PhD Defense

Introduction Database Description State of the Art AI Methods Applied An AI Tour of Sepsis Conclusions

On the Intelligent Management of Sepsis in theIntensive Care Unit

Vicent J. Ribas

LSI - SOCOTechnical University of Catalonia (UPC)

Barcelona

January 28, 2013

Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) Barcelona

On the Intelligent Management of Sepsis in the Intensive Care Unit





Contents

1 IntroductionIntroductionThesis Objectives

2 Database DescriptionDatasetAvailable Data

3 State of the Art

4 AI Methods Applied

5 An AI Tour of SepsisIncidence of SepsisProtection against SepsisMortality Prediction with a Latent Data RepresentationRisk of Death Assessment from Observed Data

6 ConclusionsIncidence of Sepsis and Coadjuvant FactorsProtective Effects of StatinsMortality Predictors and Their AccuracyContributionsOutline for Future WorkPublications




Contents



3 State of the Art







Introduction




Introduction

Introduction

Sepsis is a clinical syndrome defined by the presence ofinfection and Systemic Inflammatory Response Syndrome(SIRS).

This can lead to severe sepsis or to septic shock (severe sepsiswith hypotension refractory to fluid administration) andmulti-organ failure.

In western countries, septic patients account for as much as25% of ICU bed utilization and the pathology occurs in 1% -2% of all hospitalizations.

The mortality rates of sepsis range from 12.8% for sepsis and20.7% for severe sepsis, and up to 45.7% for septic shock.




Introduction

Introduction








Introduction

Introduction








Introduction

Introduction








Introduction

The medical management of sepsis and the study of itsprognosis and outcome is a relevant medical researchchallenge.

Provided that such methods are to be used in a clinicalenvironment (ICU), it requires prediction methods that arerobust, accurate and readily interpretable.




Introduction






Introduction






Thesis Objectives

Thesis Objectives

Improve our knowledge about the incidence of Sepsis.

Improve our understanding about Sepsis and its protectivefactors.

Study of the evolution of Sepsis into more critical states withrespect to several management/measurement variables.

Develop a system that could provide prognostic indicators ofmortality (RoD) that can be used in the ICU (acc., sens,spec), if possible, at the onset of the pathology.




Thesis Objectives

Thesis Objectives








Thesis Objectives

Thesis Objectives








Thesis Objectives

Thesis Objectives








Contents



3 State of the Art







Dataset

Available Datasets

A prospective observational cohort study of adult patients withsevere sepsis was conducted at the Critical Care Departmentof the Vall d’ Hebron University Hospital (Barcelona, Spain).

Data from 750 and 354 patients with severe sepsis wascollected in this ICU between June, 2007 and December, 2010.

55% of cases correspond to ‘medical’ sepsis.

The mean age of the patients in the database was 57.08 (withstandard deviation ±16.65) years.

40% of patients were female.




Dataset

Available Datasets









Dataset

Available Datasets









Dataset

Available Datasets









Dataset

Available Datasets









Available Data

Available Attributes

The collected data show the worst values for all variablesduring the first 24 hours of evolution of Severe Sepsis.

Organ dysfunction was evaluated by means of the SOFA scoresystem, which objectively measures organ dysfunction for 6organs/systems.

Cardiovascular (CV) 2.86 (1.62) Haematologic (HAEMATO) 0.78 (1.14)Respiratory (RESP) 2.31 (1.15) Global SOFA score 7.94 (3.86)

Central Nerv. Sys. (CNS) 0.48 (1.00) Dysf. Organs 1.68 (1.09)Hepatic (HEPA) 0.48 (0.92) Failure Organs 1.51 (1.02)

Renal (REN) 1.06 (1.20) Total Dysf. Organs 3.18 (1.32)

Severity was evaluated by means of the APACHE II score,which was 23.03± 9.62 for the population under study.The mortality rate intra-ICU for our study population was26.32%.




Available Data


The collected data show the worst values for all variablesduring the first 24 hours of evolution of Severe Sepsis.Organ dysfunction was evaluated by means of the SOFA scoresystem, which objectively measures organ dysfunction for 6organs/systems.








Available Data






Severity was evaluated by means of the APACHE II score,which was 23.03± 9.62 for the population under study.

The mortality rate intra-ICU for our study population was26.32%.




