IDEAS home Printed from https://ideas.repec.org/p/bep/uwabio/1052.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    Note: oai:bepress.com:uwbiostat-1052
    as

    Download full text from publisher

    File URL: http://www.bepress.com/cgi/viewcontent.cgi?article=1052&context=uwbiostat
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Tianxi Cai & Yingye Zheng, 2007. "Model Checking for ROC Regression Analysis," Biometrics, The International Biometric Society, vol. 63(1), pages 152-163, March.
    9. 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.
    10. 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.
    11. 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.
    12. 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).
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Claire L Heslop & Gregory E Miller & John S Hill, 2009. "Neighbourhood Socioeconomics Status Predicts Non-Cardiovascular Mortality in Cardiac Patients with Access to Universal Health Care," PLOS ONE, Public Library of Science, vol. 4(1), pages 1-8, January.
    4. Chin-Tsang Chiang & Shr-Yan Huang, 2009. "Estimation for the Optimal Combination of Markers without Modeling the Censoring Distribution," Biometrics, The International Biometric Society, vol. 65(1), pages 152-158, March.
    5. Sebastian Cremer & Lisa Pilgram & Alexander Berkowitsch & Melanie Stecher & Siegbert Rieg & Mariana Shumliakivska & Denisa Bojkova & Julian Uwe Gabriel Wagner & Galip Servet Aslan & Christoph Spinner , 2021. "Angiotensin II receptor blocker intake associates with reduced markers of inflammatory activation and decreased mortality in patients with cardiovascular comorbidities and COVID-19 disease," PLOS ONE, Public Library of Science, vol. 16(10), pages 1-17, October.
    6. Te-Ling Ma & Tsung-Hui Hu & Chao-Hung Hung & Jing-Houng Wang & Sheng-Nan Lu & Chien-Hung Chen, 2019. "Incidence and predictors of retreatment in chronic hepatitis B patients after discontinuation of entecavir or tenofovir treatment," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-16, October.
    7. Liu Xinhua & Jin Zhezhen, 2009. "A Non-Parametric Approach to Scale Reduction for Uni-Dimensional Screening Scales," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-22, January.
    8. 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.
    9. Patrick Heagerty & Yingye Zheng, 2004. "Survival Model Predictive Accuracy and ROC Curves," UW Biostatistics Working Paper Series 1051, Berkeley Electronic Press.
    10. Shannon M Lynch & Elizabeth Handorf & Kristen A Sorice & Elizabeth Blackman & Lisa Bealin & Veda N Giri & Elias Obeid & Camille Ragin & Mary Daly, 2020. "The effect of neighborhood social environment on prostate cancer development in black and white men at high risk for prostate cancer," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-18, August.
    11. Nir Y. Krakauer & Jesse C. Krakauer, 2021. "Association of X-ray Absorptiometry Body Composition Measurements with Basic Anthropometrics and Mortality Hazard," IJERPH, MDPI, vol. 18(15), pages 1-13, July.
    12. Weining Shen & Jing Ning & Ying Yuan, 2015. "A direct method to evaluate the time-dependent predictive accuracy for biomarkers," Biometrics, The International Biometric Society, vol. 71(2), pages 439-449, June.
    13. Matthias Schmid & Thomas Hielscher & Thomas Augustin & Olaf Gefeller, 2011. "A Robust Alternative to the Schemper–Henderson Estimator of Prediction Error," Biometrics, The International Biometric Society, vol. 67(2), pages 524-535, June.
    14. Si Cheng & Kathleen F Kerr & Heather Thiessen-Philbrook & Steven G Coca & Chirag R Parikh, 2020. "BioPETsurv: Methodology and open source software to evaluate biomarkers for prognostic enrichment of time-to-event clinical trials," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-11, September.
    15. Tim Johnson & Valen Johnson, 2004. "A Bayesian Hierarchical Approach to Multirater Correlated ROC Analysis," The University of Michigan Department of Biostatistics Working Paper Series 1027, Berkeley Electronic Press.
    16. P. Saha & P. J. Heagerty, 2010. "Time-Dependent Predictive Accuracy in the Presence of Competing Risks," Biometrics, The International Biometric Society, vol. 66(4), pages 999-1011, December.
    17. Lori E. Dodd, 2010. "ROC Curves for Continuous Data by KRZANOWSKI, W. J. and HAND, D. J," Biometrics, The International Biometric Society, vol. 66(2), pages 657-658, June.
    18. Janez Stare & Maja Pohar Perme & Robin Henderson, 2011. "A Measure of Explained Variation for Event History Data," Biometrics, The International Biometric Society, vol. 67(3), pages 750-759, September.
    19. Minta Thomas & Yu-Ru Su & Elisabeth A. Rosenthal & Lori C. Sakoda & Stephanie L. Schmit & Maria N. Timofeeva & Zhishan Chen & Ceres Fernandez-Rozadilla & Philip J. Law & Neil Murphy & Robert Carreras-, 2023. "Combining Asian and European genome-wide association studies of colorectal cancer improves risk prediction across racial and ethnic populations," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    20. Yingye Zheng & Tianxi Cai & Ziding Feng, 2006. "Application of the Time-Dependent ROC Curves for Prognostic Accuracy with Multiple Biomarkers," Biometrics, The International Biometric Society, vol. 62(1), pages 279-287, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bep:uwabio:1052. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: http://www.bepress.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.