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A Comparison of the Lehmann and GLM ROC Models

Received: 8 December 2020     Accepted: 25 March 2021     Published: 7 May 2021
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Abstract

Recently, several regression methods have been developed to model the receiver operating characteristic curve (ROC), as a measure of accuracy for potential biomarker use in diagnostic testing and disease detection. In this paper, we investigate the Lehmann ROC regression model and compare it to more commonly used ROC regression methods that are found in the literature. The comparative performance of the methods are evaluated using simulated data from the normal, extreme value, and the Weibull distributions. Theory suggests that the Lehmann method should only work well when using the Weibull distribution. Our simulation results suggest that the performance of these methods is more complicated than the theory might suggest. The methods were demonstrated using data from a study concerning the clinical effectiveness of leukocyte elastase determination in the diagnosis of coronary artery disease (CAD).

Published in Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 2)
DOI 10.11648/j.sjams.20210902.13
Page(s) 57-72
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Cox’s Model, Youden Index, Extreme Value, Beta and Weibull Distributions

References
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[18] Margaret Sullivan Pepe and Tianxi Cai. The analysis of placement values for evaluating discriminatory measures. Biometrics, 60 (2): 528–535, 2004.
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Cite This Article
  • APA Style

    Melissa Innerst, Jack D. Tubbs, Musie Ghebremichael. (2021). A Comparison of the Lehmann and GLM ROC Models. Science Journal of Applied Mathematics and Statistics, 9(2), 57-72. https://doi.org/10.11648/j.sjams.20210902.13

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    ACS Style

    Melissa Innerst; Jack D. Tubbs; Musie Ghebremichael. A Comparison of the Lehmann and GLM ROC Models. Sci. J. Appl. Math. Stat. 2021, 9(2), 57-72. doi: 10.11648/j.sjams.20210902.13

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    AMA Style

    Melissa Innerst, Jack D. Tubbs, Musie Ghebremichael. A Comparison of the Lehmann and GLM ROC Models. Sci J Appl Math Stat. 2021;9(2):57-72. doi: 10.11648/j.sjams.20210902.13

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  • @article{10.11648/j.sjams.20210902.13,
      author = {Melissa Innerst and Jack D. Tubbs and Musie Ghebremichael},
      title = {A Comparison of the Lehmann and GLM ROC Models},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {9},
      number = {2},
      pages = {57-72},
      doi = {10.11648/j.sjams.20210902.13},
      url = {https://doi.org/10.11648/j.sjams.20210902.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210902.13},
      abstract = {Recently, several regression methods have been developed to model the receiver operating characteristic curve (ROC), as a measure of accuracy for potential biomarker use in diagnostic testing and disease detection. In this paper, we investigate the Lehmann ROC regression model and compare it to more commonly used ROC regression methods that are found in the literature. The comparative performance of the methods are evaluated using simulated data from the normal, extreme value, and the Weibull distributions. Theory suggests that the Lehmann method should only work well when using the Weibull distribution. Our simulation results suggest that the performance of these methods is more complicated than the theory might suggest. The methods were demonstrated using data from a study concerning the clinical effectiveness of leukocyte elastase determination in the diagnosis of coronary artery disease (CAD).},
     year = {2021}
    }
    

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    T1  - A Comparison of the Lehmann and GLM ROC Models
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    AB  - Recently, several regression methods have been developed to model the receiver operating characteristic curve (ROC), as a measure of accuracy for potential biomarker use in diagnostic testing and disease detection. In this paper, we investigate the Lehmann ROC regression model and compare it to more commonly used ROC regression methods that are found in the literature. The comparative performance of the methods are evaluated using simulated data from the normal, extreme value, and the Weibull distributions. Theory suggests that the Lehmann method should only work well when using the Weibull distribution. Our simulation results suggest that the performance of these methods is more complicated than the theory might suggest. The methods were demonstrated using data from a study concerning the clinical effectiveness of leukocyte elastase determination in the diagnosis of coronary artery disease (CAD).
    VL  - 9
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Author Information
  • Mathematics Department, Juniata College, Huntingdon, the United States

  • Department of Statistical Science, Baylor University, Waco, the United States

  • Biostatistics, Harvard University and Ragon Institute, Boston, the United States

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