Thursday 15h45 vicent_ribas ESANN

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Thursday 15h45 vicent_ribas ESANN

  1. 1. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsA Quotient Basis Kernel for the prediction ofmortality in severe sepsis patientsVicent J. RibasLSI - SOCOTechnical University of Catalonia (UPC)BarcelonaApril 19, 2013Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  2. 2. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsContents1 Introduction2 Database Description3 Risk of Death Assessment from Observed Data4 ConclusionsVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  3. 3. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsContents1 Introduction2 Database Description3 Risk of Death Assessment from Observed Data4 ConclusionsVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  4. 4. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  5. 5. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsIntroductionSepsis is a clinical syndrome defined by the presence ofinfection and Systemic Inflammatory Response Syndrome(SIRS).Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  6. 6. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsIntroductionSepsis 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  7. 7. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsIntroductionSepsis 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  8. 8. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsIntroductionSepsis 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  9. 9. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsThe medical management of sepsis and the study of itsprognosis and outcome is a relevant medical researchchallenge.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  10. 10. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsThe 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  11. 11. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsThe 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  12. 12. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsContents1 Introduction2 Database Description3 Risk of Death Assessment from Observed Data4 ConclusionsVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  13. 13. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsDatasetA prospective observational cohort study of adult patients withsevere sepsis was conducted at the Critical Care Departmentof the Vall d’ Hebron University Hospital (Barcelona, Spain).Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  14. 14. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsDatasetA 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 354 patients with severe sepsis was collected inthis ICU between June, 2007 and December, 2010.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  15. 15. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsDatasetA 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 354 patients with severe sepsis was collected inthis ICU between June, 2007 and December, 2010.55% of cases correspond to ‘medical’ sepsis.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  16. 16. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsDatasetA 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 354 patients with severe sepsis was collected inthis 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  17. 17. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsDatasetA 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 354 patients with severe sepsis was collected inthis 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  18. 18. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsAvailable AttributesThe collected data show the worst values for all variablesduring the first 24 hours of evolution of Severe Sepsis.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  19. 19. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsAvailable AttributesThe 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)Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  20. 20. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsAvailable AttributesSeverity was evaluated by means of the APACHE II score,which was 23.03 ± 9.62 for the population under study.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  21. 21. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsAvailable AttributesSeverity was evaluated by means of the APACHE II score,which was 23.03 ± 9.62 for the population under study.Mechanical ventilation was also assessed (66.71%).Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  22. 22. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsAvailable AttributesSeverity was evaluated by means of the APACHE II score,which was 23.03 ± 9.62 for the population under study.Mechanical ventilation was also assessed (66.71%).Compliance with the SSC resuscitation bundles was 31.41%.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  23. 23. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsAvailable AttributesSeverity was evaluated by means of the APACHE II score,which was 23.03 ± 9.62 for the population under study.Mechanical ventilation was also assessed (66.71%).Compliance with the SSC resuscitation bundles was 31.41%.The mortality rate intra-ICU for our study population was26.32%.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  24. 24. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsWhy generative kernels?Selection of kernel function for a given problem is not trivial.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  25. 25. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsWhy generative kernels?Selection of kernel function for a given problem is not trivial.One normally must have good insight about the problem athand.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  26. 26. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsWhy 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  27. 27. