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