Calculates the Integrated Schmid Score (ISS), 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.

The re-weighted ISS, ISS* 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, i.e. always
weighted by \(G(t)\). ISS* is strictly proper when the censoring distribution is independent
of the survival distribution and when G is fit on a sufficiently large dataset. ISS is never
proper. Use `proper = FALSE`

for ISS and `proper = TRUE`

for ISS*, in the future the default
will be changed to `proper = TRUE`

. Results may be very different if many observations are
censored at the last observed time due to division by 1/`eps`

in `proper = TRUE`

.

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.
$$L(S) = \frac{1}{NT} \sum_{i=1}^N \sum_{j=1}^T L(S_i,t_i|t^*_j)$$

If `task`

and `train_set`

are passed to `$score`

then G is fit on training data,
otherwise testing data. The first is likely to reduce any bias caused by calculating
parts of the measure on the test data it is evaluating. The training data is automatically
used in scoring resamplings.

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")

Type:

`"surv"`

Range: \([0, \infty)\)

Minimize:

`TRUE`

Required prediction:

`distr`

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
.

Other survival measures:
`mlr_measures_surv.calib_alpha`

,
`mlr_measures_surv.calib_beta`

,
`mlr_measures_surv.chambless_auc`

,
`mlr_measures_surv.cindex`

,
`mlr_measures_surv.dcalib`

,
`mlr_measures_surv.graf`

,
`mlr_measures_surv.hung_auc`

,
`mlr_measures_surv.intlogloss`

,
`mlr_measures_surv.logloss`

,
`mlr_measures_surv.mae`

,
`mlr_measures_surv.mse`

,
`mlr_measures_surv.nagelk_r2`

,
`mlr_measures_surv.oquigley_r2`

,
`mlr_measures_surv.rmse`

,
`mlr_measures_surv.song_auc`

,
`mlr_measures_surv.song_tnr`

,
`mlr_measures_surv.song_tpr`

,
`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.graf`

,
`mlr_measures_surv.intlogloss`

,
`mlr_measures_surv.logloss`

Other distr survival measures:
`mlr_measures_surv.calib_alpha`

,
`mlr_measures_surv.dcalib`

,
`mlr_measures_surv.graf`

,
`mlr_measures_surv.intlogloss`

,
`mlr_measures_surv.logloss`

`mlr3::Measure`

-> `mlr3proba::MeasureSurv`

-> `mlr3proba::MeasureSurvIntegrated`

-> `MeasureSurvSchmid`

`se`

`(logical(1))`

If`TRUE`

returns the standard error of the measure.

`new()`

Creates a new instance of this R6 class.

MeasureSurvSchmid$new( integrated = TRUE, times, method = 2, se = FALSE, proper = FALSE, eps = 0.001 )

`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.`proper`

(

`logical(1)`

)

If`TRUE`

then weights scores by the censoring distribution at the observed event time, which results in a strictly proper scoring rule if censoring and survival time distributions are independent and a sufficiently large dataset is used to weight the measure. If`FALSE`

then weights scores by the Graf method which is the more common usage but the loss is not proper. In v0.5.0, the default will be changed to`TRUE`

.`eps`

(

`numeric(1)`

)

Very small number to set zero-valued predicted probabilities to in order to prevent errors in log(0) and 1/0 calculation.

`clone()`

The objects of this class are cloneable with this method.

MeasureSurvSchmid$clone(deep = FALSE)

`deep`

Whether to make a deep clone.