title: Tools to identify linear combination of prognostic factors which maximizes area under receiver operator curve.
abstract: BACKGROUND
  The linear combination of variables is an attractive method in many medical analyses targeting a score to classify patients. In the case of ROC curves the most popular problem is to identify the linear combination which maximizes area under curve (AUC). This problem is complete closed when normality assumptions are met. With no assumption of normality search algorithm are avoided because it is accepted that we have to evaluate AUC n(d) times where n is the number of distinct observation and d is the number of variables.
  
  
  METHODS
  For d = 2, using particularities of AUC formula, we described an algorithm which lowered the number of evaluations of AUC from n(2) to n(n-1) + 1. For d > 2 our proposed solution is an approximate method by considering equidistant points on the unit sphere in R(d) where we evaluate AUC.
  
  
  RESULTS
  The algorithms were applied to data from our lab to predict response of treatment by a set of molecular markers in cervical cancers patients. In order to evaluate the strength of our algorithms a simulation was added.
  
  
  CONCLUSIONS
  In the case of no normality presented algorithms are feasible. For many variables computation time could be increased but acceptable.
authors: Oncology Institute "Prof.Dr. Ion Chiricuta", Biostatistics and Medical Informatics Department, Republicii 34-36, 400015 Cluj-Napoca, Romania.
authors: Nicolae
authors: N
authors: Todor
authors: Oncology Institute "Prof.Dr. Ion Chiricuta", Radiotherapy Department, Republicii 34-36, 400015 Cluj-Napoca, Romania.
authors: Irina
authors: I
authors: Todor
authors: Company for Applied Informatics, Republicii 101-102, 400015 Cluj-Napoca, Romania.
authors: Gavril
authors: G
authors: Săplăcan
keywords: Area under curve; Linear combination; Receiver operator characteristics; Sensitivity; Specificity