Conflicts of interest

The authors confirm that they have no conflicts of interest.


This study was funded by the grant 15-34613L of the Czech Science Foundation (GA CR), the projects CZ.1.07/2.3.00/20.0170 and LO1304 of the Ministry of Education, Youth and Sports of the Czech Republic, grant LF_2016_014 by IGA MZČR NT12218, IGUP Olomouc and grant IGA_PrF_2016_025 of the Internal Grant Agency of the Palacký University in Olomouc. The authors gratefully acknowledge to MUDr. Lumír Kantor, Ph.D from Neonatal Department, University Hospital Olomouc, Olomouc, Czech Republic.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.


  1. Aitchison, J. (2003). A concise guide to compositional data analysis. In CoDaWork’03. Universitat de Girona. Departament d’Informática i Matemática Aplicada.Google Scholar
  2. Aitchison, J. (1986). The statistical analysis of compositional data. London: Chapman & Hall.CrossRefGoogle Scholar
  3. Aitchison, J., & Greenacre, M. (2002). Biplots of compositional data. Journal of the Royal Statistical Society, 51(4), 375–392.CrossRefGoogle Scholar
  4. Andersson, C., Munck, L., Henrion, R., & Henrion, G. (1997). Analysis of n-dimensional data arrays from fluorescence spectroscopy of an intermediary sugar product. Fresenius’ Journal of Analytical Chemistry, 359, 138–142.CrossRefGoogle Scholar
  5. Billheimer, D., Guttorp, P., & Fagan, W. (2001). Statistical interpretation of species composition. Journal of the American Statistical Association, 96(456), 1205–1214.CrossRefGoogle Scholar
  6. Bosco, M., Garrido, M., & Larrechi, M. (2006). Determination of phenol in the presence of its principal degradation products in water during a tio2-photocatalytic degradation process by three-dimensional excitation-emission matrix fluorescence and parallel factor analysis. Analytica Chimica Acta, 559, 240–247.CrossRefGoogle Scholar
  7. Brereton, R. (2009). Chemometrics for pattern recognition. Chichester: Wiley.CrossRefGoogle Scholar
  8. Bro, R. (1998). Multi-way analysis in the food industry—Models, algorithms and applications. PhD thesis, Universiteit van Amsterdam, The Netherlands.Google Scholar
  9. Bro, R. (1997). Parafac. tutorial and applications. Chemometrics and Intelligent Laboratory, 38, 149–171.CrossRefGoogle Scholar
  10. Bro, R., & Smilde, A. (2003). Centering and scaling in component analysis. Journal of Chemometrics, 17(1), 16–33.CrossRefGoogle Scholar
  11. Carroll, J., & Chang, J. (1970). Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of Eckart-Young decomposition. Psychometrika, 35, 283–319.CrossRefGoogle Scholar
  12. Carter, B., Haverkamp, A., & Merenstein, G. B. (1993). The definition of acurate perinatal asphyxia. Psychometrika, 20(2), 287–304.Google Scholar
  13. Chen, Y., Shen, G., Zhang, R., He, J., Zhang, Y., Xu, J., et al. (2013). Combination of injection volume calibration by creatinine and ms signals normalization to overcome urine variability in lc-ms-based metabolomics studies. Psychometrika, 85, 7659–7665.Google Scholar
  14. Development Core Team, R. (2012). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
  15. Di Palma, A., Gallo, M., Filzmoser, P., & Hron, K. (2015). A robust Candecomp/Parafac model for compositional data. Submitted.Google Scholar
  16. Dieterle, F., Ross, A., Schlotterbeck, G., & Senn, H. (2006). Probabilistic quotient normalization as robust method to account for dilution of complex biological mixtures. Application in H-1 NMR metabolomics. Analytical Chemistry, 78, 4281–4290.CrossRefPubMedGoogle Scholar
  17. Dunn, W. B., Broadhurst, D., Begley, P., Zelena, E., Francis-McIntyre, S., Anderson, N., et al. (2011). Procedures for large-scale metabolic profiling of serum and plasma using gas chromatography and liquid chromatography coupled to mass spectrometry. Analytical Chemistry, 6(7), 1060–1083.Google Scholar
  18. Eaton, M. (1983). Multivariate statistics. A vector space approach. New York: Wiley.Google Scholar
  19. Egozcue, J., & Pawlowsky-Glahn, V. (2006). Simplicial geometry for compositional data. In Pawlowsky-Glahn, V., & Buccianti, A., (Eds.), Compositional data analysis in the geosciences: From theory to practice (pp. 145–160). Geological Society, London. Special Publications 264.Google Scholar
