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Dealing with dynamic data trajectories Huub Hoefsloot

Biosystems Data Analysis group University of Amsterdam. Dealing with dynamic data trajectories Huub Hoefsloot. www.bdagroup.nl. Outline. Univariate approach Measuring a single metabolite Multivariate example Principal Component Analysis ANOVA Simultaneous Component Analysis

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Dealing with dynamic data trajectories Huub Hoefsloot

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  1. Biosystems Data Analysis group University of Amsterdam Dealing with dynamic data trajectoriesHuub Hoefsloot www.bdagroup.nl

  2. Outline • Univariate approach Measuring a single metabolite • Multivariate example Principal Component Analysis ANOVA Simultaneous Component Analysis • Using knowledge Looking only at interesting metabolites • Validation Permutations

  3. Univariate time series analysis • Do two groups of graphs differ?

  4. Modeling the time behavior Regression coefficients T-test model Y=at P =1.8605e-004

  5. Other systems • Fitted values in differential equations • Parameters in state space models • Clinical derived parameters • Anything goes 

  6. Multiple testing • Use a multiple testing correction Univariate: P =1.8605e-004 Bonferroni correction, 1000 variables: P =1.8605e-001

  7. 3.0275 2.055 Rat 211 Rat 111 Rat 311 Rat 112 Rat 212 Rat 312 Rat 113 Rat 213 Rat 313 3.285 5.38 3.0475 3.675 3.7525 2.7175 6 hours 2.075 2.93 24 hours 10 8 6 4 2 0 48 hours chemical shift (ppm) Metabolomics example: setup Rats are given bromobenzene that affects the liver NMR spectroscopy of urine Visual inspection of the livers Time: 6, 24 and 48 hours Groups: 3 doses of BB Vehicle group, Control group Jansen et al; Bioinformatics 21 (2005) 3043-3048

  8. Toxicogenomics example: resulting data 330 Metabolomics NMR 45 • 45 = 5 (treatments) x 3 (time points) x 3 (rats) • highly structured data • few samples, many measurements

  9. Toxicogenomics example: variation

  10. J rat1 (time 1 dose 1) i11=1 ... ... t=1 rat3 (time 1 dose 1) i11=3 d=1 t=2 t=1 d=2 t=2 Toxicogenomics example: PCA

  11. Toxicogenomics example: PCA control 6 0.4 control 24 control 48 0.3 vehicle 6 vehicle 24 vehicle 48 0.2 low 6 low 24 0.1 low 48 medium 6 medium 24 0 PC 2 ( 26.3 % of variation explained) medium 48 high 6 -0.1 high 24 high 48 -0.2 -0.3 -0.4 -0.2 0 0.2 0.4 0.6 PC 1 ( 44.6 % of variation explained)

  12. control 6 0.4 control 24 ? control 48 0.3 vehicle 6 vehicle 24 vehicle 48 0.2 low 6 low 24 0.1 low 48 medium 6 medium 24 0 PC 2 ( 26.3657 % of variation explained) medium 48 high 6 -0.1 high 24 high 48 -0.2 -0.3 -0.4 -0.2 0 0.2 0.4 0.6 PC 1 ( 44.6108 % of variation explained) Toxicogenomics example: PCA (dose)

  13. 6 hrs control 6 0.4 control 24 control 48 0.3 vehicle 6 vehicle 24 vehicle 48 0.2 low 6 low 24 0.1 low 48 medium 6 PC 2 ( 26.3657 % of variation explained) medium 24 0 Low+med 24+48 medium 48 high 6 -0.1 high 24 high 48 -0.2 -0.3 -0.4 -0.2 0 0.2 0.4 0.6 PC 1 ( 44.6108 % of variation explained) Toxicogenomics example: PCA (time) 6 hrs Low+med 24+48

  14. i = animal j = chemical shift t = time d = dose group Toxicogenomics example: ANOVA model ANOVA model: Under usual constraints ( ): Collect terms in matrices (ITDxJ)

  15. Other ANOVA’s • Expressed with respect to the control • Subtract the mean of the control everywhere • Paired design • Subtract the mean of every person from the measurement on that person

  16. A = time B = dose C = individual Toxicogenomics example: in matrices Collect terms in matrices (ITDxJ): Column spaces of XM, XA, XB, XAB and XABC mutually orthogonal Consequences: 1. 2.Easy algorithms

  17. Toxicogenomics example: ASCA Time individual Treatment& interaction

  18. + + Toxicogenomics example: results Data = 100% = 25% + 57% + 18%

  19. “Dose” level control vehicle low medium high Toxicogenomics example: results Time trajectories (71%) 0.5 0.4 0.3 0.2 Scores 0.1 0 -0.1 -0.2 6 24 48 Time (Hours)

  20. “Dose” level Toxicogenomics example: results Metabolites Acetic acid TMAO …

  21. Only PCA? pls plsda N-way pls N-way plsda parafac Anything you would do on X is possible

  22. Using Knowledge • Considering only metabolites that follow a predefined model • Looking for similar profiles as the product. Peters et al. Trend analysis of time-series data: A novel method for untargeted metabolite discovery, Analytica Chimica Acta 663 (2010) 98–104 Rubingh et al. Analyzing Longitudinal MicrobialMetabolomics Data, Journal of Proteome Research2009, 8, 4319–4327 4319

  23. Validation • I like permutation tests • Vis et al. Statistical validation of megavariate effects in ASCA, BMC BIOINFORMATICS, Volume 8,  Article 322,  AUG 30 2007

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