HC 3 - Metabolomics Data Analysis 1: Exploration and Discrimination

Question 1

Goal of predictive multivariate analysis

Answer 1

Is someone sick or healthy based on metabolite profile?

Question 2

What is the input data for explorative multivariate analysis?

Answer 2

Multivariate data matrix

Question 3

Components multivariate data matrix

Answer 3

Rows: individuals, samples, countries
Columns: variables metabolites, genes, qualitative/quantitative

Question 4

Which function is the goal for explorative multivariate analysis? (predictive)

Answer 4

Y = f(X)
with Y being the class: 1 or 0 in the data matrix for sick or healthy (variable of the individuals) expressed as a function containing Xvariables

Question 5

Univariate analysis of metabolomics data: question to answer (goal)

Answer 5

Which variables show significant differences between groups/classes for one variable?

Question 6

For univariate analysis, a t-test/ANOVA or Wilcoxon test can be used. Describe the difference about these approaches

Answer 6

-T-test or ANOVA > parametric test: there is a mathematical formula which describes the distribution of the data
-Wilcoxon > nonparametric test: no knowledge about the distribution

Question 7

Problem with univariate analysis

Answer 7

It cannot detect multivariate discrimination

Question 8

If two variables set in a plot cannot separate the groups but a clear separation is visible: what needs to be done (multivariate discrimination)?

Answer 8

A new variable should be made which describes the variation (which maxamizes the between group difference). Make the formula for the multivariate solution VARclass = 1Var1 + -1Var2 so that when
-Var1 > Var 2: VARclass= positive
-Var2 < Var1: VARclass= negative

Question 9

Why do correlated metabolites occur?

Answer 9

Because of pathways and feedback mechanisms
> metabolites are dependent from each other
> both variables are needed for good discrimination

Question 10

Explorative multivariate analysis: Principal component analysis (PCA): which purposes?

Answer 10

-Data reduction: PCA reduces large data matrix into two smaller matrices which are easier to plot and interpret
-Data exploration: PCA extracts most important factors (Principal Components) from data to describe multivariate interactions between measured variables.
-Data understanding: Use PCs to classify samples, identify compound spectra, determine biomarker etc.

Question 11

What is PC1?

Answer 11

The component which describes the most variation in the data

Question 12

Basic equation PCA

Answer 12

X = t1p1^T + t2p2^T … tr*pr^T + E
= TP^t + E
X > (I x J) a data matrix
T > (I x R) are the scores (per sample)
P > (J x R) are the loadings (per variable)
E > (I x J) are the residuals
R is the number of Principal Components used to describe X.

Question 13

What are the scores?

Answer 13

The new values of the samples for PC1 and PC2 for example > gives information about the position of the samples

Question 14

Why are scores written as p^T in the equation?

Answer 14

That means transpose the vector p (the PC vector across the multivariate data) > make it into a row

Question 15

What are loadings and why are they needed?

Answer 15

Weights are needed for each variable to determine how the line is plotted (the line is the new PCA across all dimensions)
> P are the loadings (for each variable)
> 2 PCs means 2 loadings needed per variable.

Question 16

Each PC can be written as a distinct matrix. How can the scores and loading be used to describe data? Lets say there is two sample with for the five variables the values -3, -3, 0, 3, 3. and for the second sample -2, -2, 3, 2, 2

Answer 16

PC1
Scores: -6 for sample1 and -4 for sample2
Loading: 0.5,0.5,0,-0.5,-0.5
This describes:
-3 -3 0 3 3
-2 -2 0 2 2
PC2
Scores: 0 for sample1 (already done) and 3 for sample2
Loading: 0,0,1,0,0
PC1 and PC2 describe
-3 -3 0 3 3
-2 -2 3 2 2
Done!

Question 17

Why is it important to make a residual E and not make more PCs?

Answer 17

They are not insightful and you need to be able to distinguish the variation until only what seems noise remains (we do not want to describe noise)
> we only want to describe systematic variation

Question 18

What does the loading say?

