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 taking the mean over all $$T$$ unique time-points, and then the sample mean over all $$N$$ observations. $$L(S) = \frac{1}{NT} \sum_{i=1}^N \sum_{j=1}^T L(S_i,t_i|t^*_j)$$

## Format

R6::R6Class() inheriting from MeasureSurvIntegrated/MeasureSurv.

## Construction

MeasureSurvIntLogloss$new(integrated = TRUE, times, eps = 1e-15, method = 2) mlr_measures$get("surv.intlogloss")
msr("surv.intlogloss")

• integrated :: logical(1)
If TRUE (default), returns the integrated score; otherwise, not integrated.

• times :: vector()
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.

• eps :: numeric(1)
Very small number to set zero-valued predicted probabilities to, in order to prevent errors in log(0) calculation.

## Meta Information

• Type: "surv"

• Range: $$[0, \infty)$$

• Minimize: TRUE

• Required prediction: distr

## Fields

See MeasureSurv, as well as all variables passed to the constructor.

As well as

• eps :: numeric(1)
Very small number to set zero-valued predicted probabilities to, in order to prevent errors in log(0) calculation.

## 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 .

## See also

Other survival measures: MeasureSurvBeggC, MeasureSurvChamblessAUC, MeasureSurvGonenC, MeasureSurvGrafSE, MeasureSurvGraf, MeasureSurvHarrellC, MeasureSurvHungAUC, MeasureSurvIntLoglossSE, MeasureSurvLoglossSE, MeasureSurvLogloss, MeasureSurvMAESE, MeasureSurvMAE, MeasureSurvMSESE, MeasureSurvMSE, MeasureSurvNagelkR2, MeasureSurvOQuigleyR2, MeasureSurvRMSESE, MeasureSurvRMSE, MeasureSurvSongAUC, MeasureSurvSongTNR, MeasureSurvSongTPR, MeasureSurvUnoAUC, MeasureSurvUnoC, MeasureSurvUnoTNR, MeasureSurvUnoTPR, MeasureSurvXuR2

Other Probabilistic survival measures: MeasureSurvGrafSE, MeasureSurvGraf, MeasureSurvIntLoglossSE, MeasureSurvLoglossSE, MeasureSurvLogloss

Other distr survival measures: MeasureSurvGrafSE, MeasureSurvGraf, MeasureSurvIntLoglossSE, MeasureSurvLoglossSE, MeasureSurvLogloss