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Time-Dependent Predictive Accuracy in the Presence of Competing Risks

Authors

  • P. Saha,

    Corresponding author
    1. Department of Biostatistics, University of Washington, F-600 Health Sciences Building, Campus Mail Stop 357232, Seattle, Washington 98195-7232, U.S.A.
    2. Current address: Biostatistics Branch, Mail Drop A3-03, National Institute of Environmental Health Sciences, P. O. Box 12233, Research Triangle Park, North Carolina 27709, U.S.A.
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  • P. J. Heagerty

    Corresponding author
    1. Department of Biostatistics, University of Washington, F-600 Health Sciences Building, Campus Mail Stop 357232, Seattle, Washington 98195-7232, U.S.A.
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email:psaha@u.washington.edu

email:heagerty@u.washington.edu

Abstract

Summary Competing risks arise naturally in time-to-event studies. In this article, we propose time-dependent accuracy measures for a marker when we have censored survival times and competing risks. Time-dependent versions of sensitivity or true positive (TP) fraction naturally correspond to consideration of either cumulative (or prevalent) cases that accrue over a fixed time period, or alternatively to incident cases that are observed among event-free subjects at any select time. Time-dependent (dynamic) specificity (1–false positive (FP)) can be based on the marker distribution among event-free subjects. We extend these definitions to incorporate cause of failure for competing risks outcomes. The proposed estimation for cause-specific cumulative TP/dynamic FP is based on the nearest neighbor estimation of bivariate distribution function of the marker and the event time. On the other hand, incident TP/dynamic FP can be estimated using a possibly nonproportional hazards Cox model for the cause-specific hazards and riskset reweighting of the marker distribution. The proposed methods extend the time-dependent predictive accuracy measures of Heagerty, Lumley, and Pepe (2000, Biometrics56, 337–344) and Heagerty and Zheng (2005, Biometrics61, 92–105).

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