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ASCA_ analysis of multivariate data from an experimental design

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					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


For two treatments A and B the total sum of 
squares can be split into several contributions 
                                Example

Experiment:
Rats       are given Bromobenzene    that affects the liver


Measurements: NMR spectroscopy of urine
                                                          Rats




                                                     Ra 11
                                                     Ra 11


                                                     Ra 11
                                                     Ra 12
                                                     Ra 12
                                                     Ra 12
                                                     Ra 13
                                                     Ra 13
                                                                                             13
                                                       t 2
                                                       t 1


                                                       t 3
                                                       t 1
                                                       t 2
                                                       t 3
                                                       t 1
                                                       t 2
                                                       t 3
                                                     Ra
Experimental Design:                      6 hours

                                          24 hours
 Time: 6, 24 and 48 hours                 48 hours

Groups: 3 doses of BB                                                                       3.0275




 Vehicle group, Control group                                                                    2.055
                                                                                5.38        3.285
                                                                                            3.0475
 Animals: 3 rats per dose per time                                                      3.675
                                                                                       3.75252.7175
                                                                                                 2.075

 point
                                                                                             2.93


                                                              10     8    6            4        2        0
                                                                   chemical shift (ppm)
               NMR Spectroscopy
0.7
                                             3.0275

                                                                       -   Each type of H-atom 
0.6                                                                        has a specific Chemical 
                                                                           shift
0.5
                                                                       -   The peak height is 
                                                                           number of H-atoms at 
0.4
                                                                           this chemical shift = 
                                                           2.055           metabolite 
0.3                    5.38              3.285
                                                                           concentration
                                             3.0475

                                                                       -   NMR measures 
0.2
                                     3.675
                                   3.7525
                                                                           ‘concentrations’ of 
                                                 2.7175
                                                           2.075           different types of H-
0.1                                             2.93
                                                                           atoms

  0
   10   8       6             4                           2        0
            chemical shift (ppm)
                                          Different contributions
                                  Experimental Design
                                                                                                              Time
                            4

                           3.5                                         0   0.2   0.4 time 0.6       0.8   1
Metabolite concentration




                            3

                           2.5

                            2                                                                                 Dose
                           1.5

                            1
                                                                       0   0.2   0.4          0.6   0.8   1
                           0.5                                                         time

                            0

                           -0.5
                              0     0.2   0.4          0.6   0.8   1
                                                time
                                                                                                               Animal

                                   Trajectories                        0   0.2   0.4 time 0.6       0.8   1
                                                                      Symbol   Meaning



    The Method I: ANOVA
                                                                      k        Time

                                                                      h        Dose group

                                                                      ih       Individual

                                                                               Data




    Estimates of these factors:



                                                       Constraints:


0       0.2         0.4   time   0.6     0.8       1




0       0.2         0.4   time   0.6     0.8       1




    0         0.2    0.4 time 0.6      0.8     1
                The Method II
ANOVA is a Univariate technique

                             3.0275




                                  2.055
                         5.38 3.285
                              3.0475
                            3.675
                           3.7525
                              2.7175
                                 2.075
                               2.93




x                       X



                                          Structured !
                           Multivariate Data
                                             NMR Spectroscopy

 0.7                                                               0.04
                               3.0275


 0.6                                                               0.03

 0.5
                                                                   0.02




                                                        6.01 ppm
 0.4
                                         2.055                     0.01
 0.3                5.38      3.285
                               3.0475
                                                                     0
 0.2
                            3.675
                           3.7525
                                  2.7175
                                  2.93
                                        2.075                      -0.01
 0.1

  0                                                                -0.02
  10    8     6       4        2                 0                      -0.2 -0.1   0   0.1 0.2 0.3   0.4   0.5
                                                                                         2.05 ppm
            chemical shift (ppm)

Or:
Relationship                                                         Covariance between the 
between                      X                                       variables
the columns of 
X
                  The Method III: Principal Component 
                               Analysis
                                                                                            Loading PC 1
                                                                                            Loading PC 2
      3

     2.5    Loading PC 2                Loading PC 1
      2

     1.5                                                                          X
x3




      1

     0.5
                                                             Scores
      0
      1
                                                    1               0.6
                  0.5
                                      0.5                           0.4
             x2          0   0
                                            x1                      0.2

                                                             PC 2
                                                                     0
                                                 residuals
                                                                -0.2
                        scores   loadings
                                                                -0.4

                                                                -0.6
           3D à 2D … Imagine!
           350D à 2D !!!                                        -0.8-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
                                                                                       PC 1
The Method IV: ANOVA and PCA à ASCA
                           Column spaces 
                           are
                           Orthogonal




                                E

                                 Parts of the 
                                 data not 
                                 explained by 
                                 the 
                                 component 
                                 models
              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.
   Results I


                0.5                    control
                                       vehicle
                0.4                    low
                                       medium
                                       high
                0.3


       Scores   0.2

                0.1


40 %              0

                -0.1

                -0.2


                    6    24                      48
                        Time (Hours)
                                    Results II



         0.5                          control
                                      vehicle
                                                     • Quantitative 
         0.4                          low
                                      medium
                                      high
                                                       effect!
         0.3


         0.2
                                                     • No effect of  
Scores




         0.1                                           vehicle
           0
                                                     • Scores are in 
         -0.1
                                                       agreement with 
                                                       visual inspection
         -0.2


                 6    24                        48
                     Time (Hours)
         Results III à biomarkers
                                    3.0475
                   5.38


                           3.7525
                             3.675
                                                             Unique to the α submodel

                                                             Differences
                          3.9675        2.735
                                               2.055         between submodels
                                         2.5425


                                        2.5825
                                       2.6975
                                                 2.055
                                                             Interesting for Biology

                                                 2.075
                                                             Interesting for 
                                       2.91
                                    3.0275
                                       2.93                  Diagnostics
                          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)
            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 
  à BIOMARKERS
              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?

				
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posted:4/28/2014
language:English
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