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsWhy 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  28. 28. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsWhy 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 analysed in this work.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  29. 29. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsQuotient Basis KernelLet A be a set of n unique points A = {a1, . . . , an} and τ a termordering. A Gr¨obner basis of A, G = g1, . . . , gt, is a Gr¨obner basisof I(A). Therefore, the points in A can be presented as the set ofsolutions of g1(a) = 0g2(a) = 0· · ·gt(a) = 0Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  30. 30. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsQuotient Basis KernelLet A, be a set of n × s unique support points A = {a1, . . . , an}and τ a term ordering. A monomial basis of the set of polynomialfunctions over A isESTτ = {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 Gr¨obnerbasis of I(A).Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  31. 31. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsQuotient Basis KernelLet 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 matrixZ = [ESTτ ] Awhere 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  32. 32. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsRegular Exponential FamilyLet P = (P|η ∈ N) be a regular exponential family with canonicalsufficient statistic T. Then the log likelihood function takes theforml(η|T) = n(ηtT − G(η))Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  33. 33. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsKernels based on the Jensen Shannon MetricVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  34. 34. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsKernels based on the Jensen Shannon MetricLet P = (P|η ∈ N) be a regular exponential family with canonicalsufficient statistic T. Then the log likelihood function takes theforml(η|T) = n(ηtT − G(η))This function accepts a convex - conjugate (Legendre Dual) of theforml(γ|T) = n(γtT − F(γ))In our case, the dual F is the negative log-entropy function.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  35. 35. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsKernels based on the Jensen Shannon MetricJS(γ1, γ2) =F(γ1) + F(γ2)2− Fγ1 + γ22.Centred kernel:φ(x, y) = JS(x, x0) + JS(y, x0) − JS(x, y) − JS(x0, x0).Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  36. 36. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsKernels based on the Jensen Shannon MetricJS(γ1, γ2) =F(γ1) + F(γ2)2− Fγ1 + γ22.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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  37. 37. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsKernels based on the Jensen Shannon MetricJS(γ1, γ2) =F(γ1) + F(γ2)2− Fγ1 + γ22.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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  38. 38. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsContents1 Introduction2 Database Description3 Risk of Death Assessment from Observed Data4 ConclusionsVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  39. 39. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsRoD 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  40. 40. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsRoD with Generative Kernels - QBK -ESTτ =1, x4, x3, x3x4,x2, x2x4, x2x3, x2x3x4,x22 , x22 x4, x22 x3, x22 x3x4,x32 , x32 x4, x32 x3, x32 x3x4,x42 , x42 x4, x42 x3, x42 x3x4,x52 , x52 x4, x62 , x1,x1x4, x1x3, x1x3x4, x1x2,x1x2x4, x1x2x3, x1x2x3x4, x1x22 ,x1x22 x4, x1x22 x3, x1x22 x3x4, x1x32 ,x1x32 x4, x1x32 x3, x1x32 x3x4, x1x42 ,x1x42 x4, x1x42 x3, x1x52Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  41. 41. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsRoD with Generative KernelsWe 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.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  42. 42. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsThe Risk-of-Death (ROD) formula based on the APACHE II scoreis a standard method in use in the critical care field.lnROD1 − ROD= −3.517 + 0.146 · A + , (1)where A is the APACHE II score and is a correction factor thatdepends on clinical traits at admission in the ICU. For instance, ifthe patient has undergone post-emergency surgery, is set to0.613.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  43. 43. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsResultsKernel AUC Error Rate Sens. Spec. CPU time [s]Quotient 0.89 0.18 0.70 0.86 1.45Exponential 0.75 0.21 0.70 0.82 1.64Inverse 0.62 0.22 0.70 0.82 1.68Centred 0.75 0.21 0.70 0.82 1.99Gaussian 0.83 0.24 0.65 0.81 1.56Poly (order 2) 0.69 0.28 0.71 0.76 1.59Linear 0.62 0.26 0.62 0.78 1.35Apache II 0.70 0.28 0.55 0.82 n/aVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  44. 44. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsContents1 Introduction2 Database Description3 Risk of Death Assessment from Observed Data4 ConclusionsVicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  45. 45. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsConclusionsThe investigated kernels provided accurate and medicallyactionable results, whilst keeping an acceptable balancebetween the different parameters of interest (accuracy rate,sensitivity and specificity).The QBK is defined through the Gr¨obner basis of an algebraicideal.It outperforms all kernels presented in this work as well as theclinical standard method based on the APACHE II score.All kernels presented outperform the standard APACHE IIROD formula in terms of accuracy.Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients
  46. 46. Introduction Database Description Risk of Death Assessment from Observed Data ConclusionsTHANK YOU!!Vicent J. Ribas LSI - SOCO Technical University of Catalonia (UPC) BarcelonaA Quotient Basis Kernel for the prediction of mortality in severe sepsis patients

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