R: Integrated Schmid Score Survival Measure

mlr_measures_surv.schmid {mlr3proba} | R Documentation

## Integrated Schmid Score Survival Measure

### Description

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 ≤ t*, δ = 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*) = 1/N ∑_i^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) = 1/(NT) ∑_i^N ∑_j^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, Inf)

- Minimize: `TRUE`

- Required prediction: `distr`

### 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

- `MeasureSurvSchmid$new()`

- `MeasureSurvSchmid$clone()`

Inherited methods

- `mlr3::Measure$aggregate()`

- `mlr3::Measure$format()`

- `mlr3::Measure$help()`

- `mlr3::Measure$score()`

- `mlr3proba::MeasureSurv$print()`

#### Method `new()`

Creates a new instance of this R6 class.

##### Usage

    MeasureSurvSchmid$new(integrated = TRUE, times, method = 2, se = FALSE)

##### Arguments

`integrated`

  (`logical(1)`)
  If `TRUE` (default), returns the integrated score; otherwise, not integrated.

`times`

  (`numeric()`)
  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.

`method`

  (`integer(1)`)
  If `integrate == TRUE` selects the integration weighting method. `method == 1` corresponds to weighting each time-point equally and taking the mean score over discrete time-points. `method == 2` corresponds to calculating a mean weighted by the difference between time-points. `method == 2` is default to be in line with other packages.

`se`

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

#### Method `clone()`

The objects of this class are cloneable with this method.

##### Usage

    MeasureSurvSchmid$clone(deep = FALSE)

##### Arguments

`deep`

  Whether to make a deep clone.

### References

Schemper, Michael, Henderson, Robin (2000). “Predictive Accuracy and Explained Variation in Cox Regression.” Biometrics, 56, 249–255. doi: 10.1002/sim.1486.

Schmid, Matthias, Hielscher, Thomas, Augustin, Thomas, Gefeller, Olaf (2011). “A Robust Alternative to the Schemper-Henderson Estimator of Prediction Error.” Biometrics, 67(2), 524–535. doi: 10.1111/j.1541-0420.2010.01459.x.

### See Also

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.logloss_se`, `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.logloss_se`, `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.logloss_se`, `mlr_measures_surv.logloss`

[Package mlr3proba version 0.3.2 Index]