Double threshold receiver operating characteristic plot for three-modal continuous predictors

The receiver-operating characteristics (stROC) analysis depicts the performance of a population-wise bimodal-distributed, quantitative continuous random variable for distinguishing dichotomous outcomes using a single threshold. However, test results that have three-modal distributions show no-better-than-chance discriminative performance. This study proposes a parameter-free ROC plot analysis with an application to random variables with a population-wise three-modal distribution. A double-threshold ROC plot (dtROC) is constructed by replacing the single threshold by a double threshold. The sensitivity–specificity coordinates are selected for maximizing the sensitivity for a given specificity value. The generalizability of the method is investigated using computational simulations of a mixture of Gaussian distributions. The clinical application is studied by secondary data analysis of a palpation test to locate the C7 spinous process using the modified thorax-rib static method. The simulation shows a poor discrimination performance of the stROC plot (area under the ROC plot [AUROC]   0.9 in 51% of the simulated samples). The accuracy of the palpation test using dtROC (AUROC = 0.652 95%CI = [0.597; 0.775], thresholds = 24.2 to 26.8 cm) was higher as compared to the ROC (AUROC = 0.517 95%CI = [0.385; 0.659]; threshold = 25.45 cm). The dtROC plot analysis outperforms the stROC plot when applied to test results with three-modal distributions.