The document describes a study that used relevance vector machines (RVM) to predict mortality from severe sepsis based on patient data. RVM analysis of 354 patients achieved 80% accuracy in predicting mortality, identifying 4 key factors - number of dysfunctional organs, use of mechanical ventilation, APACHE II score, and early resuscitation bundles. The RVM approach improved interpretability over other methods by selecting only the most relevant predictors.

1. Introduction
Materials
Results
Conclusions
Acknowledgements
Severe Sepsis Mortality Prediction with
Relevance Vector Machines
Vicent J. Ribas
SOCO Research Group
Techical University of Catalonia (UPC)
Barcelona, Spain
August 30, 2011
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

2. Introduction
Materials
Results
Conclusions
Acknowledgements
Contents
1 Introduction
2 Materials
3 Results
4 Conclusions
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

3. Introduction
Materials
Results
Conclusions
Acknowledgements
Contents
1 Introduction
2 Materials
3 Results
4 Conclusions
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

4. Introduction
Materials
Results
Conclusions
Acknowledgements
Introduction
Sepsis is a clinical syndrome defined by the presence of both
infection and Systemic Inflammatory Response Syndrome
(SIRS).
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

5. Introduction
Materials
Results
Conclusions
Acknowledgements
Introduction
Sepsis is a clinical syndrome defined by the presence of both
infection and Systemic Inflammatory Response Syndrome
(SIRS).
This can lead to severe sepsis (organ dysfunction) or to septic
shock (severe sepsis with hypotension refractory to fluid
administration) and multiorgan failure.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

6. Introduction
Materials
Results
Conclusions
Acknowledgements
Introduction
Sepsis is a clinical syndrome defined by the presence of both
infection and Systemic Inflammatory Response Syndrome
(SIRS).
This can lead to severe sepsis (organ dysfunction) or to septic
shock (severe sepsis with hypotension refractory to fluid
administration) and multiorgan failure.
In western countries, septic patients account for as much as
25% of ICU bed utilization and the pathology occurs in 1% 2% of all hospitalizations.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

7. Introduction
Materials
Results
Conclusions
Acknowledgements
Introduction
Sepsis is a clinical syndrome defined by the presence of both
infection and Systemic Inflammatory Response Syndrome
(SIRS).
This can lead to severe sepsis (organ dysfunction) or to septic
shock (severe sepsis with hypotension refractory to fluid
administration) and multiorgan failure.
In western countries, septic patients account for as much as
25% 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 and
20.7% for severe sepsis, and up to 45.7% for septic shock.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

8. Introduction
Materials
Results
Conclusions
Acknowledgements
The medical management of sepsis and the study of its
prognosis and outcome is a relevant medical research
challenge.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

9. Introduction
Materials
Results
Conclusions
Acknowledgements
The medical management of sepsis and the study of its
prognosis and outcome is a relevant medical research
challenge.
Provided that such methods are to be used in a clinical
environment (ICU), it requires prediction methods that are
robust, accurate and readily interpretable.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

10. Introduction
Materials
Results
Conclusions
Acknowledgements
The medical management of sepsis and the study of its
prognosis and outcome is a relevant medical research
challenge.
Provided that such methods are to be used in a clinical
environment (ICU), it requires prediction methods that are
robust, accurate and readily interpretable.
Here we present a method based on Relevance Vector
Machines (RVM) and compare it with other well established
shrinkage methods.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

11. Introduction
Materials
Results
Conclusions
Acknowledgements
Contents
1 Introduction
2 Materials
3 Results
4 Conclusions
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

12. Introduction
Materials
Results
Conclusions
Acknowledgements
Materials
A prospective observational cohort study of adult patients with
severe sepsis was conducted at the Critical Care Department
of the Vall d’ Hebron University Hospital (Barcelona, Spain).
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

13. Introduction
Materials
Results
Conclusions
Acknowledgements
Materials
A prospective observational cohort study of adult patients with
severe sepsis was conducted at the Critical Care Department
of the Vall d’ Hebron University Hospital (Barcelona, Spain).
Data from 354 patients with severe sepsis was collected at
this ICU between June, 2007 and December, 2010.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

14. Introduction
Materials
Results
Conclusions
Acknowledgements
Materials
A prospective observational cohort study of adult patients with
severe sepsis was conducted at the Critical Care Department
of the Vall d’ Hebron University Hospital (Barcelona, Spain).
Data from 354 patients with severe sepsis was collected at
this ICU between June, 2007 and December, 2010.
The mean age of the patients in the database was 57.08 (with
standard deviation ±16.65) years.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

