Tools to identify linear combination of prognostic factors which maximizes area under receiver operator curve.

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.