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Semiparametric Estimation of Time-Dependent: ROC Curves for Longitudinal Marker Data

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  • Yingye Zheng

    (Fred Hutchinson Cancer Research Center)

  • Patrick Heagerty

    (University of Washington)

Abstract

One approach to evaluating the strength of association between a longitudinal marker process and a key clinical event time is through predictive regression methods such as a time-dependent covariate hazard model. For example, a time-varying covariate Cox model specifies the instantaneous risk of the event as a function of the time-varying marker and additional covariates. In this manuscript we explore a second complementary approach which characterizes the distribution of the marker as a function of both the measurement time and the ultimate event time. Our goal is to flexibly extend the standard diagnostic accuracy concepts of sensitivity and specificity to explicitly recognize both the timing of the marker measurement and the timing of disease. The accuracy of a longitudinal marker can be fully characterized using time-dependent receiver operating characteristic (ROC) curves. We detail a semiparametric estimation method for time-dependent ROC curves that adopts a regression quantile approach for longitudinal data introduced by Heagerty and Pepe (1999}. We extend the work of Heagerty and Pepe (1999} by developing asymptotic distribution theory for the ROC estimators where the distributional shape for the marker is allowed to depend on covariates. To illustrate our method, we analyze pulmonary function measurements among cystic fibrosis subjects to assemble a case-control study and estimate ROC curves that assess how well the pulmonary function measurement can distinguish subjects that progress to death from subjects that remain alive. Comparing the results from our semiparametric analysis to a fully parametric method discussed by Etzioni and Pepe (1999} suggests that the ability to relax distributional assumptions may be important in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:bep:uwabio:1052
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    1. Cai T. & Pepe M.S., 2002. "Semiparametric Receiver Operating Characteristic Analysis to Evaluate Biomarkers for Disease," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1099-1107, December.
    2. 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.
    3. Patrick J. Heagerty & Thomas Lumley & Margaret S. Pepe, 2000. "Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker," Biometrics, The International Biometric Society, vol. 56(2), pages 337-344, June.
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    1. Yingye Zheng & Patrick J. Heagerty, 2007. "Prospective Accuracy for Longitudinal Markers," Biometrics, The International Biometric Society, vol. 63(2), pages 332-341, June.
    2. 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.
    3. Tianxi Cai & Yingye Zheng, 2007. "Model Checking for ROC Regression Analysis," Biometrics, The International Biometric Society, vol. 63(1), pages 152-163, March.
    4. Alessio Farcomeni & Monia Ranalli & Sara Viviani, 2021. "Dimension reduction for longitudinal multivariate data by optimizing class separation of projected latent Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 462-480, June.
    5. Marlena Maziarz & Patrick Heagerty & Tianxi Cai & Yingye Zheng, 2017. "On longitudinal prediction with time-to-event outcome: Comparison of modeling options," Biometrics, The International Biometric Society, vol. 73(1), pages 83-93, March.
    6. Giulia Barbati & Alessio Farcomeni, 2018. "Prognostic assessment of repeatedly measured time-dependent biomarkers, with application to dilated cardiomyopathy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 545-557, August.
    7. Olli Saarela & Elja Arjas, 2015. "Non-parametric Bayesian Hazard Regression for Chronic Disease Risk Assessment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 609-626, June.
    8. Patrick J. Heagerty & Yingye Zheng, 2005. "Survival Model Predictive Accuracy and ROC Curves," Biometrics, The International Biometric Society, vol. 61(1), pages 92-105, March.
    9. Shanshan Li & Yang Ning, 2015. "Estimation of covariate‐specific time‐dependent ROC curves in the presence of missing biomarkers," Biometrics, The International Biometric Society, vol. 71(3), pages 666-676, September.
    10. Pardo-Fernandez, Juan Carlos & Rodriguez-alvarez, Maria Xose & Van Keilegom, Ingrid, 2013. "A review on ROC curves in the presence of covariates," LIDAM Discussion Papers ISBA 2013050, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. 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.
    12. R. Schoop & E. Graf & M. Schumacher, 2008. "Quantifying the Predictive Performance of Prognostic Models for Censored Survival Data with Time-Dependent Covariates," Biometrics, The International Biometric Society, vol. 64(2), pages 603-610, June.
    13. Jing Zhang & Jing Ning & Ruosha Li, 2023. "Evaluating Dynamic Discrimination Performance of Risk Prediction Models for Survival Outcomes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 353-371, July.

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