Science Journal of Applied Mathematics and Statistics

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Beta Regression for Modeling a Covariate Adjusted ROC

Received: Jul. 24, 2018    Accepted: Aug. 09, 2018    Published: Sep. 11, 2018
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Abstract

Background: Several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. In this article, we present an alternative to two existing parametric and semi-parametric methods for estimating a covariate adjusted ROC. The existing methods utilize GLMs for binary data when the expected value equals the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Objective: The new method directly models the placement values through beta regression. Methods: We compare the proposed method to the existing models with simulation and a clinical study. Conclusion: The proposed method performs favorably with the commonly used parametric method and has better performance than the semi-parametric method when modeling the covariate adjusted ROC regression.

DOI 10.11648/j.sjams.20180604.11
Published in Science Journal of Applied Mathematics and Statistics ( Volume 6, Issue 4, August 2018 )
Page(s) 110-118
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

Placement Values, Beta Regression, ROC Regression

References
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[2] Zhang, L., Zhao, Y. D., and Tubbs, J. D. (2011). Inference for semiparametric AUC regression models with discrete covariates. Journal of Data Science, 9(4):625–637.
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[4] Buros, A., Tubbs, J., van Zyl, J. S. (2017). Application of AUC Regression for the Jonckheere Trend Test. Statistics in Biopharmaceutical Research, 9(2), 147-152.
[5] van Zyl, J. S., Tubbs, J. (2018). Multiple Comparison Methods in Zero-dose Control Trials. Journal of Data Science, 16(2), 299-326.
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[7] Pepe, M. S. (2000). An interpretation for the ROC curve and inference using GLM procedures. Biometrics, 56(2):352–359.
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[9] Pepe, M. and Cai, T. (2004). The analysis of placement values for evaluating discriminatory measures. Biometrics, 60(2):528–535.
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    Sarah Stanley, Jack Tubbs. (2018). Beta Regression for Modeling a Covariate Adjusted ROC. Science Journal of Applied Mathematics and Statistics, 6(4), 110-118. https://doi.org/10.11648/j.sjams.20180604.11

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    ACS Style

    Sarah Stanley; Jack Tubbs. Beta Regression for Modeling a Covariate Adjusted ROC. Sci. J. Appl. Math. Stat. 2018, 6(4), 110-118. doi: 10.11648/j.sjams.20180604.11

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    AMA Style

    Sarah Stanley, Jack Tubbs. Beta Regression for Modeling a Covariate Adjusted ROC. Sci J Appl Math Stat. 2018;6(4):110-118. doi: 10.11648/j.sjams.20180604.11

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  • @article{10.11648/j.sjams.20180604.11,
      author = {Sarah Stanley and Jack Tubbs},
      title = {Beta Regression for Modeling a Covariate Adjusted ROC},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {6},
      number = {4},
      pages = {110-118},
      doi = {10.11648/j.sjams.20180604.11},
      url = {https://doi.org/10.11648/j.sjams.20180604.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sjams.20180604.11},
      abstract = {Background: Several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. In this article, we present an alternative to two existing parametric and semi-parametric methods for estimating a covariate adjusted ROC. The existing methods utilize GLMs for binary data when the expected value equals the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Objective: The new method directly models the placement values through beta regression. Methods: We compare the proposed method to the existing models with simulation and a clinical study. Conclusion: The proposed method performs favorably with the commonly used parametric method and has better performance than the semi-parametric method when modeling the covariate adjusted ROC regression.},
     year = {2018}
    }
    

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    JO  - Science Journal of Applied Mathematics and Statistics
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    AB  - Background: Several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. In this article, we present an alternative to two existing parametric and semi-parametric methods for estimating a covariate adjusted ROC. The existing methods utilize GLMs for binary data when the expected value equals the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Objective: The new method directly models the placement values through beta regression. Methods: We compare the proposed method to the existing models with simulation and a clinical study. Conclusion: The proposed method performs favorably with the commonly used parametric method and has better performance than the semi-parametric method when modeling the covariate adjusted ROC regression.
    VL  - 6
    IS  - 4
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Author Information
  • Department of Statistical Science, Baylor University, Waco, USA

  • Department of Statistical Science, Baylor University, Waco, USA

  • Section