| Peer-Reviewed

Beta Regression for Modeling a Covariate Adjusted ROC

Received: 24 July 2018     Accepted: 9 August 2018     Published: 11 September 2018
Views:       Downloads:
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.

Published in Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 4)
DOI 10.11648/j.sjams.20180604.11
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), 2018. Published by Science Publishing Group

Keywords

Placement Values, Beta Regression, ROC Regression

References
[1] Dodd, L. and Pepe, M. (2003). Semiparametric regression for the area under the receiver operating characteristic curve. Journal of the American Statistical Association, 98:409–417.
[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.
[3] Buros, A., Tubbs, J., van Zyl, J. S. (2017). AUC Regression for Multiple Comparisons with the Jonckheere Trend Test. Statistics in Biopharmaceutical Research, 9(3), 279-285.
[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.
[6] [6] Pepe, M. S. (1998). Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics, pages 124–135.
[7] Pepe, M. S. (2000). An interpretation for the ROC curve and inference using GLM procedures. Biometrics, 56(2):352–359.
[8] Alonzo, T. A. and Pepe, M. S. (2002). Distribution-free ROC analysis using binary regression techniques. Biostatistics, 3(3):421–432.
[9] Pepe, M. and Cai, T. (2004). The analysis of placement values for evaluating discriminatory measures. Biometrics, 60(2):528–535.
[10] Cai, T. (2004). Semi-parametric ROC regression analysis with placement values. Biostatistics, 5(1):45–60.
[11] Bamber, D. (1975). The area above the ordinal dominance graph and the area below the receiver operating characteristic graph. Journal of mathematical psychology, 12(4):387–415.
[12] Rodriguez-Alvarez, M. X., Tahoces, P. G., Cadarso-Suarez, C., and Lado, M. J. (2011). Comparative study of roc regression techniques – applications for the computer-aided diagnostic system in breast cancer detection. Computational Statistics and Data Analysis, 55(1):888–902.
[13] Ferrari, S. and Cribari-Neto, F. (2004). Beta regression for modeling rates and proportions. Journal of Applied Statistics, 31(7):799–815.
[14] Fubini, G. (1907). Sugli integrali multipli. Rend. Acc. Naz. Lincei, 16:608–614.
[15] Balakrishnan, N. and Nevzorov, V. (2003). A Primer on Statistical Distributions. Wiley, New Jersey.
[16] Elman, M. J., Ayala, A., Bressler, N. M., Browning, D., Flaxel, C. J., Glassman, A. R., Jampol, L. M., and Stone, T. W. (2015). Intravitreal ranibizumab for diabetic macular edema with prompt versus deferred laser treatment: 5-year randomized trial results. Ophthalmology, 122(2):375–381.
Cite This Article
  • APA Style

    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

    Copy | Download

    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

    Copy | Download

    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

    Copy | Download

  • @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://article.sciencepublishinggroup.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}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Beta Regression for Modeling a Covariate Adjusted ROC
    AU  - Sarah Stanley
    AU  - Jack Tubbs
    Y1  - 2018/09/11
    PY  - 2018
    N1  - https://doi.org/10.11648/j.sjams.20180604.11
    DO  - 10.11648/j.sjams.20180604.11
    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  - 110
    EP  - 118
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20180604.11
    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
    ER  - 

    Copy | Download

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

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

  • Sections