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Overall C as a measure of discrimination in survival analysis: model specific population value and confidence interval estimation

Authors

  • Michael J. Pencina,

    Corresponding author
    1. Statistics and Consulting Unit, Department of Mathematics and Statistics, Boston University, 111 Cummington St. Boston, MA 02215, U.S.A.
    • Statistics and Consulting Unit, Department of Mathematics and Statistics, Boston University, 111 Cummington St. Boston, MA 02215, U.S.A.
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  • Ralph B. D'Agostino

    1. Statistics and Consulting Unit, Department of Mathematics and Statistics, Boston University, 111 Cummington St. Boston, MA 02215, U.S.A.
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Abstract

The assessment of the discrimination ability of a survival analysis model is a problem of considerable theoretical interest and important practical applications. This issue is, however, more complex than evaluating the performance of a linear or logistic regression. Several different measures have been proposed in the biostatistical literature. In this paper we investigate the properties of the overall C index introduced by Harrell as a natural extension of the ROC curve area to survival analysis. We develop the overall C index as a parameter describing the performance of a given model applied to the population under consideration and discuss the statistic used as its sample estimate. We discover a relationship between the overall C and the modified Kendall's τand construct a confidence interval for our measure based on the asymptotic normality of its estimate. Then we investigate via simulations the length and coverage probability of this interval. Finally, we present a real life example evaluating the performance of a Framingham Heart Study model. Copyright © 2004 John Wiley & Sons, Ltd.

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