15. Introduction
Materials
Results
Conclusions
Acknowledgements
Materials
A prospective observational cohort study of adult patients with
severe sepsis was conducted at the Critical Care Department
of the Vall d’ Hebron University Hospital (Barcelona, Spain).
Data from 354 patients with severe sepsis was collected at
this ICU between June, 2007 and December, 2010.
The mean age of the patients in the database was 57.08 (with
standard deviation ±16.65) years.
40% of patients were female.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

16. Introduction
Materials
Results
Conclusions
Acknowledgements
The collected data show the worst values for all variables
during the first 24 hours of evolution of Severe Sepsis.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

17. Introduction
Materials
Results
Conclusions
Acknowledgements
The collected data show the worst values for all variables
during the first 24 hours of evolution of Severe Sepsis.
Organ dysfunction was evaluated by means of the SOFA score
system, which objectively measures organ dysfunction for 6
organs/systems.
Cardiovascular (CV)
Respiratory (RESP)
Central Nerv. Sys. (CNS)
Hepatic (HEPA)
Renal (REN)
Vicent J. Ribas
2.86
2.31
0.48
0.48
1.06
(1.62)
(1.15)
(1.00)
(0.92)
(1.20)
Haematologic (HAEMATO)
Global SOFA score
Dysf. Organs (SOFA 1-2)
Failure Organs (SOFA 3-4)
Total Dysf. Organs
0.78
7.94
1.68
1.51
3.18
(1.14)
(3.86)
(1.09)
(1.02)
(1.32)
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

18. Introduction
Materials
Results
Conclusions
Acknowledgements
The collected data show the worst values for all variables
during the first 24 hours of evolution of Severe Sepsis.
Organ dysfunction was evaluated by means of the SOFA score
system, which objectively measures organ dysfunction for 6
organs/systems.
Cardiovascular (CV)
Respiratory (RESP)
Central Nerv. Sys. (CNS)
Hepatic (HEPA)
Renal (REN)
2.86
2.31
0.48
0.48
1.06
(1.62)
(1.15)
(1.00)
(0.92)
(1.20)
Haematologic (HAEMATO)
Global SOFA score
Dysf. Organs (SOFA 1-2)
Failure Organs (SOFA 3-4)
Total Dysf. Organs
0.78
7.94
1.68
1.51
3.18
(1.14)
(3.86)
(1.09)
(1.02)
(1.32)
Severity was evaluated by means of the APACHE II score,
which was 23.03 ± 9.62 for the population under study.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

19. Introduction
Materials
Results
Conclusions
Acknowledgements
The collected data show the worst values for all variables
during the first 24 hours of evolution of Severe Sepsis.
Organ dysfunction was evaluated by means of the SOFA score
system, which objectively measures organ dysfunction for 6
organs/systems.
Cardiovascular (CV)
Respiratory (RESP)
Central Nerv. Sys. (CNS)
Hepatic (HEPA)
Renal (REN)
2.86
2.31
0.48
0.48
1.06
(1.62)
(1.15)
(1.00)
(0.92)
(1.20)
Haematologic (HAEMATO)
Global SOFA score
Dysf. Organs (SOFA 1-2)
Failure Organs (SOFA 3-4)
Total Dysf. Organs
0.78
7.94
1.68
1.51
3.18
(1.14)
(3.86)
(1.09)
(1.02)
(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 was
29.44%.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

20. Introduction
Materials
Results
Conclusions
Acknowledgements
List of attributes used in this study:
Age
Gender
Sepsis Focus
Germ Class
Polimicrobial Infection
Base Pathology
Dysfunctioning Organs for
SOFA 1-2
Haemocultures 6h
Dysfunctioning Organs for
SOFA 3-4
Volume 6h
Total Number of
Dysfunctioning Organs
Haematocrit 6h
Antibiotics 6h
O2 Central Venous Saturation 6h
Mechanical Ventilation
Transfusions 6h
Dobutamine 6h
Respiratory SOFA Score
Oxygenation Index
PaO2 /FiO2
CNS SOFA score
Vasoactive Drugs
Surviving Sepsis Campaign
Bundles 24h
Hepatic SOFA Score
Platelet Count
Glycaemia 24h
Renal SOFA Score
APACHE II Score
PPlateau
Haematologic SOFA Score
Surviving Sepsis Campaign
Bundles 6h
Worst Lactate
Cardiovascular SOFA Score
Total SOFA Score
Vicent J. Ribas
O2 Central Venous Saturation
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

