Shockomics talk about planned analysis.

1. Problem definition Methods Results Conclusions
Data Mining Activities for Shockomics
Vicent J. Ribas
Custom Software and Electronics
Barcelona, Catalonia
April 19, 2016
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

2. Problem definition Methods Results Conclusions
Contents
1 Problem definition
2 Methods
3 Results
4 Conclusions
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

3. Problem definition Methods Results Conclusions
Problem definition
Objective: detect the clinical variables, proteins and
metabolites that present the highest impact on the three
different types of shock that we are studying at three different
times (T1, T2 and discharge). Of course, attending to the
nature of this study, we will have many more variables/data
observed than patients.
Definition: ‘a small n, large p’ is a data mining problem that
tries to predict response to treatment based on data having a
very small sample size (n) but very large dimensionality (p).
This problem needs to be tackled through data visualisation,
dimensionality reduction techniques (shrinkage methods) or a
combination of both.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

4. Problem definition Methods Results Conclusions
small n large p
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

5. Problem definition Methods Results Conclusions
Contents
1 Problem definition
2 Methods
3 Results
4 Conclusions
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

6. Problem definition Methods Results Conclusions
Methods
In line with the description of WP8, the following methods are
considered for studying our n >> p problem:
Graphical models:
Factorisation of the probability densty function (Hammersley
Clifford theorem).
Conditional independence maps (CIM - mutual information
between sets of variables).
Graphical LASSO.
Ensembles of classification and regression trees (bagged trees).
Dendrograms, Kohonen Maps and Heat Maps.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

7. Problem definition Methods Results Conclusions
Methods
Regularised models:
Regularised linear regression.
LASSO.
Relevance vector machines (regularised support vector
machines with a-priori distributions).
Support Vector Machines with generative kernels (the
Quotient Basis Kernel).
Neural Networks (Restricted Boltzmann Machines/Factor
Analysis Models).
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

8. Problem definition Methods Results Conclusions
Conditional Independence for Gaussian Distribution
Let X = (X1, . . . , Xp) be a random vector with joint normal
distribution Np(µ, Σ) with mean vector µ ∈ Rp and positive
definite covariance matrix Σ. For three pairwise disjoint index sets
A, B, C ⊆ {1, . . . , p}, the sub-vectors XA and XB are conditionally
independent given XC , iff
det ΣA C×B C = 0
Here A C × B C is the minor related to the variables over
which we are calculating the marginal dependence/independence
(i.e. the resulting minor after removing the rows and columns
corresponding to the conditional independence statement).
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

9. Problem definition Methods Results Conclusions
Markov Random Fields
Given and undirected graph G, a Markov Random Field (MRF) is
defined as a set of probability distributions
MRFG := {p(x) : p(x) > 0, ∀p, x} such that ∀p ∈ MRFG and for
any three disjoint subsets A, B, C of G, if C separates A from B
then p satisfies XA ⊥⊥ XB|XC . If p ∈ MRFG, we often say p
respects G.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

10. Problem definition Methods Results Conclusions
Hammersley Clifford theorem
If a pdf p ∈ MRFG, then p(x) must also factorize according to G,
i.e. there exist functions ψc(x) on c ∈ C, such that
p(x) =
1
Z
exp
c∈C
ψc(xc) .
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

11. Problem definition Methods Results Conclusions
Statistical methods
The method above is exact but it requires the calculation of
the inverse of covariance matrices, which for the
dimenstionality that we are considering is not viable.
However, some numerical methods based on the same
framework will help.
CIM is an efficient method for finding the structure of a
graphical model. In particular, it is based on the measure of
mutual information between sets of variables. A mutual
information of zero corresponds to mutual statistical
independence.
The graphical lasso is an algorithm to estimate the precision
matrix (inverse of covariance matrix) from the available data.
The algorithm is based on a Lasso regularisation over the
estimated covariance matrix.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

