Volume 6, Issue 4, August 2018, Page: 110-118
Beta Regression for Modeling a Covariate Adjusted ROC
Sarah Stanley, Department of Statistical Science, Baylor University, Waco, USA
Jack Tubbs, Department of Statistical Science, Baylor University, Waco, USA
Received: Jul. 24, 2018;       Accepted: Aug. 9, 2018;       Published: Sep. 11, 2018
DOI: 10.11648/j.sjams.20180604.11      View  364      Downloads  40
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.
Reference
[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.
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