21. Introduction
Materials
Results
Conclusions
Acknowledgements
Contents
1 Introduction
2 Materials
3 Results
4 Conclusions
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

22. Introduction
Materials
Results
Conclusions
Acknowledgements
Mortality Prediction with RVM
The model performance was evaluated by means of 10-Fold
Cross-Validation.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

23. Introduction
Materials
Results
Conclusions
Acknowledgements
Mortality Prediction with RVM
The model performance was evaluated by means of 10-Fold
Cross-Validation.
The RVM yielded an accuracy of mortality prediction of 0.80;
a prediction error of 0.24; a sensitivity of 0.66; and a
specificity of 0.80.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

24. Introduction
Materials
Results
Conclusions
Acknowledgements
Mortality Prediction with RVM
The model performance was evaluated by means of 10-Fold
Cross-Validation.
The RVM yielded an accuracy of mortality prediction of 0.80;
a prediction error of 0.24; a sensitivity of 0.66; and a
specificity of 0.80.
RVM selected the following attributes (corresponding to
weights):
Number of dysfunctioning organs (w1 = −0.039)
Mechanical Ventilation (w2 = −0.101)
APACHE II (w3 = −0.337)
Resuscitation Bundles (6h) (w4 = 0.037)
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

25. Introduction
Materials
Results
Conclusions
Acknowledgements
The coefficients corresponding to the rest of attributes were
set to values close to zero as part of the training process. This
reduces the number of attributes (34 to just 4) and improves
its interpretability.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

26. Introduction
Materials
Results
Conclusions
Acknowledgements
The coefficients corresponding to the rest of attributes were
set to values close to zero as part of the training process. This
reduces the number of attributes (34 to just 4) and improves
its interpretability.
The negative weights (number of dysfunctioning organs,
mechanical ventilation, APACHE II) are related to a higher
mortality risk.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

27. Introduction
Materials
Results
Conclusions
Acknowledgements
The coefficients corresponding to the rest of attributes were
set to values close to zero as part of the training process. This
reduces the number of attributes (34 to just 4) and improves
its interpretability.
The negative weights (number of dysfunctioning organs,
mechanical ventilation, APACHE II) are related to a higher
mortality risk.
The SSC bundles (resuscitation bundles) are associated to a
protective effect (i.e. antibiotics administration, performance
of haemocultures, administration of volume and vasoactive
drugs and so on).
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

28. Introduction
Materials
Results
Conclusions
Acknowledgements
Comparison with Shrinkage Feature Selection Methods for
Logistic Regression
The predictive ability of the RVM has also been compared to
that of other well established shrinkage methods for regression.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

29. Introduction
Materials
Results
Conclusions
Acknowledgements
Comparison with Shrinkage Feature Selection Methods for
Logistic Regression
The predictive ability of the RVM has also been compared to
that of other well established shrinkage methods for regression.
The selected attributes and coefficients for each method were:
Lasso:
Age (w1 = 0.007)
Ridge Regression:
Number of dysfunctioning
organs for SOFA 3-4
(w1 = −0.021)
APACHE II (w2 = −0.127)
Worst Lactate
(w3 = −0.126).
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)
Logistic Regression with backward
feature selection:
Intercept (w1 = 4.16)
Number of Dysfunctioning
Organs (w1 = −0.57)
APACHE II (w2 = −0.09)
Worst Lactate (w3 = −0.30)
SvcO2 (w8 = −0.006).
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

30. Introduction
Materials
Results
Conclusions
Acknowledgements
The three shrinkage methods evaluated in this section agreed
in detecting as prognostic factors the Severity measured by
the APACHE II score and acidosis.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

31. Introduction
Materials
Results
Conclusions
Acknowledgements
The three shrinkage methods evaluated in this section agreed
in detecting as prognostic factors the Severity measured by
the APACHE II score and acidosis.
Organ dysfunction and mechanical ventilation or other
parameters related to it like PaO2 /FiO2 also play a role in the
prognosis of Sepsis.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

