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

Abstract

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).

Keywords:

• ROC curves
• mixture distributions
• double threshold
• Weibull distribution
• lognormal distribution
• Poisson distribution

Acknowledgments

The authors would like to thank Prof. Arthur de Sà Ferreira, Centro Universitário Augusto Motta, Rio de Janeiro, Brazil, for providing the real data set to conduct the study. Furthermore, the authors are grateful to associate editor and two anonymous reviews for their constructive comments to improve the quality of the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Code availability

The computational code can be requested from the corresponding author.