Available Data










Available Data


List of attributes used in this study:

Age

Gender

Sepsis Focus

Germ Class

Polimicrobial Infection

Base Pathology

Cardiovascular SOFA Score

Respiratory SOFA Score

CNS SOFA score

Hepatic SOFA Score

Renal SOFA Score

Haematologic SOFA Score

Total SOFA Score

Dysfunctional Organs forSOFA 1-2

Dysfunctional Organs forSOFA 3-4

Total Number ofDysfunctional Organs

Mechanical Ventilation

Oxygenation IndexPaO2/FiO2

Vasoactive Drugs

Platelet Count

APACHE II Score

Surviving Sepsis CampaignBundles 6h

Haemocultures 6h

Antibiotics 6h

Volume 6h

O2 Central Venous Saturation6h

Haematocrit 6h

Transfusions 6h

Dobutamine 6h

Surviving Sepsis CampaignBundles 24h

Glycaemia 24h

PPlateau

Worst Lactate

O2 Central Venous Saturation




Contents



3 State of the Art







Quantitative Analysis of the Pathophysiology of Sepsis

Reference Objective Model VariablesRackow et al. 1991 Severity ODE B. Flow

MAPArt. Res

React. HyperemiaKimberly et al. 2000 Shock Autonomic HR

Coupling BPRoss et al. 1998 Inflam. ODE Pathogen

Shock ANN (RBF) Cell DamageImmuno. Resp.

Othman et al. 2003 Shock Gastric Impedanceand 2004 Mucosa




Quantitative Analysis of the Prognosis of Sepsis (MedicalPractice)

Reference Objective Model VariablesKnaus et al. 1985 Eval. LR SOFA

MODS APACHE IILODS

Adler et al. 2008 Sepsis LR SAPS 3Paetz et al. 2001 Shock RBF SBP

Thrombocit.Lact.

Savkin et al. 2010 Sepsis SVM CultureRR, HR

Lact.White cell

Brause et al. 2002 Sepsis HMM Sep. StatesFull Obs.




Contents



3 State of the Art







AI Methods Applied




AI Methods Applied

Graphical models from Algebraic Statistics chapter 6.

CART chapter 6.

Logistic regression over latent factors chapter 7.

Shrinkage methods chapter 8. [Hastie]

Support Vector Machines chapter 8 [Scholkopf, Christianini].

Generative kernels chapter 8.

Simplified Fisher kernel.Quotient Basis Kernel.Kernels based on the JS metric.

Relevance Vector Machines chapter 8 [Tipping, Fletcher].




Shrinkage methods

Linear Regression: minw Lλ(w, y, x) =∑M

i=1 (yi − g(xi))2 ,

Ridge regression:minw Lλ(w, y, x) = minw λ‖w‖2 +

∑Mi=1 (yi − g(xi))2 ,

Lasso (L1 loss function):minw Lλ(w, y, x) = minw λ|w|1 +

∑Mi=1 (yi − g(xi))2 ,

Relevance vector machine (SVM with priors) [Tipping,Fletcher].




Shrinkage methods


i=1 (yi − g(xi))2 ,


∑Mi=1 (yi − g(xi))2 ,


∑Mi=1 (yi − g(xi))2 ,





Shrinkage methods


i=1 (yi − g(xi))2 ,


∑Mi=1 (yi − g(xi))2 ,


∑Mi=1 (yi − g(xi))2 ,





Shrinkage methods


i=1 (yi − g(xi))2 ,


∑Mi=1 (yi − g(xi))2 ,


∑Mi=1 (yi − g(xi))2 ,





Why generative kernels?

Selection of kernel function for a given problem is not trivial.

One normally must have good insight about the problem athand.

Mapping over higher dimensions simplifies the problem butcomputational cost grows with ∼ d3.

Solution: exploit the statistical structure of the data to buildthe kernel!

Requirement: pdf must be a regular exponential family. Thisrequirement is fulfilled by the dataset of this Ph.D.!








































Generative kernels

We propose three generative approaches:

exploit the algebraic structure of the dataset (Quotient Basis).exploit the momentum generation properties of regularexponential families (i.e. the second derivative of thelog-Laplace function G corresponds to the covariance) tocalculate the Fisher kernel.use the dual of the log-Laplace function, which corresponds tothe negative entropy, and a metric (Jensen-Shannon) to buildthe kernels through application of the properties for pd and ndfunctions (i.e. centering, inversion and exponentiation).




Generative kernels


exploit the algebraic structure of the dataset (Quotient Basis).

exploit the momentum generation properties of regularexponential families (i.e. the second derivative of thelog-Laplace function G corresponds to the covariance) tocalculate the Fisher kernel.use the dual of the log-Laplace function, which corresponds tothe negative entropy, and a metric (Jensen-Shannon) to buildthe kernels through application of the properties for pd and ndfunctions (i.e. centering, inversion and exponentiation).




