Integrated Schmid Score Survival Measure

Calculates the Integrated Schmid Score (ISS), aka integrated absolute loss.

Details

For an individual who dies at time \(t\), with predicted Survival function, \(S\), the Schmid Score at time \(t^*\) is given by $$L_{ISS}(S,t|t^*) = [(S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] + [((1 - S(t^*)))I(t > t^*)(1/G(t^*))]$$ where \(G\) is the Kaplan-Meier estimate of the censoring distribution.

The re-weighted ISS, RISS is given by $$L_{RISS}(S,t|t^*) = [(S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] + [((1 - S(t^*)))I(t > t^*)(1/G(t))]$$ where \(G\) is the Kaplan-Meier estimate of the censoring distribution, i.e. always weighted by \(G(t)\). RISS 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 RISS. 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 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.

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")

Parameters

Id	Type	Default	Levels	Range
integrated	logical	TRUE	TRUE, FALSE	-
times	untyped	-		-
t_max	numeric	-		\([0, \infty)\)
p_max	numeric	-		\([0, 1]\)
method	integer	2		\([1, 2]\)
se	logical	FALSE	TRUE, FALSE	-
proper	logical	FALSE	TRUE, FALSE	-
eps	numeric	0.001		\([0, 1]\)
ERV	logical	FALSE	TRUE, FALSE	-

Meta Information

• Type: "surv"

• Range: \([0, \infty)\)

• Minimize: TRUE

• Required prediction: distr

Parameter details

• integrated (logical(1))
  If TRUE (default), returns the integrated score (eg across time points); otherwise, not integrated (eg at a single time point).

• 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.

• t_max (numeric(1))
  Cutoff time (i.e. time horizon) to evaluate the measure up to. Mutually exclusive with p_max or times.

• p_max (numeric(1))
  The proportion of censoring to integrate up to in the given dataset. Mutually exclusive with times or t_max.

• method (integer(1))
  If integrate == TRUE, this 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 the default value, to be in line with other packages.

• se (logical(1))
  If TRUE then returns standard error of the measure otherwise returns the mean across all individual scores, e.g. the mean of the per observation scores. Default is FALSE (returns the mean).

• 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. If FALSE then weights scores by the Graf method which is the more common usage but the loss is not proper.

• eps (numeric(1))
  Very small number to substitute zero values in order to prevent errors in e.g. log(0) and/or division-by-zero calculations. Default value is 0.001.

• ERV (logical(1))
  If TRUE then the Explained Residual Variation method is applied, which means the score is standardized against a Kaplan-Meier baseline. Default is FALSE.

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.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.rcll, 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, mlr_measures_surv.rcll

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, mlr_measures_surv.rcll

Super classes

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

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(ERV = FALSE)

Arguments

ERV

(logical(1))
Standardize measure against a Kaplan-Meier baseline (Explained Residual Variation)

---

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.