title: Sepsis mortality prediction with the Quotient Basis Kernel.
abstract: OBJECTIVE
  This paper presents an algorithm to assess the risk of death in patients with sepsis. Sepsis is a common clinical syndrome in the intensive care unit (ICU) that can lead to severe sepsis, a severe state of septic shock or multi-organ failure. The proposed algorithm may be implemented as part of a clinical decision support system that can be used in combination with the scores deployed in the ICU to improve the accuracy, sensitivity and specificity of mortality prediction for patients with sepsis.
  
  
  METHODS
  In this paper, we used the Simplified Acute Physiology Score (SAPS) for ICU patients and the Sequential Organ Failure Assessment (SOFA) to build our kernels and algorithms. In the proposed method, we embed the available data in a suitable feature space and use algorithms based on linear algebra, geometry and statistics for inference. We present a simplified version of the Fisher kernel (practical Fisher kernel for multinomial distributions), as well as a novel kernel that we named the Quotient Basis Kernel (QBK). These kernels are used as the basis for mortality prediction using soft-margin support vector machines. The two new kernels presented are compared against other generative kernels based on the Jensen-Shannon metric (centred, exponential and inverse) and other widely used kernels (linear, polynomial and Gaussian). Clinical relevance is also evaluated by comparing these results with logistic regression and the standard clinical prediction method based on the initial SAPS score.
  
  
  RESULTS
  As described in this paper, we tested the new methods via cross-validation with a cohort of 400 test patients. The results obtained using our methods compare favourably with those obtained using alternative kernels (80.18% accuracy for the QBK) and the standard clinical prediction method, which are based on the basal SAPS score or logistic regression (71.32% and 71.55%, respectively). The QBK presented a sensitivity and specificity of 79.34% and 83.24%, which outperformed the other kernels analysed, logistic regression and the standard clinical prediction method based on the basal SAPS score.
  
  
  CONCLUSIONS
  Several scoring systems for patients with sepsis have been introduced and developed over the last 30 years. They allow for the assessment of the severity of disease and provide an estimate of in-hospital mortality. Physiology-based scoring systems are applied to critically ill patients and have a number of advantages over diagnosis-based systems. Severity score systems are often used to stratify critically ill patients for possible inclusion in clinical trials. In this paper, we present an effective algorithm that combines both scoring methodologies for the assessment of death in patients with sepsis that can be used to improve the sensitivity and specificity of the currently available methods.
authors.affiliation: Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona), Spain. Electronic address: vribas@crm.cat.
authors.forename: Vicent J
authors.initials: VJ
authors.lastname: Ribas Ripoll
authors.affiliation: Soft Computing (SOCO) Research Group, Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Edifici Omega, Campus Nord, 08034 Barcelona, Spain.
authors.forename: Alfredo
authors.initials: A
authors.lastname: Vellido
authors.affiliation: Soft Computing (SOCO) Research Group, Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Edifici Omega, Campus Nord, 08034 Barcelona, Spain.
authors.forename: Enrique
authors.initials: E
authors.lastname: Romero
authors.affiliation: Shock Organ Dysfunction and Resuscitation (SODIR) Research Group, Critical Care Service, Vall d'Hebron University Hospital, Vall d'Hebron Research Institute, Universitat Autònoma de Barcelona, Passeig de la Vall d'Hebron, 119-129, 08035 Barcelona, Spain.
authors.forename: Juan Carlos
authors.initials: JC
authors.lastname: Ruiz-Rodríguez
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D006801:Humans; D018570:Risk Assessment / Q000379:methods*; D012680:Sensitivity and Specificity; D018805:Sepsis / Q000401:mortality*
keywords: Critical care; Kernels; Mortality prediction; Sepsis; Support vector machines