Integrated Schmid Score Survival Measure

Source: R/MeasureSurvSchmid.R

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

References

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 .

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.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.

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.