Modelling receiver operating characteristic curves using Gaussian mixtures

The receiver operating characteristic (ROC) curve is widely applied in measuring the performance of diagnostic tests. Many direct and indirect approaches have been proposed for modelling the ROC curve and, because of its tractability, the Gaussian distribution has typically been used to model both diseased and non-diseased populations. Using a Gaussian mixture model leads to a more flexible approach that better accounts for atypical data. The Monte Carlo method can be used to circumvent the absence of a closed-form for a functional form of the ROC curve. The proposed method, in which a Gaussian mixture is used in conjunction with the Monte Carlo method, performs favourably when compared to the crude binormal curve and the semi-parametric frequentist binormal ROC using the well-known LABROC procedure.