Generative kernels


exploit the algebraic structure of the dataset (Quotient Basis).exploit the momentum generation properties of regularexponential families (i.e. the second derivative of thelog-Laplace function G corresponds to the covariance) tocalculate the Fisher kernel.

use the dual of the log-Laplace function, which corresponds tothe negative entropy, and a metric (Jensen-Shannon) to buildthe kernels through application of the properties for pd and ndfunctions (i.e. centering, inversion and exponentiation).




Generative kernels


exploit the algebraic structure of the dataset (Quotient Basis).exploit the momentum generation properties of regularexponential families (i.e. the second derivative of thelog-Laplace function G corresponds to the covariance) tocalculate the Fisher kernel.use the dual of the log-Laplace function, which corresponds tothe negative entropy, and a metric (Jensen-Shannon) to buildthe kernels through application of the properties for pd and ndfunctions (i.e. centering, inversion and exponentiation).




Quotient Basis Kernel

Let A be a set of n unique points A = a1, . . . , an and τ a termordering. A Grobner basis of A, G = g1, . . . , gt , is a Grobner basisof I (A). Therefore, the points in A can be presented as the set ofsolutions of

g1(a) = 0g2(a) = 0· · ·

gt(a) = 0





Let A, be a set of n × s unique support points A = a1, . . . , anand τ a term ordering. A monomial basis of the set of polynomialfunctions over A is

ESTτ = xα : xα /∈ 〈LT(g) : g ∈ I (A)〉

This means that ESTτ comprises the elements xα that are notdivisible by any of the leading terms of the elements of the Grobnerbasis of I (A).





Let τ be a term ordering and let us consider an ordering over thesupport points A = a1, . . . , an. We call design matrix (i.e. ESTτevaluated in A) the following n × c matrix

Z = [ESTτ ]∣∣A

where c is the cardinality of ESTτ and n is the number of supportpoints. The covariance of the design matrix of ESTτ , which is akernel, is the QBK.




Simplified Fisher Kernel

Let P = (P|η ∈ N) be a regular exponential family with canonicalsufficient statistic T . Then the log likelihood function takes theform

l(η|T ) = n(ηtT − G (η))

The score function is the gradient

U(T , η) =∂l(η|T )

∂η= nT − ∂

∂ηG (η)

So the simplified Fisher Kernel is:

k(x , z) = U(Tx , η)U(Tz , η)t




Kernels based on the Jensen Shannon Metric





Let P = (P|η ∈ N) be a regular exponential family with canonicalsufficient statistic T . Then the log likelihood function takes theform

l(η|T ) = n(ηtT − G (η))

This function accepts a convex - conjugate (Legendre Dual) of theform

l(γ|T ) = n(γtT − F (γ))

In our case, the dual F is the negative log-entropy function.





JS(γ1, γ2) =F (γ1) + F (γ2)

2− F

(γ1 + γ2

2

).

Centred kernel:φ(x , y) = JS(x , x0) + JS(y , x0)− JS(x , y)− JS(x0, x0).

Exponentiated kernel: φ(x , y) = exp(−tJS(x , y)) ∀t > 0.

Inverse kernel: φ(x , y) = 1t+JS(x ,y) ∀t > 0.





JS(γ1, γ2) =F (γ1) + F (γ2)

2− F

(γ1 + γ2

2

).








JS(γ1, γ2) =F (γ1) + F (γ2)

2− F

(γ1 + γ2

2

).







Contents



3 State of the Art







Route map




Incidence of Sepsis

SOFA Score and Sepsis

Study based on the basal SOFA scale.

A SOFA≥2 is demonstrative of MODS while a SOFA-CV > 2is demonstrative of Septic Shock.

By the definition of SOFA it is obvious that Severe Sepsis,Shock and MODS are dependent on each other (i.e. all implyorgan dysfunction).




Incidence of Sepsis








Incidence of Sepsis








Incidence of Sepsis

Bayes Network for Sepsis

X1 X2

X3 X4

node X1 corresponds to theunobserved number ofSevere Sepsis.

node X2 corresponds toSeptic Shock.

node X3 corresponds toMODS.

node X4 corresponds to ICUresult.




Incidence of Sepsis

Incidence of Sepsis

Bayes Network yields an incidence of 164 cases / 100000 hab(i.e. 164 vs 118 in our database).

The incidence reported in Madrid is 141 cases / 100000 hab.and Castilla Leon is 250 cases / 100000 hab.

