1 / 18

ASCA: analysis of multivariate data from an experimental design,

ASCA: analysis of multivariate data from an experimental design,. Biosystems Data Analysis group Universiteit van Amsterdam. Contents. ANOVA SCA ASCA Conclusions. ANOVA. different design factors contribute to the variation.

lilac
Download Presentation

ASCA: analysis of multivariate data from an experimental design,

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ASCA: analysis of multivariate data from an experimental design, Biosystems Data Analysis group Universiteit van Amsterdam

  2. Contents • ANOVA • SCA • ASCA • Conclusions

  3. ANOVA • different design factors contribute to the variation For two treatments A and B the total sum of squares can be split into several contributions

  4. Experiment: Rats are given Bromobenzene that affects the liver 3.0275 2.055 3.285 5.38 3.0475 Rats 3.675 3.7525 2.7175 2.075 2.93 Experimental Design: 10 8 6 4 2 0 Time: 6, 24 and 48 hours chemical shift (ppm) Rat 211 Rat 111 Rat 311 Rat 112 Rat 212 Rat 312 Rat 113 Rat 213 Rat 313 Groups: 3 doses of BB 6 hours 24 hours Animals: 3 rats per dose per time point 48 hours Example Measurements: NMR spectroscopy of urine Vehicle group, Control group

  5. 0.7 3.0275 0.6 0.5 0.4 2.055 0.3 3.285 5.38 3.0475 0.2 3.675 3.7525 2.7175 2.075 2.93 0.1 0 10 8 6 4 2 0 chemical shift (ppm) NMR Spectroscopy • Each type of H-atom has a specific Chemical shift • The peak height is number of H-atoms at this chemical shift = metabolite concentration • NMR measures ‘concentrations’ of different types of H-atoms

  6. Experimental Design Time 4 3.5 3 Dose 2.5 Metabolite concentration 2 1.5 1 0 0.2 0.4 0.6 0.8 1 time 0.5 0 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.2 0.4 0.6 0.8 1 time 0 0.2 0.4 0.6 0.8 1 time time Animal Trajectories Different contributions

  7. Symbol Meaning k Time h Dose group ih Individual Data Estimates of these factors: Constraints: 0 0.2 0.4 0.6 0.8 1 time 0 0.2 0.4 0.6 0.8 1 time 0 0.2 0.4 0.6 0.8 1 time The Method I: ANOVA

  8. 3.0275 2.055 3.285 5.38 3.0475 3.675 3.7525 2.7175 2.075 2.93 X x Structured ! The Method II ANOVA is a Univariate technique

  9. 0.7 3.0275 0.6 0.04 0.5 0.03 0.02 0.4 6.01 ppm 0.01 2.055 0.3 3.285 5.38 0 Or: Relationship between the columns of X X 3.0475 Covariance between the variables -0.01 0.2 3.675 3.7525 -0.02 2.7175 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 2.075 2.05 ppm 2.93 0.1 0 10 8 6 4 2 0 chemical shift (ppm) Multivariate Data NMR Spectroscopy

  10. Loading PC 1 Loading PC 2 X 3 2.5 Loading PC 1 Loading PC 2 2 1.5 3 x 1 Scores 0.5 0.6 0 0.4 1 0.2 1 0.5 residuals 0.5 0 PC 2 0 0 x -0.2 scores loadings x 2 1 -0.4 -0.6 -0.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 PC 1 The Method III: Principal Component Analysis 3D  2D … Imagine! 350D  2D !!!

  11. E Parts of the data not explained by the component models The Method IV: ANOVA and PCA  ASCA Column spaces are Orthogonal

  12. In Words: • ASCA models the different contributions to the variation in the data • ASCA takes the covariance between the variables into account • ASCA gives a solution for the problem at hand.

  13. 0.5 control vehicle low 0.4 medium high 0.3 0.2 Scores 0.1 40 % 0 -0.1 -0.2 6 24 48 Time (Hours) Results I

  14. 0.5 control vehicle low 0.4 medium high 0.3 0.2 Scores 0.1 0 -0.1 -0.2 6 24 48 Time (Hours) Results II • Quantitative effect! • No effect of vehicle • Scores are in agreement with visual inspection

  15. 3.0475 5.38 Unique to the α submodel 3.7525 3.675 Differences between submodels 3.9675 2.735 2.055 2.5425 Interesting for Biology 2.5825 2.6975 2.055 Interesting for Diagnostics 2.075 2.91 3.0275 2.93 3.9675 2.735 2.6975 2.5825 3.285 3.2625 2.075 2.93 3.0475 2.055 3.73 3.8875 2.735 3.0275 3.285 10 8 6 4 2 0 chemical shift (ppm) Results III  biomarkers

  16. Conclusions • Metabolomics (and other –omics) techniques give multivariate datasets with an underlying experimental design • For this type of data, ASCA can be used • The results observed for this experiment are in accordance with clinical observations • The metabolites that are responsible for this variation can be found using ASCA  BIOMARKERS

  17. Discussion • How can I perform statistics on the ASCA model? (e.g. Significance testing) • Are there other constraints possible for this model? (e.g. stochastic independence) • Are there alternative methods for solving this problem?

More Related