Calculates the integrated logarithmic (log), 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 $$L(S,t|t^*) = - [log(1 - S(t^*))I(t \le t^*, \delta = 1)(1/G(t))] - [log(S(t^*))I(t > t^*)(1/G(t^*))]$$ 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():

MeasureSurvIntLogloss$new() mlr_measures$get("surv.intlogloss")
msr("surv.intlogloss")

## Meta Information

• Type: "surv"

• Range: $$[0, \infty)$$

• Minimize: TRUE

• Required prediction: distr

## References

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>3.0.co;2-5 .

## Super classes

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

## Active bindings

eps

(numeric(1))
Very small number used to prevent log(0) error.

## Methods

### Public methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

### Arguments

deep

Whether to make a deep clone.