IDEAS home Printed from https://ideas.repec.org/p/bep/uwabio/1051.html
   My bibliography  Save this paper

Survival Model Predictive Accuracy and ROC Curves

Author

Listed:
  • Patrick Heagerty

    (University of Washington)

  • Yingye Zheng

    (Fred Hutchinson Cancer Research Center)

Abstract

The predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model, or R^2, commonly used for continuous response models, or using extensions of sensitivity and specificity which are commonly used for binary response models.In this manuscript we propose new time-dependent accuracy summaries based on time-specific versions of sensitivity and specificity calculated over risk sets. We connect the accuracy summaries to a previously proposed global concordance measure which is a variant of Kendall's tau. In addition, we show how standard Cox regression output can be used to obtain estimates of time-dependent sensitivity and specificity, and time-dependent reciever operating characteristic (ROC) curves. Semi-parametric estimation methods appropriate for both proportional hazards and non-proportional hazards data are introduced, evaluated in simulations, and illustrated using two familiar survival data sets.

Suggested Citation

  • Patrick Heagerty & Yingye Zheng, 2004. "Survival Model Predictive Accuracy and ROC Curves," UW Biostatistics Working Paper Series 1051, Berkeley Electronic Press.
    • Handle: RePEc:bep:uwabio:1051
    Note: oai:bepress.com:uwbiostat-1051
    as

    Download full text from publisher

    File URL: http://www.bepress.com/cgi/viewcontent.cgi?article=1051&context=uwbiostat
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zongwu Cai & Yanqing Sun, 2003. "Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 93-111, March.
    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. Michael Schemper & Robin Henderson, 2000. "Predictive Accuracy and Explained Variation in Cox Regression," Biometrics, The International Biometric Society, vol. 56(1), pages 249-255, March.
    4. Ronghui Xu & John O'Quigley, 2000. "Proportional hazards estimate of the conditional survival function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 667-680.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Yingye Zheng & Patrick J. Heagerty, 2005. "Partly Conditional Survival Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 61(2), pages 379-391, June.
    3. 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.
    4. Hongyuan Cao & Mathew M. Churpek & Donglin Zeng & Jason P. Fine, 2015. "Analysis of the Proportional Hazards Model With Sparse Longitudinal Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1187-1196, September.
    5. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    6. 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.
    7. Kornelis J J van Hateren & Gijs W D Landman & Jarinke F H Arnold & Hanneke Joosten & Klaas H Groenier & Gerjan J Navis & Andrea Sparwasser & Stephan J L Bakker & Henk J G Bilo & Nanne Kleefstra, 2015. "Serum Proenkephalin A Levels and Mortality After Long-Term Follow-Up in Patients with Type 2 Diabetes Mellitus (ZODIAC-32)," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-10, July.
    8. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    9. 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.
    10. 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.
    11. Dimitris Rizopoulos, 2011. "Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 67(3), pages 819-829, September.
    12. Ying Hung & Li‐Hsiang Lin & C. F. Jeff Wu, 2022. "Varying coefficient frailty models with applications in single molecular experiments," Biometrics, The International Biometric Society, vol. 78(2), pages 474-486, 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. Eleni†Rosalina Andrinopoulou & Paul H. C. Eilers & Johanna J. M. Takkenberg & Dimitris Rizopoulos, 2018. "Improved dynamic predictions from joint models of longitudinal and survival data with time†varying effects using P†splines," Biometrics, The International Biometric Society, vol. 74(2), pages 685-693, June.
    15. Shiyuan Chen & Sally Wallace, 2008. "Determinants of Education Duration in Jamaica," International Center for Public Policy Working Paper Series, at AYSPS, GSU paper0803, International Center for Public Policy, Andrew Young School of Policy Studies, Georgia State University.
    16. 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.
    17. Jun Jin & Tiefeng Ma & Jiajia Dai, 2021. "New efficient spline estimation for varying-coefficient models with two-step knot number selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 693-712, July.
    18. Lu Tian & David Zucker & L. J. Wei, 2004. "On the Cox Model with Time-Varying Regression Coefficients," Harvard University Biostatistics Working Paper Series 1004, Berkeley Electronic Press.
    19. Honda, Toshio & Yabe, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 103-122.
    20. C. Jason Liang & Patrick J. Heagerty, 2017. "A risk-based measure of time-varying prognostic discrimination for survival models," Biometrics, The International Biometric Society, vol. 73(3), pages 725-734, September.

    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:1051. 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.