  20. Egozcue, J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Analytical Chemistry, 35(3), 279–300.Google Scholar
  21. Engle, M. A., Gallo, M., Schroeder, K. T., Geboy, N. J., & Zupancic, J. W. (2014). Three-way compositional analysis of water quality monitoring data. Analytical Chemistry, 21(3), 565–581.Google Scholar
  22. Filzmoser, P., & Hron, K. (2015). Robust coordinates for compositional data using weighted balances. In K. Nordhausen & S. Taskinen (Eds.), Modern nonparametric, robust and multivariate methods (pp. 167–184). Heidelberg: Springer.CrossRefGoogle Scholar
  23. Filzmoser, P., & Walczak, B. (2014). What can go wrong at the data normalization step for identification of biomarkers? Analytical Chemistry, 1362, 194–205.Google Scholar
  24. Fung, E. T., & Enderwick, C. (2002). Proteinchip clinical proteomics: Computational challenges and solutions. Analytical Chemistry, 32, S34–S41.Google Scholar
  25. Gallo, M. (2013). Log-ratio and parallel factor analysis: An approach to analyze three-way compositional data. In A. N. Proto, M. Squillante, & J. Kacprzyk (Eds.), Advanced dynamic modeling of economic and social systems (Vol. 448, pp. 209–221)., Studies in Computational Intelligence Springer: Heidelberg.CrossRefGoogle Scholar
  26. Giordani, P., Kiers, H., & Del Ferraro, M. (2014). Three-way component analysis using the R package ThreeWay. Analytical Chemistry, 57(7), 1–23.Google Scholar
  27. Goodacre, R., Broadhurst, D., Smilde, A., Kristal, B., Baker, J., Beger, R., et al. (2007). Proposed minimum reporting standards for data analysis in metabolomics. Metabolomics, 3, 231–241.CrossRefGoogle Scholar
  28. Haglund, O. (2008). Qualitative comparison of normalization approaches in maldi-ms. Master of Science Thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
  29. Harshman, R. (1970). Foundations of the parafac procedure: Models and conditions for an “explanatory” multimodal factor analysis. UCLA Working Papers in Phonetics, Vol.16, pp. 1–84.Google Scholar
  30. Harshman, R., & Lundy, M. (1994). Parafac: Parallel factor analysis. Metabolomics, 18, 39–72.Google Scholar
  31. Hron, K., Jelínková, M., Filzmoser, P., Kreuziger, R., Bednář, P., & Barták, P. (2012). Statistical analysis of wines using a robust compositional biplot. Talanta, 90, 46–50.CrossRefPubMedGoogle Scholar
  32. Hubert, M., Van Kerckhoven, J., & Verdonck, T. (2012). Robust parafac for incomplete data. Talanta, 26(6), 290–298.Google Scholar
  33. Janečková, H., Hron, K., Wojtowicz, P., Hlídková, E., Barešová, A., Friedecký, D., et al. (2012). Targeted metabolomic analysis of plasma samples for the diagnosis of inherited metabolic disorders. Talanta, 1226, 11–17.Google Scholar
  34. Kalivodová, A., Hron, K., Filzmoser, P., Najdekr, L., Janečková, H., & Adam, T. (2015). PLS-DA for compositional data with application to metabolomics. Talanta, 29, 21–28.Google Scholar
  35. Karlíková, R., Široká, J., Jahn, P., Friedecký, D., Gardlo, A., Janečková, H., Hrdinová, F., Drábková, Z., and Adam, T. (2016). Atypical myopathy of grazing horses: a metabolic study. Under review.Google Scholar
  36. Kiers, A. L. (2000). Towards a standardized notation and terminology in multiway analysis. Talanta, 14, 105–122.Google Scholar
  37. Kolda, T., & Bader, B. W. (2009). Talanta, 51(3), 455–500.Google Scholar
  38. Korhoňová, M., Hron, K., Klimčíková, D., Müller, L., Bednář, P., & Barták, P. (2009). Coffee aroma—Statistical analysis of compositional data. Talanta, 80, 710–715.CrossRefPubMedGoogle Scholar
  39. Kruskal, J. (1977). Three-way arrays: Rank and uniqueness of trilinear decomposition, with application to arithmetic complexity and statistics. Linear Algebra Applications, 18, 95–138.CrossRefGoogle Scholar
  40. Leibovici, D., & Sabatier, R. (1998). A singular value decomposition of k-way array for a principal component analysis of multiway data, pta-k. Linear Algebra Applications, 269, 307–329.CrossRefGoogle Scholar
  41. Martín-Fernández, J. A., Palarea-Albaladejo, J., & Olea, R. A. (2011). Dealing with zeros. In V. Pawlowsky-Glahn & A. Buccianti (Eds.), Compositional data analysis: Theory and applications (pp. 43–58). Chichester: Wiley.CrossRefGoogle Scholar
