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 either taking the sample mean over all $$T$$ unique time-points (method == 1), or by taking a mean weighted by the difference between time-points (method == 2). Then the sample mean is taken over all $$N$$ observations. $$L(S) = \frac{1}{NT} \sum_{i=1}^N \sum_{j=1}^T L(S_i,t_i|t^*_j)$$

## Dictionary

This Measure can be instantiated via the dictionary mlr_measures or with the associated sugar function msr():

MeasureSurvGraf$new() mlr_measures$get("surv.graf")
msr("surv.graf")


## Meta Information

• Type: "surv"

• Range: $$[0, \infty)$$

• Minimize: TRUE

• Required prediction: distr

## References

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>3.0.co;2-5 .

## See also

Other survival measures: MeasureSurvBeggC, MeasureSurvChamblessAUC, MeasureSurvGonenC, MeasureSurvGrafSE, MeasureSurvHarrellC, MeasureSurvHungAUC, MeasureSurvIntLoglossSE, MeasureSurvIntLogloss, MeasureSurvLoglossSE, MeasureSurvLogloss, MeasureSurvMAESE, MeasureSurvMAE, MeasureSurvMSESE, MeasureSurvMSE, MeasureSurvNagelkR2, MeasureSurvOQuigleyR2, MeasureSurvRMSESE, MeasureSurvRMSE, MeasureSurvSongAUC, MeasureSurvSongTNR, MeasureSurvSongTPR, MeasureSurvUnoAUC, MeasureSurvUnoC, MeasureSurvUnoTNR, MeasureSurvUnoTPR, MeasureSurvXuR2

Other Probabilistic survival measures: MeasureSurvGrafSE, MeasureSurvIntLoglossSE, MeasureSurvIntLogloss, MeasureSurvLoglossSE, MeasureSurvLogloss

Other distr survival measures: MeasureSurvGrafSE, MeasureSurvIntLoglossSE, MeasureSurvIntLogloss, MeasureSurvLoglossSE, MeasureSurvLogloss

## Super classes

mlr3::Measure -> mlr3proba::MeasureSurv -> mlr3proba::MeasureSurvIntegrated -> MeasureSurvGraf

## Methods

### Public methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

### Arguments

deep

Whether to make a deep clone.