12. Problem definition Methods Results Conclusions
CIM
I(A, B) =
a,b
P(a, b) log
P(a, b)
P(a)P(b)
and the conditional mutual information, with respect to the
condition set C,
I(A, B|C) =
a,b,c
P(a, b, c) log
P(a, b|c)
P(a|c)P(b|c)
.
The conditional mutual information is consistent with Hammersley
Clifford and Factorisation because mutual information will be 0 iff
A ⊥⊥ B|C.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

13. Problem definition Methods Results Conclusions
Shrinkage methods
Linear Regression: minw Lλ(w, y, x) = M
i=1 (yi − g(xi))2
,
Regularised linear regression:
minw Lλ(w, y, x) = minw λ w 2 + M
i=1 (yi − g(xi))2
,
Lasso (L1 loss function):
minw Lλ(w, y, x) = minw λ|w|1 + M
i=1 (yi − g(xi))2
,
Regularised support vector machines with a-priori
distributions:
ln p(t | s, σ−2) = 1
2
M
i=1 ln si − N
2 ln σ−2 + ln(2π)
−1
2 σ−2tT t − µT Σ−1µ + ln|Σ| ,
which has to be maximized w.r.t. σ−2 and s.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

14. Problem definition Methods Results Conclusions
Contents
1 Problem definition
2 Methods
3 Results
4 Conclusions
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

15. Problem definition Methods Results Conclusions
ProteoSepsis
Objective: assess the metabolites of the ProteoSepsis biobank
showing the strongest interaction with organ dysfunction
assessed through the SOFA score and Lactate levels.
Methodology: graphical models with Conditional
Independence Maps.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

16. Problem definition Methods Results Conclusions
ProteoSepsis
At ICU admission, there was a significant interaction between
C3-DC / C4-OH (Hydroxybutyrylcarnitine) and C5
(Valerylcarnitine).
We also found a significant interaction between C3-DC /
C4-OH (Hydroxybutyrylcarnitine) and C5 (Valerylcarnitine)
and Isoleucine (Ile) at 48h and ICU discharge.
A separate conditional analysis for each metabolite family
yielded the interactions in the following table.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

17. Problem definition Methods Results Conclusions
Phosphatidylcholines LysoPC a C18:1
PC aa C28:1
PC aa C38:1
MUPC / SPC
Amines and Amino-acids Creatinine
Kynurenine
Putrescine
t4-OH-Pro
Taurine
Total DMA
Glu
Ile
Ala
Leu
Arg
Sphingolipids SM C24:1
SM C18:0
SM C20:2
SM C24:0
SM C24:1
SM C26:1
Acylcarnitines C14:1
C14:2
C2
C5
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

18. Problem definition Methods Results Conclusions
Albios
Objective: assess the proteins of the Albios biobank showing
the strongest interaction with organ dysfunction assessed
through Lactate levels.
Methodology: Graphical Lasso and Elastic Network (Lasso)
over a set of 660 proteins (graph with 662 nodes and 28370
edges).
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

19. Problem definition Methods Results Conclusions
Albios
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

20. Problem definition Methods Results Conclusions
Albios
At ICU admission, there was a significant interaction with:
Angiotensinogen P01019 (p = 0.01).
Neural cell adhesion molecule L1-like protein O00533
(p = 0.02).
Complement C3 P01024 (p = 0.01)
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

21. Problem definition Methods Results Conclusions
Albios
At day 7, there was a significant interaction with:
Phosphatidylnositol-glycan biosynthesis class X protein
Q8TBF5 (p = 0.024).
Myosin 9 P35579 (p = 0.078).
Beta-2-Glycoprotein P02749 (p = 0.0614)
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

22. Problem definition Methods Results Conclusions
Contents
1 Problem definition
2 Methods
3 Results
4 Conclusions
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics

23. Problem definition Methods Results Conclusions
Conclusions
Methodology
We propose to analyse the interactions between the different
’omics’ and clinical data for each shock.
If possible, we will provide a stratification framework to study
the evolution of patients over time.
Vicent J. Ribas Custom Software and Electronics Barcelona, Catalonia
Data Mining Activities for Shockomics