Modelling receiver operating characteristic curves using Gaussian mixtures

A comparison of single- and double-threshold ROC plots for mixture distributions

The receiver operating characteristics (ROC) analysis is commonly used in clinical settings to check the performance of a single threshold for distinguishing population-wise bimodal-distributed test results. However, for population-wise three-modal distributed test results, a single threshold ROC (stROC) analysis showed poor discriminative performance. The purpose of this study is to use a double-threshold ROC analysis for the three-modal distributed test results to provide better discriminative performance than the stROC analysis. A double-threshold receiver operating characteristic plot (dtROC) is constructed by replacing the single threshold with a double threshold. The sensitivity and specificity coordinates are chosen to maximize sensitivity for a given specificity value. Besides a simulation study assuming a mixture of lognormal, Poisson, and Weibull distributions, a clinical application is examined by a secondary data analysis of palpation test results of the C7 spinous process using the modified thorax-rib static technique. For the assumed mixture models, the discrimination performance of dtROC analysis outperforms the stROC analysis (area under ROC (AUROC) increased from 0.436 to 0.983 for lognormal distributed test results, 0.676 to 0.752 for the Poisson distribution, and 0.674 to 0.804 for Weibull distribution).

Efficient nonparametric confidence bands for receiver operating-characteristic curves

Receiver operating-characteristic curve is a popular graphical method frequently used in order to study the diagnostic capacity of continuous (bio)markers. In spite of the existence of a huge number of papers devoted to both theoretical and practical aspects of this topic, the construction of confidence bands has had little impact in the specialized literature. As far as the authors know, in the CRAN there are only three R packages providing receiver operating-characteristic curve confidence regions: plotROC, pROC and fbroc. This work tries to fill this gap studying and proposing a new nonparametric method to build confidence bands for both the standard receiver operating-characteristic curve and its generalization for nonmonotone relationships. The behavior of the proposed procedure is studied via Monte Carlo simulations and the methodology is applied on two real-world biomedical problems. In addition, an R function to compute the proposed and some of the previously existing methodologies is provided as online supplementary material.