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 $$L(S,t|t^*) = [(S(t^*)^2)I(t \le t^*, \delta = 1)(1/G(t))] + [((1 - S(t^*))^2)I(t > t^*)(1/G(t^*))]$$ # nolint where $$G$$ is the Kaplan-Meier estimate of the censoring distribution.

Note: If comparing the integrated graf score to other packages, e.g. 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

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 .

Other survival measures: mlr_measures_surv.beggC, mlr_measures_surv.calib_alpha, mlr_measures_surv.calib_beta, mlr_measures_surv.chambless_auc, mlr_measures_surv.cindex, mlr_measures_surv.gonenC, mlr_measures_surv.grafSE, mlr_measures_surv.harrellC, mlr_measures_surv.hung_auc, mlr_measures_surv.intloglossSE, mlr_measures_surv.intlogloss, mlr_measures_surv.loglossSE, mlr_measures_surv.logloss, mlr_measures_surv.maeSE, mlr_measures_surv.mae, mlr_measures_surv.mseSE, mlr_measures_surv.mse, mlr_measures_surv.nagelk_r2, mlr_measures_surv.oquigley_r2, mlr_measures_surv.rmseSE, mlr_measures_surv.rmse, mlr_measures_surv.schmid, mlr_measures_surv.song_auc, mlr_measures_surv.song_tnr, mlr_measures_surv.song_tpr, mlr_measures_surv.unoC, mlr_measures_surv.uno_auc, mlr_measures_surv.uno_tnr, mlr_measures_surv.uno_tpr, mlr_measures_surv.xu_r2

Other Probabilistic survival measures: mlr_measures_surv.grafSE, mlr_measures_surv.intloglossSE, mlr_measures_surv.intlogloss, mlr_measures_surv.loglossSE, mlr_measures_surv.logloss, mlr_measures_surv.schmid

Other distr survival measures: mlr_measures_surv.calib_alpha, mlr_measures_surv.grafSE, mlr_measures_surv.intloglossSE, mlr_measures_surv.intlogloss, mlr_measures_surv.loglossSE, mlr_measures_surv.logloss, mlr_measures_surv.schmid

## Super classes

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

## Active bindings

se

(logical(1))
If TRUE returns the standard error of the measure.

## Methods

### Public methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

### Arguments

deep

Whether to make a deep clone.