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A General Regression Methodology for ROC Curve Estimation

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  • Anna N. Angelos Tosteson
  • Colin B. Begg

Abstract

A method for applying generalized ordinal regression models to categorical rating data to estimate and analyze receiver operating characteristic (ROC) curves is presented. These models permit parsimonious adjustment of ROC curve parameters for relevant covariates through two regression equations that correspond to location and scale. Particular shapes of ROC curves are interpreted in relation to the kind of covariates included in the two regressions. The model is shown to be flexible because it is not restricted to the assumption of binormality that is commonly employed in smoothed ROC curve estimation, although the binormal model is one particular form of the more general model. The new method provides a mechanism for pinpointing the effect that interobserver variability has on the ROC curve. It also allows for the adjustment of ROC curves for temporal variation and case mix, and provides a way to assess the incremental diagnostic value of a test. The new methodology is recommended because it substantially improves the ability to assess diagnostic tests using ROC curves. Key words: ROC curves; ordinal regression; technology assessment; diagnostic tests. (Med Decis Making 8:204-215, 1988)

Suggested Citation

  • Anna N. Angelos Tosteson & Colin B. Begg, 1988. "A General Regression Methodology for ROC Curve Estimation," Medical Decision Making, , vol. 8(3), pages 204-215, August.
    • Handle: RePEc:sae:medema:v:8:y:1988:i:3:p:204-215
    DOI: 10.1177/0272989X8800800309
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    References listed on IDEAS

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    1. James A. Hanley, 1988. "The Robustness of the "Binormal" Assumptions Used in Fitting ROC Curves," Medical Decision Making, , vol. 8(3), pages 197-203, August.
    2. Peter Doubilet & Colin B. Begg & Milton C. Weinstein & Peter Braun & Barbara J. McNeil, 1985. "Probabilistic Sensitivity Analysis Using Monte Carlo Simulation," Medical Decision Making, , vol. 5(2), pages 157-177, June.
    3. James A. Hanley & Colin B. Begg, 1987. "Response to ROC Steady," Medical Decision Making, , vol. 7(4), pages 244-246, December.
    4. Anila Wijesinha & Colin B. Begg & H. Harris Funkenstein & Barbara J. McNeil, 1983. "Methodology for the Differential Diagnosis of a Complex Data Set," Medical Decision Making, , vol. 3(2), pages 133-154, June.
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    Citations

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    1. Rodríguez-Álvarez, María Xosé & Roca-Pardiñas, Javier & Cadarso-Suárez, Carmen, 2011. "A new flexible direct ROC regression model: Application to the detection of cardiovascular risk factors by anthropometric measures," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3257-3270, December.
    2. B Rey deCastro, 2019. "Cumulative ROC curves for discriminating three or more ordinal outcomes with cutpoints on a shared continuous measurement scale," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-16, August.
    3. repec:jss:jstsof:08:i12 is not listed on IDEAS
    4. Rodríguez-Álvarez, María Xosé & Tahoces, Pablo G. & Cadarso-Suárez, Carmen & Lado, María José, 2011. "Comparative study of ROC regression techniques--Applications for the computer-aided diagnostic system in breast cancer detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 888-902, January.
    5. Wilbert B. van den Hout, 2003. "The Area under an ROC Curve with Limited Information," Medical Decision Making, , vol. 23(2), pages 160-166, March.
    6. Benjamin R. Shear & Sean F. Reardon, 2021. "Using Pooled Heteroskedastic Ordered Probit Models to Improve Small-Sample Estimates of Latent Test Score Distributions," Journal of Educational and Behavioral Statistics, , vol. 46(1), pages 3-33, February.
    7. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.
    8. Nasim Vahabi & Anoshirvan Kazemnejad & Somnath Datta, 2018. "A Marginalized Overdispersed Location Scale Model for Clustered Ordinal Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 103-134, December.
    9. Yang, Hanfang & Zhao, Yichuan, 2012. "Smoothed empirical likelihood for ROC curves with censored data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 254-263.
    10. Maria G.M. Hunink & Douglas K. Richardson & Peter M. Doubilet & Colin B. Begg, 1990. "Testing for Fetal Pulmonary Maturity," Medical Decision Making, , vol. 10(3), pages 201-211, August.
    11. Lang, Joseph B., 1999. "Bayesian ordinal and binary regression models with a parametric family of mixture links," Computational Statistics & Data Analysis, Elsevier, vol. 31(1), pages 59-87, July.
    12. Ziyi Li & Yijian Huang & Dattatraya Patil & Martin G. Sanda, 2023. "Covariate adjustment in continuous biomarker assessment," Biometrics, The International Biometric Society, vol. 79(1), pages 39-48, March.
    13. Jin, Hua & Lu, Ying, 2009. "The ROC region of a regression tree," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 936-942, April.
    14. Sean F. Reardon & Benjamin R. Shear & Katherine E. Castellano & Andrew D. Ho, 2017. "Using Heteroskedastic Ordered Probit Models to Recover Moments of Continuous Test Score Distributions From Coarsened Data," Journal of Educational and Behavioral Statistics, , vol. 42(1), pages 3-45, February.

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