A Comparison of the Lehmann and GLM ROC Models

Melissa Innerst; Jack D. Tubbs; Musie Ghebremichael

doi:doi:10.11648/j.sjams.20210902.13

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A Comparison of the Lehmann and GLM ROC Models

Melissa Innerst, Jack D. Tubbs, Musie Ghebremichael

Published in Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 2)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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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TY  - JOUR
T1  - A Comparison of the Lehmann and GLM ROC Models
AU  - Melissa Innerst
AU  - Jack D. Tubbs
AU  - Musie Ghebremichael
Y1  - 2021/05/07
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210902.13
DO  - 10.11648/j.sjams.20210902.13
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 57
EP  - 72
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210902.13
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
IS  - 2
ER  -

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Author Information

Melissa Innerst

Mathematics Department, Juniata College, Huntingdon, the United States
Jack D. Tubbs

Department of Statistical Science, Baylor University, Waco, the United States
Musie Ghebremichael

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - A Comparison of the Lehmann and GLM ROC Models
AU  - Melissa Innerst
AU  - Jack D. Tubbs
AU  - Musie Ghebremichael
Y1  - 2021/05/07
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210902.13
DO  - 10.11648/j.sjams.20210902.13
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 57
EP  - 72
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210902.13
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
IS  - 2
ER  -

Copy | Download