32. Introduction
Materials
Results
Conclusions
Acknowledgements
The three shrinkage methods evaluated in this section agreed
in detecting as prognostic factors the Severity measured by
the APACHE II score and acidosis.
Organ dysfunction and mechanical ventilation or other
parameters related to it like PaO2 /FiO2 also play a role in the
prognosis of Sepsis.
The accuracy of each method was the following:
Method
RVM
Logistic
Ridge
Lasso
Vicent J. Ribas
AUC
0.80
0.77
0.69
0.70
Error Rate
0.24
0.27
0.28
0.32
Sens.
0.66
0.66
0.67
0.67
Spec.
0.80
0.76
0.73
0.68
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

33. Introduction
Materials
Results
Conclusions
Acknowledgements
Comparison with the APACHE II Mortality Score
The Risk-of-Death (ROD) formula based on the APACHE II
score can be expressed as:
ln
ROD
1 − ROD
= −3.517 + 0.146 · A +
where A is the APACHE II score and is a correction factor
depending on clinical traits at admission in the ICU.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

34. Introduction
Materials
Results
Conclusions
Acknowledgements
Comparison with the APACHE II Mortality Score
The Risk-of-Death (ROD) formula based on the APACHE II
score can be expressed as:
ln
ROD
1 − ROD
= −3.517 + 0.146 · A +
where A is the APACHE II score and is a correction factor
depending on clinical traits at admission in the ICU.
The application of this ROD formula to the population under
study yields an error rate of 0.28 (higher than RVM), a
sensitivity of 0.55 (very low) and a specificity of 0.80. The
AUC was 0.70 (lower than RVM).
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

35. Introduction
Materials
Results
Conclusions
Acknowledgements
Contents
1 Introduction
2 Materials
3 Results
4 Conclusions
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

36. Introduction
Materials
Results
Conclusions
Acknowledgements
Conclusions
In the assessment of ROD for critically ill patients, sensitivity
is important due to the fact that more aggressive treatment
and therapeutic actions may result in better outcomes for high
risk patients.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

37. Introduction
Materials
Results
Conclusions
Acknowledgements
Conclusions
In the assessment of ROD for critically ill patients, sensitivity
is important due to the fact that more aggressive treatment
and therapeutic actions may result in better outcomes for high
risk patients.
We have put forward an RVM-based method for the
prediction of ROD in septic patients, which has been shown to
produce accurate, specific results, while improving the
interpretability and actionability of the results.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

38. Introduction
Materials
Results
Conclusions
Acknowledgements
Conclusions
In the assessment of ROD for critically ill patients, sensitivity
is important due to the fact that more aggressive treatment
and therapeutic actions may result in better outcomes for high
risk patients.
We have put forward an RVM-based method for the
prediction of ROD in septic patients, which has been shown to
produce accurate, specific results, while improving the
interpretability and actionability of the results.
This method has proven to be superior in terms of accuracy
(error rate, specificity and AUC) than other well established
shrinkage methods (Lasso and Ridge).
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

39. Introduction
Materials
Results
Conclusions
Acknowledgements
From a medical viewpoint, this study shows that it is possible
to derive a reliable prognostic score from a parsimonious set of
physiopathologic and therapeutic variables, which are available
at the onset of severe sepsis for medical experts at the ICU.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

40. Introduction
Materials
Results
Conclusions
Acknowledgements
From a medical viewpoint, this study shows that it is possible
to derive a reliable prognostic score from a parsimonious set of
physiopathologic and therapeutic variables, which are available
at the onset of severe sepsis for medical experts at the ICU.
The method may be understood as a generalization of the
ROD formula which takes not only the contribution of the
APACHE II score into consideration, but also other important
life-threatening clinical traits
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

41. Introduction
Materials
Results
Conclusions
Acknowledgements
From a medical viewpoint, this study shows that it is possible
to derive a reliable prognostic score from a parsimonious set of
physiopathologic and therapeutic variables, which are available
at the onset of severe sepsis for medical experts at the ICU.
The method may be understood as a generalization of the
ROD formula which takes not only the contribution of the
APACHE II score into consideration, but also other important
life-threatening clinical traits
The performance of the proposed method has been evaluated
in a single ICU and a limited population sample. Future work
should lead towards a multi-centric prospective study, in order
to validate its generalizability.
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines

42. Introduction
Materials
Results
Conclusions
Acknowledgements
THANK YOU
Vicent J. Ribas
SOCO Research Group Techical University of Catalonia (UPC) Barcelona, Spain
Severe Sepsis Mortality Prediction with Relevance Vector Machines