Modelisation de la courbe ROC a partir des distributions de Pearson

Abstract

The Receiver Operating Characteristic curve (ROC) is frequently used in medical studies to assess the efficiency of a diagnostic test. There exists two different ways to model the curve theoretically: direct and indirect. The direct method consists of constructing the curve based on the observed data. This method is less appealing in that the curve obtained is not easily interpretable. In the indirect method, a distribution is assumed for both the diseased and non-diseased patients. The normal distribution has been used to model both types of patients owing to the ease of its manipulation. In this thesis, we propose the use of the Pearsonian system of distributions in order to select the distribution for the diseased and non-diseased patients. An approach using a Monte Carlo simulation provides a confidence band for the derived ROC. The approach is evaluated using normal, gamma and beta distributed data. It is also tested on a real data set. It is seen that the Pearson based estimation of the ROC is at least as accurate as the normal theory based approach and often superior. Key words : ROC curve, Pearson distribution, AUC, pAUC, trapezoidal rule, Mann-Whitney U-Stat, Monte-Carlo simulation.