Beta Regression for Modeling a Covariate Adjusted ROC
Science Journal of Applied Mathematics and Statistics
Volume 6, Issue 4, August 2018, Pages: 110-118
Received: Jul. 24, 2018; Accepted: Aug. 9, 2018; Published: Sep. 11, 2018
Views 1001      Downloads 136
Authors
Sarah Stanley, Department of Statistical Science, Baylor University, Waco, USA
Jack Tubbs, Department of Statistical Science, Baylor University, Waco, USA
Article Tools
Follow on us
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.
Keywords
Placement Values, Beta Regression, ROC Regression
To cite this article
Sarah Stanley, Jack Tubbs, Beta Regression for Modeling a Covariate Adjusted ROC, Science Journal of Applied Mathematics and Statistics. Vol. 6, No. 4, 2018, pp. 110-118. doi: 10.11648/j.sjams.20180604.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186