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.

Note: If comparing the integrated graf score to other packages, e.g. pec::pec(), then method = 2 should be used, however the results may still be very slightly different as this package uses survfit to estimate the censoring distribution, in line with the Graf 1999 paper. Whereas some other packages use prodlim with reverse = TRUE (meaning Kaplan-Meier is not used).

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, method = 2)
  • 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, Schumacher M (1999). “Assessment and comparison of prognostic classification schemes for survival data.” Statistics in Medicine, 18(17-18), 2529--2545. doi: 10.1002/(sici)1097-0258(19990915/30)18:17/18<2529::aid-sim274>;2-5 .

See also