The discrepancy between these figures lies mainly in the studydesign (haemocultures at admission vs. people being treatedfor Sepsis).




Protection against Sepsis

Statins

Statins is a common drug for the treatment of highcholesterol levels.

Beyond their hypolipemic properties, they also exerciseanti-inflammatory, immunomodulator and antioxidant actions.

Statins modulate vasoreactivity in the coagulation system.

Recent studies suggest that they present beneficial effects forinfection prevention and treatment, impacting the ICUoutcome.

These results are still controversial in the medical community.

In our dataset with 750 patients, 106 (i.e. 14.13%) receivedpreadmission treatment with statins.





Hypothesis

In our dataset with 750 patients, 106 (i.e. 14.13%) receivedpreadmission treatment with statins.

Do statins play a protective role in the prognosis of Sepsis?

Does this role depend on the Sepsis continuum (MODS andSeptic Shock)?





Models of Conditional Independence

We aim to find the relation between the administration of statindrugs prior to ICU admission and the mortality rate in SevereSepsis patients. Thus, we test the null hypothesis that the ICUoutcome is independent of the preadmission use of statinsfor given APACHE II and SOFA scores. Ho :

Ho : X1 ⊥⊥ X4|X2, X3. (1)

where X1 is the ICU outcome, X4 the preadmission use ofstatins, X3 the SOFA score, and X2 the APACHE II score.






We have two options based on Algebraic Models to reject Ho :

study the rank of the minors of our observation matrix(tedious for large datasets).

Algebraic Interpolation (more fun):Assume that our observed dataset are the zeroes of polynomialset of equations (and an order on the variables).

On a first level of abstraction there is a Polynomial Idealassociated to this set of equations (vanishing ideal).On a second level of abstraction, this ideal is generated by afinite basis (Hilbert basis theorem). This is a Grobner basis.On a third level of abstraction, the terms of the ordering thatare not divided by the leading terms of the Grobner basis aredefined as a Quotient Basis.








Algebraic Interpolation (more fun):Assume that our observed dataset are the zeroes of polynomialset of equations (and an order on the variables).On a first level of abstraction there is a Polynomial Idealassociated to this set of equations (vanishing ideal).

On a second level of abstraction, this ideal is generated by afinite basis (Hilbert basis theorem). This is a Grobner basis.On a third level of abstraction, the terms of the ordering thatare not divided by the leading terms of the Grobner basis aredefined as a Quotient Basis.








Algebraic Interpolation (more fun):Assume that our observed dataset are the zeroes of polynomialset of equations (and an order on the variables).On a first level of abstraction there is a Polynomial Idealassociated to this set of equations (vanishing ideal).On a second level of abstraction, this ideal is generated by afinite basis (Hilbert basis theorem). This is a Grobner basis.

On a third level of abstraction, the terms of the ordering thatare not divided by the leading terms of the Grobner basis aredefined as a Quotient Basis.








Algebraic Interpolation (more fun):Assume that our observed dataset are the zeroes of polynomialset of equations (and an order on the variables).On a first level of abstraction there is a Polynomial Idealassociated to this set of equations (vanishing ideal).On a second level of abstraction, this ideal is generated by afinite basis (Hilbert basis theorem). This is a Grobner basis.On a third level of abstraction, the terms of the ordering thatare not divided by the leading terms of the Grobner basis aredefined as a Quotient Basis.





Algebraic Interpolation

Statins SOFA APACHE II1 1 12 1 11 2 12 2 11 1 22 1 21 2 22 2 2

The resulting products betweenterms of the Quotient Basisshow theinteraction/dependencebetween terms.

By the Hammersley - Cliffordtheorem (factorisation of theterms of the Quotient Basis)show that there is a GraphicalModel associated to thevanishing ideal.






x1 x2

x3 x4

Ordering: x1x2x3 x1x2 x1x3 x1 x2x3 x2 x3 1

Ideal I =〈x2

3 −3x3 +2, x22 −3x2 +2, x2

1 −3x1 +2〉.Grobner G =〈x2

3 −3x3 +2, x22 −3x2 +2, x2

1 −3x1 +2〉.Quotient Basis

B = 1, x3, x2, x2x3, x1, x1x3, x1x2, x1x2x3.






