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$new(integrated = TRUE, times, eps = 1e-15) mlr_measures$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.

Graf, E., Schmoor, C., Sauerbrei, W. and Schumacher, M. (1999).
Assessment and comparison of prognostic classification schemes for survival data.
Statistics in Medicine, 18(17), 2529-2545.
doi: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2529::AID-SIM274>3.0.CO;2-5

Other survival measures: MeasureSurvBeggC, MeasureSurvChamblessAUC, MeasureSurvGonenC, MeasureSurvGrafSE, MeasureSurvGraf, MeasureSurvHarrellC, MeasureSurvHungAUC, MeasureSurvIntLoglossSE, MeasureSurvLoglossSE, MeasureSurvLogloss, MeasureSurvNagelkR2, MeasureSurvOQuigleyR2, MeasureSurvSongAUC, MeasureSurvSongTNR, MeasureSurvSongTPR, MeasureSurvUnoAUC, MeasureSurvUnoC, MeasureSurvUnoTNR, MeasureSurvUnoTPR, MeasureSurvXuR2
Other Probabilistic survival measures: MeasureSurvGrafSE, MeasureSurvGraf, MeasureSurvIntLoglossSE, MeasureSurvLoglossSE, MeasureSurvLogloss