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 |
Placement Values, Beta Regression, ROC Regression
| [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. |
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
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
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
Share This Article
Twitter
Linked In
Facebook
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}
}
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 -
Email: