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Calculates the integrated survival logarithmic (log) (ISLL), loss, aka integrated cross entropy.

For an individual who dies at time \(t\), with predicted Survival function, \(S\), the probabilistic log loss at time \(t^*\) is given by $$L(S,t|t^*) = - [log(1 - S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] - [log(S(t^*))I(t > t^*)(1/G(t^*))]$$ # nolint where \(G\) is the Kaplan-Meier estimate of the censoring distribution.

The re-weighted ISLL, ISLL* is given by $$L(S,t|t^*) = - [log(1 - S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] - [log(S(t^*))I(t > t^*)(1/G(t))]$$ # nolint where \(G\) is the Kaplan-Meier estimate of the censoring distribution, i.e. always weighted by \(G(t)\). ISLL* is strictly proper when the censoring distribution is independent of the survival distribution and when G is fit on a sufficiently large dataset. ISLL is never proper. Use proper = FALSE for ISLL and proper = TRUE for ISLL*, 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():


Meta Information

  • Type: "surv"

  • Range: \([0, \infty)\)

  • Minimize: TRUE

  • Required prediction: distr


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>;2-5 .

Super classes

mlr3::Measure -> mlr3proba::MeasureSurv -> MeasureSurvIntLogloss


Inherited methods

Method new()

Creates a new instance of this R6 class.


MeasureSurvIntLogloss$new(ERV = FALSE)



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

Method clone()

The objects of this class are cloneable with this method.


MeasureSurvIntLogloss$clone(deep = FALSE)



Whether to make a deep clone.