R: Integrated Graf Score Survival Measure

mlr_measures_surv.graf {mlr3proba} | R Documentation

## Integrated Graf Score Survival Measure

### Description

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 ≤ t*, δ = 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*) = 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():

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

### Meta Information

- Type: `"surv"`

- Range: [0, Inf)

- Minimize: `TRUE`

- Required prediction: `distr`

### 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

- `MeasureSurvGraf$new()`

- `MeasureSurvGraf$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

    MeasureSurvGraf$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

    MeasureSurvGraf$clone(deep = FALSE)

##### Arguments

`deep`

  Whether to make a deep clone.

### 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: `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.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.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.logloss_se`, `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.logloss_se`, `mlr_measures_surv.logloss`, `mlr_measures_surv.schmid`

[Package mlr3proba version 0.3.2 Index]