P(x4) = η7x1x2x3 + η6x1x2 + η5x1x3

− η4x2x3 − η3x1 + η2x2 + η1x3 + η0

Solving for x1, x2, x3 by substitution and also knowing thatη0 = 1−

∑7i=1 ηi yields the interpolation polynomial

P(x4) = −1/50x1x2x3 + 3/100x1x2 + 9/100x1x3

− 3/25x2x3 − 21/100x1 + 27/100x2 + 8/25x3 + 7/25






Statins SOFA APACHE II Result=1 Result=2

1 1 1 0.64 0.36

2 1 1 0.53 0.47

1 2 1 0.80 0.20

2 2 1 0.70 0.30

1 1 2 0.91 0.09

2 1 2 0.87 0.13

1 2 2 0.93 0.07

2 2 2 0.88 0.12






Statins SOFA APACHE II Result=1 Result=2

1 1 1 0.64 0.36

2 1 1 0.53 0.47

1 2 1 0.80 0.20

2 2 1 0.70 0.30

1 1 2 0.91 0.09

2 1 2 0.87 0.13

1 2 2 0.93 0.07

2 2 2 0.88 0.12





Analysis with Decision Trees




Mortality Prediction with a Latent Data Representation

Factor Analysis





Factor Analysis

A Factor Analysis (FA) model concerns a Gaussian hiddenvariable model with d observed variables Xi and k hiddenvariables Yi .

FA assumes (X ,Y ) follows a joint multivariate normaldistribution with positive definite covariance matrix.

What is sought is a model of the form x− µ = Λ + ε.





Factor Analysis

The FA model Fd,k is the family of multivariate normaldistributions Nd(µ,Σ) on Rd whose mean vector µ is an arbitraryvector in Rd and whose covariance matrix Σ lies in the(non-convex) cone

Fd,k = Ω + ΛΛt ∈ Rd×d : Ω 0 diagonal, Λ ∈ Rd×k

= Ω + Ψ ∈ Rd×d : Ω 0 diagonal, Ψ 0 symmetric, rank (Ψ) ≤ k.





Factor Analysis

Factor 1: cardiovascular function, cardiovascular SOFA scoreand vasoactive drugs.

Factor 2: haematologic function (haematologic SOFA scoreand platelet count).

Factor 3: respiratory function, Respiratory SOFA score andPaO2/FiO2 ratio.

Factor 4: use of mechanical ventilation and PPlateau.

Factor 5: 24h SSC bundles and glycaemic indices.

Factor 6: micro-organism producing the Sepsis and whetherthis sepsis polimicrobial or not.

Factor 7: renal function measured by the SOFA score andtotal SOFA score.





Factor Analysis

Factor 8: antibiotics and haemocultures during the first 6h ofICU stay.

Factor 9: number of organs in dysfunction.

Factor 10: hepatic function measured by the SOFA score.

Factor 11: CNS function and number of organs in dysfunction.

Factor 12: loci of Sepsis and poly-microbial.

Factor 13: APACHE II score and worst lactate levels.

Factor 14: Total number of organs in dysfunction.





Logistic Regression

Log-odd ratio of a Binomial distribution is

log

(p

1− p

)= β0 + βX. (2)

Where β0 is the intercept and β is vector of logistic regressioncoefficients estimated through ML with a generalised linear model.





Experiment setting

10-Fold cross-validation.

LR over Latent Factors (backward feature selection).

Subset selection of the Original Variables (backward featureselection).

Comparison with RoD formula based on the APACHE II score

ln(

ROD1−ROD

)= −3.517 + 0.146 · A + ε.





Logistic Regression over Latent Factors

β Coeff MAX MIN Z-score

Intercept 1.22 1.53 .87 7.11

F4 -0.54 -0.23 -0.86 -3.38

F10 -0.69 -0.38 -1.05 -4.26

F9 -0.51 -0.21 -0.81 -3.36

F13 -0.49 -0.24 -0.74 -3.80





Logistic Regression over Latent Factors

β Coeff MAX MIN Z-score

Intercept 4.20 3.11 5.29 7.56

APACHE II -0.08 -0.13 -0.04 -3.77

Worst Lact. -0.25 -0.38 -0.11 -3.63





Results

Method AUC Error Rate Sens. Spec. Dataset

LR-FA 0.78 0.24 0.65 0.80 FA

LR 0.75 0.30 0.64 0.72 LR

APACHE II 0.70 0.28 0.82 0.55 N/A




Risk of Death Assessment from Observed Data

RoD with RVM

The model performance was evaluated by means of 10-FoldCross-Validation.

The RVM yielded an accuracy of mortality prediction of 0.86;a prediction error of 0.18; a sensitivity of 0.67; and aspecificity of 0.87.

