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

5. Example Experiment: Time: 6, 24 and 48 hours Experimental Design: Rats are given Bromobenzene that affects the liver Groups: 3 doses of BB Animals: 3 rats per dose per time point Vehicle group, Control group Rat 1 11 Rat 2 11 Rat 3 11 Rat 1 12 Rat 2 12 Rat 3 12 Rat 1 13 Rat 2 13 Rat 3 13 Rats 6 hours 24 hours 48 hours 0246810 chemical shift (ppm) 2.93 2.7175 2.075 3.7525 3.675 3.0475 5.38 3.285 2.055 3.0275 Measurements: NMR spectroscopy of urine

6. 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

7. Different contributions 00.20.40.60.81 time Time Animal 00.20.40.60.81 time Dose 00.20.40.60.81 time Trajectories Experimental Design

8. The Method I: ANOVA Constraints: 00.20.40.60.81 time 00.20.40.60.81 time 00.20.40.60.81 time Data Individualihih Dose grouph Timek MeaningSymbol Estimates of these factors:

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

10. Multivariate Data NMR Spectroscopy Covariance between the variables -0.2-0.100.10.20.30.40.5 -0.02 -0.01 0 0.01 0.02 0.03 0.04 2.05 ppm 6.01 ppm Or: Relationship between the columns of X X

11. The Method III: Principal Component Analysis 3D  2D … Imagine! 350D  2D !!! 1 0 0.5 1 0 1 x x 2 0 1 1.5 2 2.5 3 x 3 X Loading PC 1 Loading PC 2 loadingsscores residuals -0.8-0.6-0.4-0.200.20.40.60.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 PC 1 PC 2 Scores

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

13. 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.

14. Results I 40 % 62448 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Time (Hours) Scores control vehicle low medium high

15. Results II Quantitative effect! No effect of vehicle Scores are in agreement with visual inspection 62448 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Time (Hours) Scores control vehicle low medium high

16. Results III  biomarkers 3.9675 2.735 3.675 3.7525 2.055 2.5425 5.38 3.0475 2.5825 2.6975 3.9675 2.735 2.6975 2.933.0275 2.91 2.5825 2.075 3.285 2.055 3.8875 3.73 2.055 3.0475 2.93 2.075 2.735 3.0275 3.2625 3.285 0246810 chemical shift (ppm) Differences between submodels Interesting for Biology Interesting for Diagnostics Unique to the α submodel

17. 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

18. Discussion 1.How can I perform statistics on the ASCA model? (e.g. Significance testing) 2.Are there other constraints possible for this model? (e.g. stochastic independence) 3.Are there alternative methods for solving this problem?