Answer 18

How each variable contributes to the multivariate direction of the PC

Question 19

What does a score plot show?

Answer 19

The samples/individuals as dots in a plot with PC1 and PC2 as axes for example.
> the first PC does not have to distinguish the classes the best, this could also be the second PC.

Question 20

What does a loading plot show? If a dot is around 0, what does this mean.

Answer 20

The loading plot also uses PC1 and PC2 as axes and therefore the dots do show correlation with the sample dots from the score plot. The dots are the variables (metabolites etc.) and loadings around zero mean that these variables have only small effect on the model.

Question 21

The residuals (E), the non-systematic part of the data can be described as sums across objects or variables. What do high E values mean for either individuals or variables?

Answer 21

Individual: a high E means that the individual is poorly described by the PCA model
Variable: a high E means that the metabolite/variable is poorly described by the PCA model and might be an outlier

Question 22

Why is centering and scaling of the data necessary?

Answer 22

Because we are interested in the differences between objects, not in their absolute values
> scaling is needed because when different variables are measured in different unts, scaling gives each variable an equal chance of contributing to the model

Question 23

Mean-centering

Answer 23

Subtract the mean of each column from all values of each column of X to determine variation within the group and not how much the variation differs from zero
> the new means are around zero
> the column with the highest values after mean-centering show the largest variation

Question 24

Why is variable/feature scaling needed

Answer 24

To make variables comparable to their biological effects (are large peaks more important than small peaks?) or equalize their relative importance.

Question 25

Variable / Feature Scaling

Answer 25

Divide each value of each column of X by the scaling factor (for example standard deviation of the column).
> at the end of this, all standard deviations for the columns are 1.0

Question 26

Types of scaling with scaling factors

Answer 26

-Range scaling: scaling factor is the biological range (Max-Min) of all values
-Standardization/autoscaling: scaling factor is standard deviation of all values.

Question 27

Log transformation

Answer 27

Take log from each individual
> make data distribution somewhat normal (Gaussian)

Question 28

Differnce centering and scaling methods with log transformation

Answer 28

Transformation is performed for each value instead of per column

Question 29

Problems with log transformation

Answer 29

Small values are problematic > 0
-Square root is less problematic

Question 30

When is log transformation needed?

Answer 30

If the data looks uneven distributed

Question 31

When is log transformation performed?

Answer 31

Before centering and scaling

Question 32

Why is Discriminant PLS needed when PCA exists?

Answer 32

PCA scores are good summarizers of the X data, but do not necessarly of Y (classes/groups) > first PCA doesn’t discriminate the groups in many cases.
-DPLS scores are used to predict the class Y for data X

Question 33

How is Y calculated for each X variable in DPLS?

Answer 33

Per variable a different bPLS coefficient is calculated: regression coefficient for prediction Y.
> PLS scores are chosen so that they can predict the Y value

Question 34

Formula X in DPLS

Answer 34

X = T-PLS * P-T + E

Question 35

Regression of Class y in DPLS

Answer 35

y-pred = T-PLS * b-PLS + f

Question 36

What does the T-PLS mean in DPLS?

Answer 36

The PLS scores

Question 37

What does a high and low b-value value mean?

Answer 37

High: Y is predictable
Low: Y is not predictable very well

Question 38

Difference b-value and b-PLS in DPLS

Answer 38

b-value gives information which PC is important for prediction in general, not per variable

Question 39

What is f in the DPLS?

Answer 39

The residue

Question 40

Two goals of DPLS

Answer 40

-Model of data > X formula
> is the data well described
> clustering/outliers
> do new samples fit the model of the data?
-Calibration model between scores and class > y formula
> is there relationship between T-PLS and Y
> what is the prediction error?

Question 41

How is y-pred interpreted?

Answer 41

Negative values > Y=0
Positive values > Y=1
both binary values for Y are classes
or cutff 0.5

Question 42

Prediction model for new data of DPLS

Answer 42

for x-new
> y-new = x-new * b-PLS

Question 43

What do the PLS scores do (function)?

Answer 43

Describe X and predict Y