RVM selected the following attributes (corresponding toweights):

Number of dysfunctional organs (w1 = −0.039)Mechanical Ventilation (w2 = −0.101)APACHE II (w3 = −0.337)Resuscitation Bundles (6h) (w4 = 0.037)





RoD with RVM









RoD with RVM









The coefficients corresponding to the rest of attributes wereset to values close to zero as part of the training process. Thisreduces the number of attributes (34 to just 4) and improvesits interpretability.

The negative weights (number of dysfunctional organs,mechanical ventilation, APACHE II) are related to a highermortality risk.

The SSC bundles (resuscitation bundles) are associated to aprotective effect (i.e. antibiotics administration, performanceof haemocultures, administration of volume and vasoactivedrugs and so on).



















Comparison with other shrinkage methods

The predictive ability of the RVM has also been compared tothat of other well established shrinkage methods for regression.

The selected attributes and coefficients for each method were:

Ridge Regression:

Number of dysfunctionalorgans for SOFA 3-4(w1 = −0.021)

APACHE II (w2 = −0.127)

Worst Lactate(w3 = −0.126).

Lasso:

Age (w1 = 0.007)

Germ Class (w2 = 0.005)

PaO2/FiO2 (w3 = 0.001)

APACHE II (w4 = −0.006)

SvcO2 6h (w5 = −0.001)

Haematocrit 6h(w6 = 0.009)

Worst Lactate(w7 = −0.023)

SvcO2 (w8 = −0.006).

Logistic Regression with backwardfeature selection:

Intercept (w1 = 4.20)

Number of DysfunctionalOrgans (w1 = −0.12)

APACHE II (w2 = −0.08)

Worst Lactate (w3 = −0.25)





Comparison with other shrinkage methods

The predictive ability of the RVM has also been compared tothat of other well established shrinkage methods for regression.

The selected attributes and coefficients for each method were:

Ridge Regression:

Number of dysfunctionalorgans for SOFA 3-4(w1 = −0.021)

APACHE II (w2 = −0.127)

Worst Lactate(w3 = −0.126).

Lasso:

Age (w1 = 0.007)

Germ Class (w2 = 0.005)

PaO2/FiO2 (w3 = 0.001)

APACHE II (w4 = −0.006)

SvcO2 6h (w5 = −0.001)

Haematocrit 6h(w6 = 0.009)

Worst Lactate(w7 = −0.023)

SvcO2 (w8 = −0.006).

Logistic Regression with backwardfeature selection:

Intercept (w1 = 4.20)

Number of DysfunctionalOrgans (w1 = −0.12)

APACHE II (w2 = −0.08)

Worst Lactate (w3 = −0.25)





The three shrinkage methods evaluated in this section agreedin detecting as prognostic factors the Severity measured bythe APACHE II score and acidosis.

Organ dysfunction and mechanical ventilation or otherparameters related to it like PaO2/FiO2 also play a role in theprognosis of Sepsis.

The accuracy of each method was the following:

Method AUC Error Rate Sens. Spec.RVM 0.86 0.18 0.67 0.87

Logistic 0.75 0.30 0.64 0.72Ridge 0.70 0.25 0.63 0.79Lasso 0.70 0.32 0.67 0.68























RoD with Generative Kernels - QBK -

x1 is the Number of Dysfunctional Organs as measured by theSOFA Score.

x2 corresponds to Mechanical Ventilation (yes/no).

x3 corresponds to Severity as Measured by the APACHE IIScore.

x4 corresponds to the SSC Resuscitation Bundles (i.e.administration of antibiotics, performance of haemoculturesand so on). This is also a binary variable.





RoD with Generative Kernels - QBK -

ESTτ =

1, x4, x3, x3x4,x2, x2x4, x2x3, x2x3x4,x2

2 , x22 x4, x

22 x3, x

22 x3x4,

x32 , x

32 x4, x

32 x3, x

32 x3x4,

x42 , x

42 x4, x

42 x3, x

42 x3x4,

x52 , x

52 x4, x

62 , x1,

x1x4, x1x3, x1x3x4, x1x2,x1x2x4, x1x2x3, x1x2x3x4, x1x2

2 ,x1x2

2 x4, x1x22 x3, x1x2

2 x3x4, x1x32 ,

x1x32 x4, x1x3

2 x3, x1x32 x3x4, x1x4

2 ,x1x4

2 x4, x1x42 x3, x1x5

2





RoD with Generative Kernels

We have used Matlab’s Support Vector Machine QP solverimplemented in the BioInformatics and Optimization Toolboxes.We have also used 10-fold cross validation to evaluate theclassification performance for the different kernels. A grid searchyielded the appropriate values for C parameters for each Kernel.More particularly,

Quotient Basis and Fisher C = 1.

