Calculates the Integrated Schmid Score, aka integrated absolute loss.

For an individual who dies at time $$t$$, with predicted Survival function, $$S$$, the Schmid Score at time $$t^*$$ is given by $$L(S,t|t^*) = [(S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] + [((1 - S(t^*)))I(t > t^*)(1/G(t^*))]$$ # nolint 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 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():

MeasureSurvSchmid$new() mlr_measures$get("surv.schmid")
msr("surv.schmid")


## Meta Information

• Type: "surv"

• Range: $$[0, \infty)$$

• Minimize: TRUE

• Required prediction: distr

Schemper M, Henderson R (2000). “Predictive Accuracy and Explained Variation in Cox Regression.” Biometrics, 56, 249--255. ISSN 02776715, doi: 10.1002/sim.1486 . Schmid M, Hielscher T, Augustin T, Gefeller O (2011). “A Robust Alternative to the Schemper-Henderson Estimator of Prediction Error.” Biometrics, 67(2), 524--535. ISSN 0006341X, doi: 10.1111/j.1541-0420.2010.01459.x .

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.graf, 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.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.graf, mlr_measures_surv.intloglossSE, mlr_measures_surv.intlogloss, mlr_measures_surv.loglossSE, mlr_measures_surv.logloss

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

## Super classes

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

## 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.