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      Time-dependent ROC curves for censored survival data and a diagnostic marker.

      1 , ,
      Biometrics
      Wiley

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          Abstract

          ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.

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          Author and article information

          Journal
          Biometrics
          Biometrics
          Wiley
          0006-341X
          0006-341X
          Jun 2000
          : 56
          : 2
          Affiliations
          [1 ] Department of Biostatistics, University of Washington, Seattle 98195, USA. heagerty@biostat.washington.edu
          Article
          10.1111/j.0006-341x.2000.00337.x
          10877287
          5eec9ff6-0af8-41a9-bbb8-bac8e165741e
          History

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