Calculates the Integrated Graf Score, aka integrated Brier score or squared loss.

For an individual who dies at time \(t\), with predicted Survival function, \(S\), the Graf Score at time \(t^*\) is given by $$L(S,t|t^*) = [(S(t^*)^2)I(t \le t^*, \delta = 1)(1/G(t))] + [((1 - S(t^*))^2)I(t > t^*)(1/G(t^*))]$$ where \(G\) is the Kaplan-Meier estimate of the censoring distribution.

If integrated == FALSE then the sample mean is taken for the single specified times, \(t^*\), and the returned score is given by $$L(S,t|t^*) = \frac{1}{N} \sum_{i=1}^N L(S_i,t_i|t^*)$$ where \(N\) is the number of observations, \(S_i\) is the predicted survival function for individual \(i\) and \(t_i\) is their true survival time.

If integrated == TRUE then an approximation to integration is made by taking the mean over all \(T\) unique time-points, and then the sample mean over all \(N\) observations. $$L(S) = \frac{1}{NT} \sum_{i=1}^N \sum_{j=1}^T L(S_i,t_i|t^*_j)$$


R6::R6Class() inheriting from MeasureSurvIntegrated/MeasureSurv.


MeasureSurvGraf$new(integrated = TRUE, times)
  • integrated :: logical(1)
    If TRUE (default), returns the integrated score; otherwise, not integrated.

  • times :: vector()
    If integrate == TRUE then a vector of time-points over which to integrate the score. If integrate == FALSE then a single time point at which to return the score.

Meta Information

  • Type: "surv"

  • Range: \([0, \infty)\)

  • Minimize: TRUE

  • Required prediction: distr


See MeasureSurv, as well as all variables passed to the constructor.


Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher, M. (1999).
Assessment and comparison of prognostic classification schemes for survival data.
Statistics in Medicine, 18(17), 2529-2545.
doi: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2529::AID-SIM274>3.0.CO;2-5

See also