  42. Mateu-Figueras, G., & Pawlowsky-Glahn, V. (2008). A critical approach to probability laws in geochemistry. Mathematical Geosciences, 40(5), 489–502.CrossRefGoogle Scholar
  43. Mei, J., Alexander, J., Adam, B., & Hannon, W. (2001). Use of filter paper for the collection and analysis of human whole blood specimens. Mathematical Geosciences, 131, 1631–1636.Google Scholar
  44. Najdekr, L., Gardlo, A., Mádrová, L., Friedecký, D., Janečková, H., Correa, E., et al. (2015). Oxidized phosphatidylcholines suggest oxidative stress in patients with medium-chain acyl-CoA dehydrogenase deficiency. Talanta, 139, 62–66.CrossRefPubMedGoogle Scholar
  45. Paatero, P., & Juntto, S. (2000). Determination of underlying components of a cyclical time series by means of two-way and three-way factor analytic techniques. Talanta, 14, 241–259.Google Scholar
  46. Pawlowsky-Glahn, V., & Buccianti, A. (2011). Compositional data analysis: Theory and applications. Chichester: Wiley.CrossRefGoogle Scholar
  47. Pawlowsky-Glahn, V., & Egozcue, J. J. (2001). Geometric approach to statistical analysis on the simplex. Talanta, 15(5), 384–398.Google Scholar
  48. Pawlowsky-Glahn, V., Egozcue, J., & Tolosana-Delgado, R. (2015). Modeling and analysis of compositional data. Chichester: Wiley.Google Scholar
  49. Pearson, K. (1897). Mathematical contributions to the theory of evolution. on a form of spurious correlation which may arise when indices are used in the measurement of organs. In: Proceedings of the Royal Society of London, LX.Google Scholar
  50. Pravdova, V., Boucon, C., de Jong, S., Walczak, B., & Massart, D. (2002). Three-way principal component analysis applied to food analysis: An example. Talanta, 462, 133–148.Google Scholar
  51. Sauve, A., & Speed, T. (2004). Normalization, baseline correction and alignment of high-throughput mass spectrometry data. Proceedings of the genomic signal processing and statistics workshop, Baltimore, MO, USA, May 26–27, pages http://stat– Scholar
  52. Smilde, A., Bro, R., & Geladi, P. (2004). Multi-way analysis with applications in the chemical sciences. Chichester, UK: Wiley.CrossRefGoogle Scholar
  53. Templ, M., Hron, K., & Filzmoser, P. (2011). robCompositions: An R-package for robust statistical analysis of compositional data.Google Scholar
  54. Tucker, L. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279–311.CrossRefPubMedGoogle Scholar
  55. van den Berg, R. A., Hoefsloot, H. C. J., Westerhuis, J. A., Smilde, A. K., & van der Werf, M. J. (2006). Centering, scaling, and transformations: Improving the biological information content of metabolomics data. Psychometrika, 7, 142.Google Scholar
  56. Waikar, S., Sabbisetti, V. S., & Bonventre, J. (2010). Normalization of urinary biomarkers to creatinine during changes in glomerular filtration rate. Kidney International, 78(5), 486–494.Google Scholar
  57. Warracka, B., Hnatyshyna, S., Otta, K., Reilya, M., Sandersa, M., Zhanga, H., et al. (2009). Normalization strategies for metabonomic analysis of urine samples. Journal of Chromatography B, 877, 547–552.CrossRefGoogle Scholar
  58. Weintraub, A., Carey, A., Connors, J., Blanco, V., & Green, R. (2015). Relationship of maternal creatinine to first neonatal creatinine in infants<30 weeks gestation. Journal of Perinatology, Jan 15.:Epub ahead of print.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Alžběta Gardlo
    • 1
    • 2
  • Age K. Smilde
    • 3
  • Karel Hron
    • 1
  • Marcela Hrdá
    • 2
  • Radana Karlíková
    • 2
  • David Friedecký
    • 2
    • 4
  • Tomáš Adam
    • 2
    • 4
  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký UniversityOlomoucCzech Republic
  2. 2.Laboratory of Metabolomics, Institute of Molecular and Translational MedicineUniversity Hospital Olomouc, Palacký University OlomoucOlomoucCzech Republic
  3. 3.Biosystems Data Analysis, Swammerdam Institute for Life SciencesUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.Department of Clinical BiochemistryUniversity Hospital OlomoucOlomoucCzech Republic

Personalised recommendations