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Survival Model Predictive Accuracy and ROC Curves

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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.
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