Generative Kernels C = 10. Also the parameter t for theExponential and Inverse Kernels was set to 2.

Gaussian, Linear and Polynomial Kernels C = 10.





RoD with Generative Kernels

Kernel AUC Error Rate Sens. Spec. CPU time [s]

Quotient 0.89 0.18 0.70 0.86 1.45

Fisher 0.76 0.18 0.68 0.86 1.39

Exponential 0.75 0.21 0.70 0.82 1.64

Inverse 0.62 0.22 0.70 0.82 1.68

Centred 0.75 0.21 0.70 0.82 1.99

Gaussian 0.83 0.24 0.65 0.81 1.56

Poly (order 2) 0.69 0.28 0.71 0.76 1.59

Linear 0.62 0.26 0.62 0.78 1.35




Contents



3 State of the Art







Incidence of Sepsis and Coadjuvant Factors

Incidence of Sepsis and Coadjutant Factors

SIRS pathology has proven to be a very sensitive indicator ofSepsis but also one of poor specificity.

Castilla y Leon report an incidence of 250 cases /100.000 hab.and Madrid 141 cases/100.000 hab.Our Bayes Network yielded an estimation of 164 cases /100.000 hab (i.e. 164 vs 118 in our database).There are different comorbidities and coadjuvant factors thatclearly play a role in Sepsis.Two important factors to be taken into consideration aresurgery or the infectious diseases such as pneumonia.These two factors play a very important role in the datasetanalysed.






SIRS pathology has proven to be a very sensitive indicator ofSepsis but also one of poor specificity.Castilla y Leon report an incidence of 250 cases /100.000 hab.and Madrid 141 cases/100.000 hab.

Our Bayes Network yielded an estimation of 164 cases /100.000 hab (i.e. 164 vs 118 in our database).There are different comorbidities and coadjuvant factors thatclearly play a role in Sepsis.Two important factors to be taken into consideration aresurgery or the infectious diseases such as pneumonia.These two factors play a very important role in the datasetanalysed.






SIRS pathology has proven to be a very sensitive indicator ofSepsis but also one of poor specificity.Castilla y Leon report an incidence of 250 cases /100.000 hab.and Madrid 141 cases/100.000 hab.Our Bayes Network yielded an estimation of 164 cases /100.000 hab (i.e. 164 vs 118 in our database).

There are different comorbidities and coadjuvant factors thatclearly play a role in Sepsis.Two important factors to be taken into consideration aresurgery or the infectious diseases such as pneumonia.These two factors play a very important role in the datasetanalysed.






SIRS pathology has proven to be a very sensitive indicator ofSepsis but also one of poor specificity.Castilla y Leon report an incidence of 250 cases /100.000 hab.and Madrid 141 cases/100.000 hab.Our Bayes Network yielded an estimation of 164 cases /100.000 hab (i.e. 164 vs 118 in our database).There are different comorbidities and coadjuvant factors thatclearly play a role in Sepsis.

Two important factors to be taken into consideration aresurgery or the infectious diseases such as pneumonia.These two factors play a very important role in the datasetanalysed.






SIRS pathology has proven to be a very sensitive indicator ofSepsis but also one of poor specificity.Castilla y Leon report an incidence of 250 cases /100.000 hab.and Madrid 141 cases/100.000 hab.Our Bayes Network yielded an estimation of 164 cases /100.000 hab (i.e. 164 vs 118 in our database).There are different comorbidities and coadjuvant factors thatclearly play a role in Sepsis.Two important factors to be taken into consideration aresurgery or the infectious diseases such as pneumonia.

These two factors play a very important role in the datasetanalysed.






SIRS pathology has proven to be a very sensitive indicator ofSepsis but also one of poor specificity.Castilla y Leon report an incidence of 250 cases /100.000 hab.and Madrid 141 cases/100.000 hab.Our Bayes Network yielded an estimation of 164 cases /100.000 hab (i.e. 164 vs 118 in our database).There are different comorbidities and coadjuvant factors thatclearly play a role in Sepsis.Two important factors to be taken into consideration aresurgery or the infectious diseases such as pneumonia.These two factors play a very important role in the datasetanalysed.




Protective Effects of Statins


We have studied the role of pre-admission use of Statins inthe incidence of Septic Shock and Prognosis.

This has been done through Graphical Models (AlgebraicStatistics) and Regression Trees.

There is a clear dependence between pre-admission use ofstatins the outcome of Sepsis.

We have seen that the higher the severity and organdysfunction, the higher the protection.

