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Incorporating the Time Dimension in Receiver Operating Characteristic Curves: A Case Study of Prostate Cancer

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  • Ruth Etzioni
  • Margaret Pepe
  • Gary Longton
  • Chengcheng Hu
  • Gary Goodman

Abstract

Early diagnosis of disease has potential to reduce morbidity and mortality. Biomarkers may be useful for detecting disease at early stages before it becomes clinically ap parent. Prostate-specific antigen (PSA) is one such marker for prostate cancer. This article is concerned with modeling receiver operating characteristic (ROC) curves as sociated with biomarkers at various times prior to the time at which the disease is detected clinically, by two methods. The first models the biomarkers statistically using mixed-effects regression models, and uses parameter estimates from these models to estimate the time-specific ROC curves. The second directly models the ROC curves as a function of time prior to diagnosis and may be implemented using software pack ages with binary regression or generalized linear model routines. The approaches are applied to data from 71 prostate cancer cases and 71 controls who participated in a lung cancer prevention trial. Two biomarkers for prostate cancer were considered: total serum PSA and the ratio of free to total PSA. Not surprisingly, both markers performed better as the interval between PSA measurement and clinical diagnosis decreased. Although the two markers performed similarly eight years prior to diagnosis, it appears that total PSA performed better than the ratio measure at times closer to diagnosis. The area under the ROC curve was consistently greater for total PSA than for the ratio four and two years prior to diagnosis and at the time of diagnosis. Key words : time- dependent ROC curves; biomarkers; diagnosis; prostate-specific antigen. (Med Decis Making 1999; 19:242-251)

Suggested Citation

  • Ruth Etzioni & Margaret Pepe & Gary Longton & Chengcheng Hu & Gary Goodman, 1999. "Incorporating the Time Dimension in Receiver Operating Characteristic Curves: A Case Study of Prostate Cancer," Medical Decision Making, , vol. 19(3), pages 242-251, August.
  • Handle: RePEc:sae:medema:v:19:y:1999:i:3:p:242-251
    DOI: 10.1177/0272989X9901900303
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    Cited by:

    1. Susana Díaz-Coto & Pablo Martínez-Camblor & Sonia Pérez-Fernández, 2020. "smoothROCtime: an R package for time-dependent ROC curve estimation," Computational Statistics, Springer, vol. 35(3), pages 1231-1251, September.
    2. Daniel J. Luckett & Eric B. Laber & Samer S. El‐Kamary & Cheng Fan & Ravi Jhaveri & Charles M. Perou & Fatma M. Shebl & Michael R. Kosorok, 2021. "Receiver operating characteristic curves and confidence bands for support vector machines," Biometrics, The International Biometric Society, vol. 77(4), pages 1422-1430, December.
    3. Debashis Ghosh, 2004. "Semiparametric methods for the binormal model with multiple biomarkers," The University of Michigan Department of Biostatistics Working Paper Series 1046, Berkeley Electronic Press.
    4. Yingye Zheng & Patrick Heagerty, 2004. "Semiparametric Estimation of Time-Dependent: ROC Curves for Longitudinal Marker Data," UW Biostatistics Working Paper Series 1052, Berkeley Electronic Press.
    5. Sudesh Pundir & R. Amala, 2015. "Detecting diagnostic accuracy of two biomarkers through a bivariate log-normal ROC curve," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2671-2685, December.
    6. Debashis Ghosh, 2004. "Semiparametic models and estimation procedures for binormal ROC curves with multiple biomarkers," The University of Michigan Department of Biostatistics Working Paper Series 1038, Berkeley Electronic Press.
    7. Patrick Heagerty & Yingye Zheng, 2004. "Survival Model Predictive Accuracy and ROC Curves," UW Biostatistics Working Paper Series 1051, Berkeley Electronic Press.

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