Normalization techniques for PARAFAC modeling of urine metabolomic data
- 510 Downloads
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.
KeywordsParallel 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.
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.
- Aitchison, J. (2003). A concise guide to compositional data analysis. In CoDaWork’03. Universitat de Girona. Departament d’Informática i Matemática Aplicada.Google Scholar
- 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
- Bro, R. (1998). Multi-way analysis in the food industry—Models, algorithms and applications. PhD thesis, Universiteit van Amsterdam, The Netherlands.Google Scholar
- Carter, B., Haverkamp, A., & Merenstein, G. B. (1993). The definition of acurate perinatal asphyxia. Psychometrika, 20(2), 287–304.Google Scholar
- 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
- Development Core Team, R. (2012). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
- Di Palma, A., Gallo, M., Filzmoser, P., & Hron, K. (2015). A robust Candecomp/Parafac model for compositional data. Submitted.Google Scholar
- 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
- Eaton, M. (1983). Multivariate statistics. A vector space approach. New York: Wiley.Google Scholar
- 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
- 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
- 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
- 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
- Fung, E. T., & Enderwick, C. (2002). Proteinchip clinical proteomics: Computational challenges and solutions. Analytical Chemistry, 32, S34–S41.Google Scholar
- 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
- 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
- Haglund, O. (2008). Qualitative comparison of normalization approaches in maldi-ms. Master of Science Thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
- 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
- Harshman, R., & Lundy, M. (1994). Parafac: Parallel factor analysis. Metabolomics, 18, 39–72.Google Scholar
- Hubert, M., Van Kerckhoven, J., & Verdonck, T. (2012). Robust parafac for incomplete data. Talanta, 26(6), 290–298.Google Scholar
- 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
- 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
- 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
- Kiers, A. L. (2000). Towards a standardized notation and terminology in multiway analysis. Talanta, 14, 105–122.Google Scholar
- Kolda, T., & Bader, B. W. (2009). Talanta, 51(3), 455–500.Google Scholar
- 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
- 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
- Pawlowsky-Glahn, V., & Egozcue, J. J. (2001). Geometric approach to statistical analysis on the simplex. Talanta, 15(5), 384–398.Google Scholar
- Pawlowsky-Glahn, V., Egozcue, J., & Tolosana-Delgado, R. (2015). Modeling and analysis of compositional data. Chichester: Wiley.Google Scholar
- 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
- 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
- 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–www.berkeley.edu/users/terry/Group/publications/Final2Gensips2004Sauve.pdf.Google Scholar
- Templ, M., Hron, K., & Filzmoser, P. (2011). robCompositions: An R-package for robust statistical analysis of compositional data.Google Scholar
- 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
- 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
- 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