There is no clear dependence between statins and theincidence of Septic Shock.












































Mortality Predictors and Their Accuracy


The main limitation of current indicators for scoring theevolution of sepsis is their lack of specificity.

Not only does this affect incidence rates but also prognosissince many patients are given treatment that is not required.

We have analysed 17 different approaches to assess RoD andcompared them with standard practice (APACHE II).

The set of variables selected through RVM are consistent withclinical practice and the SSC guidelines.

































Method AUC Error Rate Sens. Spec. DatasetLR-FA 0.78 0.24 0.65 0.80 FA

LR 0.75 0.30 0.64 0.72 LRAPACHE II 0.70 0.28 0.82 0.55 N/A

RVM 0.86 0.18 0.67 0.87 RVMRidge 0.70 0.25 0.63 0.79 RVMLasso 0.70 0.32 0.67 0.68 RVM

SVM-Quotient 0.89 0.18 0.70 0.86 RVMSVM-Fisher 0.76 0.18 0.68 0.86 RVMSVM-EXP 0.75 0.21 0.70 0.82 RVMSVM-INV 0.62 0.22 0.70 0.82 RVM

SVM-CENT 0.75 0.21 0.70 0.82 RVMSVM-GAUSS 0.83 0.24 0.65 0.81 RVM

SVM-LIN 0.62 0.26 0.62 0.78 RVMSVM-POLY 0.69 0.28 0.71 0.76 RVM




Contributions

Contributions

The application of Algebraic Models and the study of QuotientBasis resulted in the definition of the Quotient Basis Kernel.

The application of Algebraic Models also resulted in thedefinition of a simplified version of the Fisher kernel.

We have provided a set of actionable ROD indicators forSevere Sepsis, which are readily interpretable and used in anICU setting (LR and LR-FA).

Preadmission use of Statins for septic patients is closelyrelated to severity and organ dysfunction.




Contributions

Contributions








Contributions

Contributions








Contributions

Contributions








Outline for Future Work


Generalise the methods and algorithms proposed in this Ph.D.to other general datasets.

Study Sepsis from a proteomics point of view (i.e.identification of biomarkers for Sepsis or other inflammatorymediators).

Exploit the algebraic relation between the FA model andDBN-RBM to obtain efficient algorithms to train the latter.

Study the algebraic relation between the simplified Fisherkernel and the QBK.































Publications

Publications

Ribas, V., Ruiz-Rodrıguez, J.D., Wojdel, A., Caballero-Lopez, J., Ruiz-Sanmartın A., Rello, J. and Vellido,A. Severe sepsis mortality prediction with Relevance Vector Machines. In Procs. of the 33rd AnnualInternational Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2011).

Ribas, V.J., Caballero-Lopez, J., Saez de Tejada, A., Ruiz-Rodrıguez, J.C., Ruiz-SanmartAn, A., Rello, J.,Vellido, A. Graphical models for ICU outcome prediction in sepsis patients treated with statin drugs, InProcs. of the Eigth International Meeting on Computational Intelligence Methods in Bioinformatics andBiostatistics, (CIBB 2011).

Ribas, V., Caballero-Lopez, J., Ruiz-Rodrıguez, J.C., Ruiz Sanmartın, A., Rello, J., and Vellido, A. On theuse of decision trees for ICU outcome prediction in sepsis patients treated with statins. In Procs. of theIEEE Symposium Series on Computational Intelligence / IEEE Symposium on Computational Intelligenceand Data Mining (IEEE SSCI CIDM 2011), pp.37-43.

Ribas, V.J, Vellido, A., Ruiz-Rodrıguez, J.C., Intelligent Management of Sepsis in the Intensive Care Unitin Intelligent Data Analysis for Real-Life Applications: Theory and Practice, IGI pub., in press.

Ribas V.J., Romero E., Ruiz-Rodrıguez, J.C., Vellido A., A Quotient Basis Kernel for the prediction ofmortality in severe sepsis patients, ESANN 2013. Accepted.

Ribas V.J., Romero E., Ruiz-Rodrıguez, J.C., Vellido A., A Quotient Basis Kernel for the prediction ofmortality in severe sepsis patients, ESANN 2013. Accepted.

Ribas V.J., Vellido A., Romero E., Ruiz-Rodrıguez, J.C., Sepsis Mortality Prediction with Quotient Basis,Medical & Biological Eng & Computing (MBEC), Springer. Submitted.




Publications

THANK YOU!!



PhD Defense

Technology

hebron university

soco technical

canonical

intensive

computational

future work

future work

critical care