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

Author

Listed:
  • Arthur De Sá Ferreira

    (Postgraduate Program of Rehabilitation Science, Centro Universitário Augusto Motta)

  • Ney Meziat-Filho

    (Postgraduate Program of Rehabilitation Science, Centro Universitário Augusto Motta)

  • Ana Paula Antunes Ferreira

    (Postgraduate Program of Rehabilitation Science, Centro Universitário Augusto Motta
    Instituto Brasileiro de Osteopatia)

Abstract

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.

Suggested Citation

  • Arthur De Sá Ferreira & Ney Meziat-Filho & Ana Paula Antunes Ferreira, 2021. "Double threshold receiver operating characteristic plot for three-modal continuous predictors," Computational Statistics, Springer, vol. 36(3), pages 2231-2245, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01080-9
    DOI: 10.1007/s00180-021-01080-9
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    References listed on IDEAS

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    1. Jørgen Hilden, 1991. "The Area under the ROC Curve and Its Competitors," Medical Decision Making, , vol. 11(2), pages 95-101, June.
    2. Takaya Saito & Marc Rehmsmeier, 2015. "The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-21, March.
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